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Hayabusa2’s superior solar conjunction mission operations: planning and post-operation results

Hayabusa2’s superior solar conjunction mission operations: planning and post-operation results Astrodynamics Vol. 4, No. 4, 265–288, 2020 https://doi.org/10.1007/s42064-020-0076-7 Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 1,2 2 3 2 2 Stefania Soldini (), Hiroshi Takeuchi , Sho Taniguchi , Shota Kikuchi ,Yuto Takei ,Go 2 3 3 2 2 2 Ono , Masaya Nakano , Takafumi Ohnishi , Takanao Saiki , Yuichi Tsuda , Fuyuto Terui , 2 2 2 2 2 Naoko Ogawa , Yuya Mimasu , Tadateru Takahashi , Atsushi Fujii , Satoru Nakazawa , 2 2 2 2 2,4 Kent Yoshikawa , Yusuke Oki ,Chikako Hirose , Hirotaka Sawada , Tomohiro Yamaguchi , and Makoto Yoshikawa 1. Department of Mechanical, Materials and Aerospace Engineering, University of Liverpool, Liverpool L69 3BX, UK 2. Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara 252-5210, Japan 3. Fujitsu Limited, Tokyo 105-7123, Japan 4. Mitsubishi Electric Corporation, Tokyo 100-8310, Japan ABSTRACT KEYWORDS In late 2018, the asteroid Ryugu was in the Sun’s shadow during the superior solar conjunction superior solar conjunction phase. As the Sun–Earth–Ryugu angle decreased to below 3 , the Hayabusa2 spacecraft Hayabusa2 experienced 21 days of planned blackout in the Earth–probe communication link. This Ryugu was the first time a spacecraft had experienced solar conjunction while hovering around a hovering satellite minor body. For the safety of the spacecraft, a low energy transfer trajectory named Ayu mission operations was designed in the Hill reference frame to increase its altitude from 20 to 110 km. The trajectory was planned with the newly developed optNEAR tool and validated with real Research Article time data. This article shows the results of the conjunction operation, from planning to Received: 18 Januany 2020 flight data. Accepted: 26 March 2020 © The Author(s) 2020 Contrary to NASA’s OSIRIS-REx mission [2], the 1 Introduction Hayabusa2 spacecraft did not orbit Ryugu, but instead The Hayabusa2 mission was a Japanese robotic mission hovered at a relative distance of 20 km from its center, to Ryugu [1]. Since rendezvousing with Ryugu less than known as the home position (HP) point [3]. Navigation one year ago, Hayabusa2 has set a new first for Japan by was performed in the HP frame, with the z-axis aligned successfully performing the first ever impact experiment with the asteroid–Earth line. Hayabusa2 typically on an asteroid (April 2019). The impact experiment was operates at around 20 km altitude in +z ,known HP executed after successful completion of another critical as controlled BOX-A [3]. To maintain Hayabusa2’s operation: the touchdown operation for sampling position in BOX-A, a ΔV command was sent to Ryugu’s surface (February 2018). The first touchdown the spacecraft every 1–2 days. A decrease in the was followed by a second successful touchdown at the Sun–Earth–probe (SEP) angle below 3 caused a location of the small carry-on impactor’s (SCI) artificial substantial increase in data noise in the Doppler crater site in July 2019. After entering the Sun’s measurements [4], thus making it difficult to correctly shadow in late 2018 with the start of the superior solar send commands to the spacecraft. JAXA’s previous conjunction phase, Hayabusa2 successfully deployed two Hayabusa mission experienced solar conjunction during rovers (September 2018) and a lander (October 2018). the transfer phase [5], when it was placed in a In November 2019, Hayabusa2 completed its exploration heliocentric orbit towards Itokawa. It was the first time phase and began its return journey towards the Earth. that a spacecraft experienced superior solar conjunction stefania.soldini@liverpool.ac.uk 266 S. Soldini, H. Takeuchi, S. Taniguchi, et al. Nomenclature AIT asteroid image tracking AOCS attitude orbit control system AU astronomic unit COI conjunction orbit insertion FD flight dynamics FOV field of view GCP-NAV ground control point navigation goNEAR gravitational orbits near earth asteroid regions HGA highgainantenna HP home position (20 km from Ryugu) HPNAV home position NAVigation HRM home position recovery maneuver JATOPS JAXA approach trajectory optimizer with stochastic constraints OD orbit determination optNEAR optimum trajectory near Earth asteroid regions RCS reaction control system SEP Sun–Earth–probe SRP solar radiation pressure TCM trajectory control maneuver ToF time of flight UTC universal coordinated time while in the hovering phase. This condition lasted 21 free mode (ballistic capture). As a first approximation, days for Hayabusa2, making the standard 1–2 days the conjunction trajectory was designed in the Hill HP maintenance operation infeasible. As a 20 km frame of the Sun–asteroid system and the solution altitude is usually artificially maintained, it was too was then refined in the full-ephemeris problem [6, 7]. risky to leave the spacecraft uncontrolled in proximity The time of flight (ToF) of the flown ayu conjunction to Ryugu. To prevent a close approach with the trajectory was around 38 days, with two deterministic asteroid, or an undesired escape from Ryugu’s sphere of ΔV designed at the conjunction orbit insertion (COI) influence, the optimum trajectory near-Earth asteroid point (home position (HP) before the conjunction) and regions (optNEAR) tool was developed for the design of at the home position recovery (HRM) point (HP after a low energy transfer trajectory for hovering satellites. the conjunction). Two trajectory correction maneuvers The trajectory was designed in the Hill frame and (TCMs) were scheduled before and after the deep due to its fish-like shape was named “ayu” (Japanese conjunction phase. The trajectory designed with the sweetfish) trajectory [6, 7]. For the case of Hayabusa2, optNEAR tool was validated in real time operations the ayu trajectory was designed to reach an altitude and used for testing the JAXA’s trajectory design of 110 km in deep conjunction (minimum SEP angle). JATOPS (JAXA approach trajectory optimizer with Only two deterministic maneuvers were required, with a stochastic constraints) tool for high altitude operations. ΔV budget of less than 1 m/s. The shooting method The results of the post-flight operations are presented developed in optNEAR takes advantage of the natural here. dynamics of the asteroid–Sun system, knowing that in the Hill problem the spacecraft motion is opposed by the 2 Solar conjunction mission design and solar radiation pressure (SRP) acceleration, for a fixed operation planning initial energy level. This principle was previously used by JAXA’s Hiten mission [8], for the design of a recovery The ayu conjunction trajectory was designed in the trajectory in the patched Sun–Earth and Earth–Moon Hill reference frame, as shown in Soldini et al. [6, 7]. systems [9]. The ayu trajectory aimed to direct the Thedynamicsofthemotherspacecraft waswritten spacecraft towards the zero velocity curves of the Hill in a rotating reference frame, where the system was problem (boundary of possible motion), where the centered on Ryugu and the Sun, and the asteroid was maximum altitude of 110 km was reached and the return placed along the x-axis. The Sun was in the negative to a 20 km altitude could therefore be executed in fuel- x coordinates. Depending on how the initial energy of Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 267 the spacecraft (state vector) was set, it was possible [6, 7]. As a result of an uncertainty analysis in the to distinguish regions of motion where the spacecraft deterministic maneuvers at COI and HRM, Soldini et dynamics was not permitted [10]. This information was al. concluded that at least two stochastic TCMs were used to increase the spacecraft’s altitude from 20 km to a required [6, 7], as shownbytheredpointin Fig. 1. safety altitude during deep conjunction. On 2018/12/11, The conjunction operation required four maneuvers the spacecraft reached the deep conjunction position to be performed. The solution in the Hill reference located at the boundary of the permitted motion, as frame was the first guess solution. The trajectory was seen in the Hill reference frame. In deep conjunction, then refined and recomputed in the full ephemeries the SEP angle was at its minimum value of 0.4 . planetary equations via the use of NASA’s SPICE The conjunction operation started and ended when toolkit, interfaced with the optNEAR tool. the SEP angle was equal to 5 and the gravity constant Table 1 shows the epochs of the Hayabusa2’s superior 3 2 of Ryugu, μ ,was set to 30 m /s ,as in Soldini et al. [6,7]. solar conjunction operations as afunctionoftheSEP Figure 1 shows the nominal conjunction trajectory as angle. The overall solar conjunction phase lasted for seen from the Hill reference frame and HP reference 37 days and for 21 days the spacecraft was kept free frame (Figs. 1(a) and 1(b)). The trajectory’s fish-like from on ground control, while in deep conjunction. Note shape in the Hill coordinates can be seen in Fig. 1(a). that on 2018/12/28, it was decided to modify the ΔV The z-axis of the HP reference frame was along the planning at HRM (last line in Table 1) and the home Earth-asteroid line pointing towards the Earth. The position keeping (HPK) maneuver for hovering position Sun–asteroid line belonged to the positive coordinates maintenance (20 km from Ryugu along the z axis) HP of the x–z plane and the y axis was given such that the was merged with the HRM maneuver. HP frame was a right-handed coordinate system. Figure In Soldini et al. [6, 7], it was demonstrated that 1(b) shows that the ayu trajectory was a periodic orbit the ayu conjunction trajectory allowed a low fuel when placed in the HP reference frame. Indeed, COI expenditure and Ryugu was always in the field of view and HRM share the same coordinates in this frame. (FOV) of Hayabusa2’s wide angle navigation camera Figure 1 also shows the epochs of the TCMs (red points) and the deep conjunction epoch (green point). Table 1 Scheduled maneuvers for the Hayabusa2’s superior solar conjunction The ayu conjunction trajectory requires two deterministic maneuvers: before and after the superior Maneuver Epoch (UTC) SEP angle ( ) COI 2018/11/23 5 solar conjunction at the COI point and the HRM, TCM1 2018/11/30 3 respectively (Fig. 1)[6, 7]. The total contribution of TCM2 2018/12/25 4 the two deterministic ΔV maneuvers at COI and HRM HRM+HPK 2018/12/29 5 computed with the optNEAR tool was 0.2359 m/s Fig. 1 Design of the solar conjunction ayu trajectory as seen in the Hill reference frame (a) and HP reference frame (b). 268 S. Soldini, H. Takeuchi, S. Taniguchi, et al. ONC-W1 (60 ). Figure 2 shows the ayu trajectory in deep conjunction. A radio science experiment 3 2 for μ =32m /s and for a conjunction maneuver was carried out during the deep conjunction epoch starting at a SEP angle of 6 . Figure 2(a) shows (the green point in Fig. 1) for testing the Ka- thetrajectorybyforward (black) and backward (green) band capability for retrieving telemetry data to integration from the deep conjunction point (-H), as estimate the spacecraft’s position and velocity. The shown by the green point in Fig. 1. The geometry of the spacecraft remained in deep conjunction for 21 days camera was verified when the spacecraft was kept Earth- with no commands sent from Earth. pointing (∼ Sun-pointing in deep conjunction). Figure (3) Recovery phase: TCM2 (2018/12/22)–HRM 2(b) shows the angle between the x-axis direction and (2018/12/29). The recovery phase required a thespacecraft–Ryuguline(halfofthecameraFOV). second TCM2 maneuver when the SEP angle was The asteroid was always in the FOV of the ONC-W1 4 .The HRM was performed when the SEP angles camera and in some cases was within the ONC-T camera was 5 . FOV (6 ). (4) Home position keeping: HPK (2018/12/29). At the For the solar conjunction mission planning, four main HRM epoch, a ΔV for HPK maintenance was added phases were defined and the epoch of the maneuvers are with the scope of bringing the spacecraft to 20 km giveninTable 1: altitude on 2018/12/31. (1) Preparation phase: COI (2018/11/23)–TCM1 2.1 Maneuver operation (2018/11/30). During the preparation phase, the spacecraft performed a 180 slew maneuver around The conjunction orbit took into account the solar the z -axis to ensure the correct orientation of HP radiation pressure perturbation and was designed to the 12 thrusters after the deep conjunction phase stay in the +z region without any deterministic HP (flip of the HP frame). The COI maneuver was maneuvers between COI and HRM. The maximum performed when the SEP angle was 5 and TCM1 distance from Ryugu was 109 km on 2018/12/11 (deep was performed when the SEP angle was 3 . conjunction epoch, green point in Fig. 1). The COI (2) Deep conjunction phase: TCM1 (2018/12/01)– and HRM ΔV s were 2 cm/s in x and 12 cm/s in HP TCM2 (2018/12/21). When the spacecraft was in y . The maneuvers were calculated based on the HP deep conjunction (SEP angle < 3 ), the spacecraft results of the orbit determination (OD) team, who did not perform any orbit maneuvers, only attitude made use of radiometric data and ONC-W1’s asteroid maintenance. Beacon operations were carried out image tracking (AIT) data to estimate the state of to monitor the status of the spacecraft while the spacecraft. The AIT data was verified using the Fig. 2 The left panel shows the two arcs of the conjunction trajectory from deep conjunction to COI (green line) and from deep conjunction to HRM (black line). The right panel shows that Ryugu is always in the ONC-W1 camera FOV (60 ) and in some cases in theFOV oftheONC-Tcamera (6 ). Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 269 raw ONC-W1 images. Each maneuver was supported onboard camera-based asteroid direction determination via 2 days of navigation campaign. The minimum (asteroid image tracking-AIT) were combined [6, 7, 11]. ΔV threshold for the reaction control system (RCS) To guarantee a precise relative navigation, three was 1 mm/s and any maneuver below 1 mm/s was techniques were run in parallel. These are shown in cancelled. If the planned ΔV was above 10 cm/s than Fig. 3, Phase (2): (a) NAV1, called HPNAV (home the maneuver was divided into main and trim ΔV s. The position navigation), a hybrid navigation technique that ΔV was measured by the 2-way Doppler, while the combines radiometric (RARR) and optical navigation HP ΔV was measured by the accelerometers (ACMs). (ONC-T camera) techniques. It is a method for x,y HP The trim, ΔV , was also used as a minor correction of the finding the position and speed of the spacecraft, using main ΔV during the same pass (contingency case). The the direction to the image center and attitude data Hayabusa2 spacecraft was kept Earth-pointing during [11]. (b) NAV2, called GCP-NAV (ground control the conjunction phase, for radio-science purposes. The point navigation), a technique of finding the position spacecraft made use of the star trackers to maintain and speed of the spacecraft by observing features on its attitude. The attitude maneuvers were scheduled the asteroid surface [11]. (c) NAV3, a full asteroid– every three days to keep the high gain antenna (HGA) spacecraft simultaneous orbit determination technique Earth-pointing. Every attitude slew was below 3 .The (Fujitsu team and JAXA team) [11]. Earth moved at a rate of about 0.75 ( )/day and the Once the results of the navigation were validated, half-band-width of the HGA was 1.2 . Note that it was the ΔV planning phase started (Phase (3) in Fig. 3). verified that Ryugu was always visible from ONC-W1 The optNEAR tool was used as the main baseline for (60 FOV). During the entire sequence, the SEP angle the ΔV planning, which is the subject of this article. was below 2 . The JATOPS tool, which was used during the approach Figure 3 shows a schematic representation of the phase, now became the backup solution for the solar operation planing. Similar to Hayabuas2’s approach conjunction phase [11]. Theresultsof theguidanceare phase [11], the operation planning for the solar givenina.way fileformattobeusedasinputstothe conjunction phase can be divided into: Phase (1), spacecraft operation (Phase (4) in Fig. 3). onboard image-based optical measurements (before Finally, the spacecraft operation phase consisted of 7:00 UTC in Fig. 3); Phase (2), radio-optical hybrid transforming the .way file, ΔV , from the HP reference navigation (7:00–13:00 UTC in Fig. 3); Phase (3), frame to the spacecraft’s asteroid fixed frame [6, 7]and guidance (13:00–16:00 UTC in Fig. 3); and Phase (4), sending the command to the spacecraft. The operation spacecraft operation (from 16:00 UTC in Fig. 3). planning and the results of the mission operations The operation planning started two days before the are presented in this article. The mission operation maneuver planning, known as the observation campaign, process described here was followed for each of the four by downloading the telemetry from the spacecraft; scheduled maneuvers at COI, TCM1, TCM2, and HRM Phase (1) in Fig. 3. The range-rate (RARR) and the epochs described in Table 1. 2.2 Attitude maintenance The Hayabusa2 team considered three options for the attitude maintenance of the spacecraft during deep conjunction: 1) Safe mode (spinning). This method is safe as the spacecraft is passively stabilized. Only range and rangeratearepossibleinthismode. However, its major drawback is it requires fuel and time to de-spin the spacecraft and progress to three-axis stabilisation. 2) Hayabusa2 acting as a solar sail. This mode makes use of 1 reaction wheel control [12, 13]. The Fig. 3 Mission operation plan for each of the four scheduled conjunction maneuvers. spacecraft is passively stabilized using the SRP 270 S. Soldini, H. Takeuchi, S. Taniguchi, et al. torque. The passive stabilisation makes this method or written more compactly: very safe to use. This method was inspired by X = F (X,t) (2) JAXA’s IKAROS mission [14] and the Hayabusa2 spacecraft tested this method during cruise mode 3 2 where μ is the gravity constant of Ryugu (30 m /s ). [12]. However, the major disadvantage of this The 3rd body acceleration is given by method is that the HGA can’t be used when the Δ d spacecraft is in “solar sail” mode as the spacecraft a = −μ + (3) Pj Pj 3 3 Δ d would need to be maintained as Sun-pointing, not Earth-pointing [13]. with Δ = r − d,where r is the spacecraft’s position 3) Hayabusa2 is kept Earth-pointing during deep vector from Ryugu and d is the position vector of the conjunction. The spacecraft makes use of the perturbing body (Pj) from Ryugu. Note that when star trackers to maintain its attitude. Attitude the optNEAR tool calls the NASA’s SPICE Toolkit, maneuvers are required during deep conjunction, the ephemeris are downloaded from a reference frame which makes this method less safe than both options centered on the solar system barycenter (SSB), and 1) and 2). However, the HGA can be used without therefore the vector d is given by the position vector of any difficulties. the planet in SSB coordinates minus the position vector Since the Hayabusa2 team selected option 3) for radio- of Ryugu in SSB coordinates. For a non-diffusive Earth- science purposes (testing of the Ka-band capability tracking flat surface, the SRP acceleration is in deep conjunction) [15], attitude maneuvers were P A AU r 0 ls scheduled every three days to maintain the HGA as a = − cos θ (1 − ) +2 cos θn ˆ SRP c m r r ls ls Earth-pointing. (4) where the Sun–line direction (r ) is given by considering ls the distance of the spacecraft from Ryugu minus the 3 n-body propagator in J2000EQ distance of the Sun from Ryugu. The normal vector (n ˆ) coordinates centered at Ryugu to Hayabusa2’s solar panels is kept Earth-pointing, thus (J2000EQ-Ry): optNEAR tool Earth n ˆ = (5) The optNEAR tool is a trajectory optimizer that make Earth use of an n-body propagator written in J2000 equatorial and coordinates, with the reference frame centered on Ryugu r · r ls Earth cos θ = (6) (J2000EQ-Ry). The optNEAR’s propagator (known as r r ls Earth goNEAR [6, 16]) was written in python language and r is the Ryugu–Earth distance where the vector Earth makes use of NASA’s SPICE Toolkit package to import is pointing toward the Earth. In Eq. (4), A is the the ephemeris of Ryugu, all the planets, the Earth, spacecraft’s reflective area, assumed as 13.276 m (i.e., Moon, and Sun. The effect of the SRP acceleration was the solar panels), the spacecraft’s mass, m, is 580 kg, also taken into account. In this case, the spacecraft was 2 P is the solar flux of 1366 W/m , c is the speed of considered as Earth-pointing and the flat plate model light of 2.99792458 × 10 m/s, and  is the reflectivity was used for the SRP acceleration [17]. The n-body of the spacecraft, assumed to be 0.321. Note that planetary equations are given by = C − 1,with C being the reflectivity coefficient of r r ⎡ ⎤ ⎧ ⎫ ⎡ ⎤ the spacecraft ( =0 complete absorption and  =1 X F ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎢ ⎥ complete specular reflection). A very simple way to ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎢ ⎥ Y F ⎪ ⎪ ⎢ ⎥ 2 demonstrate the relationship between  and C is to ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎢ ⎥ ⎨ ⎬ ⎢ ⎥ ˙ Z ⎢ ⎥ Z F consider that ρ +ρ +ρ =1,with ρ being the specular ⎢ ⎥ s a d s ⎢ ⎥ =⎢ NP ⎥ = μ j ⎢ ⎥ ⎪ ¨ ⎪ ⎢ − X + a | + a | ⎥ reflectivity coefficient, ρ the absorption coefficient, and 3 P x SRP x a ⎪ X ⎪ r j=1 ⎢ F ⎥ ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎢ ⎥ ρ the diffusive coefficient. If the diffusion term is ⎪ ⎪ NP ⎢ ⎥ d μ j ¨ a ⎪ ⎪ ⎢ ⎥ Y − Y + a | + a | F ⎪ ⎪ 3 P y SRP y 5 j ⎣ ⎦ r j=1 ⎪ ⎪ ⎣ ⎦ ⎪ ⎪ neglected (ρ =0), it is possible to write that ρ =1−ρ d a s ⎩ ⎭ NP μ j Z a F − Z + a | + a | and also that C =1+ ρ . ρ and ρ were renamed here 3 P z SRP z r s s a j=1 j (1) as  and C , respectively. The linearized equations of r Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 271 Eq. (1) are conjunction. To achieve high accuracy in the final error x˙ (t)= A(t)x(t) (7) position at HP, a constrained optimization was used such that: where the matrix of the linearized equation can be min |ΔV | (12) derived as x,α,δ ⎡ ⎤ with 0 0 0 100 V = V cos δ cos α ⎢ ⎥ x ⎢ ⎥ 0 0 0 010 ⎢ ⎥ V = V cos δ sin α (13) ⎢ ⎥ y ⎢ 0 0 0 001 ⎥ ⎢ ⎥ V = V sin δ A = ⎢ ⎥ (8) ∂F ∂F ∂F 4 4 4 ⎢ ⎥ ∂x ∂y ∂z ⎢ ⎥ 2 2 2 ⎢ ⎥ where V = V (1 + sin x) and ΔV = V + V + V , ∂F ∂F ∂F max 5 5 5 x y z ⎢ ⎥ ∂x ∂y ∂z ⎣ ⎦ subject to the following constraints: ∂F ∂F ∂F 6 6 6 ∂x ∂y ∂z |x(t ) − x ¯|− toll = 0 The derivatives in Eq. (8) were computed analytically (14) |y(t ) − y¯|− toll = 0 and their equations are given in Appendix A. To relate |z(t ) − z¯|− toll = 0 astate toaspecificepoch, t, from an initial state, t , the state transition matrix is needed: The toll is usually set to 0.1 m. Note that the ∂X(t) minimization of ΔV is reduced to finding three angles, Φ(t, t )= (9) ∂X(t ) α (in-plane angle), δ (out-of-plane angle), and x (e.g., V = V ,with x =0 ). At t , after the ODE max 1 that it is numerically computed as integration of Eq. (1), the final desired position of Φ(t, t )= A(t)Φ(t, t ) (10) the spacecraft was to be equal to the nominal state 0 0 r¯ =[0, 0, 20 km], in HP coordinates, at the end of the HP with Φ(t ,t )= I. Therefore, 0 0 conjunction epoch (2018/12/29 in Table 1). Note that the ODE integration was performed in the J2000EQ- δx(t)= Φ(t, t )δx(t ) (11) 0 0 Ry reference frame, and therefore a transformation was The computation of the STM can be done by deriving required to move r¯ into J2000EQ-Ry coordinates (r¯), HP the analytic expression of the linearized equations as shown in Soldini et al. [6, 7]. matrix A and by solving Eq. (10) numerically, together 4.1 Deterministic ΔV maneuver at COI: with the equations of motion in Eq. (3). The derivatives Refinement of the Hill trajectory in the in Appendix A were tested by comparing the analytical n-body dynamics derivatives with the numerical derivatives. At the beginning of the conjunction phase (COI epoch in Table 1), the shooting method (optNEAR tool) 4 optNAER’s single shooting method described made use of the ayu conjunction trajectory for the ΔV planning designed in the Hill coordinates [6, 7]. The ayu The shooting methods developed in the optNEAR tool trajectory designed in Refs. [6,7] was therefore the first were used for the ΔV planning during Hayabusa2’s guess for the two-boundary value problem in the full superior solar conjunction operation. The aim was ephemeris model (goNEAR tool [6,16]) where the initial to minimize the overall ΔV budget required to place (COI) and final (HRM) positions were fixed. In Fig. 4, the spacecraft in the ayu conjunction trajectory. The the black line is the un-optimized trajectory (goNEAR operation aimed to depart from the hovering location propagator), while the red trajectory is optimized with at HP and return to HP after the spacecraft left the the optNEAR tool. The magenta point is the location of Sun’s shadow. optNEAR’s shooting method aimed to the HP at HRM (2018/12/29 in Table 1). Tables 2 and minimize the ΔV maneuver such that following the 3 show the ΔV designed at COI and HRM in the HP integration of the non-linear dynamics in Eq. (1), the and J2000EQ-Ry coordinates, respectively. Each table spacecraft returned to HP at the end of the solar shows the epoch of the maneuver in UTC and the ΔV is 272 S. Soldini, H. Takeuchi, S. Taniguchi, et al. Fig. 5 Shooting method: reference trajectory (solid line) and perturbed trajectory (dashed line). in the system of Eq. (15)is Φ (t ,t )δr + Φ (t ,t )δv = 0 (16) 11 1 0 0 12 1 0 0 so that −1 δv = −Φ (t ,t )Φ (t ,t )δr (17) Fig. 4 Conjunction trajectory optimized (red) with the n-body 0 1 0 11 1 0 0 optimizer (optNEAR tool) and the propagated trajectory in black (goNEAR tool) as seen from Ryugu, Eq. (1). with Φ (t ,t ) as 11 1 0 ⎡ ⎤ Φ Φ Φ 11 12 13 given for each axis direction in HP coordinates (Table 2) ⎢ ⎥ ⎢ ⎥ Φ (t ,t )= (18) Φ Φ Φ and in J2000 coordinates (Table 3). Note that due to 11 1 0 21 22 23 ⎣ ⎦ the mounting direction of the thrusters a ΔV margin Φ Φ Φ 31 32 33 (t ,t ) 1 0 (Table 2) was added to include thrust losses in the y HP and Φ (t ,t ) as direction [6, 7]. ThesettingsusedintheoptNEARtool 12 1 0 ⎡ ⎤ for the COI maneuver planning were V =0.0004 max Φ Φ Φ 14 15 16 km/s. The lower and the upper boundaries of the angles ⎢ ⎥ ⎢ ⎥ ◦ ◦ ◦ ◦ ◦ ◦ Φ (t ,t )= Φ Φ Φ (19) 12 1 0 24 25 26 were set as: x (−90 ,0 ), α (0 ,30 ), and δ (0 ,90 ). ⎣ ⎦ Φ Φ Φ 34 35 36 (t ,t ) 1 0 4.2 Trajectory correction maneuvers: TCM1 and TCM2 The initial state is therefore After COI, every initial state guess at the TCM epoch x = δx + x ¯ 0 0 0 (20) t (time of maneuver) can be found analytically through v = δv + v¯ 0 0 0 the state transition matrix: and is used as the initial guess for the shooting method δr Φ Φ δr 1 11 12 0 = (15) in optNEAR. The settings used for the optNEAR tool δv Φ Φ δv 1 21 22 0 t ,t 1 0 at TCMs are with the objective of bringing the final position state to a) TCM1 maneuver settings: V was set to 0.002 km/s. The lower and the upper zero, as shown in Fig. 5(b) (δr =0). The first equation 0 max 3 2 ◦ Table 2 ΔV in HP reference frame for the Earth-pointing spacecraft (μ =32m /s and SEP = 5 ) ΔV (HP) Epoch UTC ΔV (HP) ΔV (HP) x ◦ z cos(75 ) (ET) (date) (m/s) (m/s) (m/s) COI 596,203,269.18 2018/11/23 T00:00 1.891E−02 −6.0322E−03 1.175E−01 HRM 599,313,669.18 2018/12/29 T00:00 −1.8058E−02 1.5744E−02 −1.1549E−01 Total 3.6977E−02 2.177E−02 2.3299E−01 3 2 ◦ Table 3 ΔV in J2000 reference frame for the Earth-pointing spacecraft (μ =32m /s and SEP = 5 ) Epoch UTC ΔV (J2000) ΔV (J2000) ΔV (J2000) x y z (ET) (date) (m/s) (m/s) (m/s) COI 596,203,269.18 2018/11/23 T00:00 3.1793E−02 1.05487E−01 4.50463E−02 HRM 599,313,669.18 2018/12/29 T00:00 1.4375E−02 1.07179E−01 4.4575E−02 Total 4.6168E−02 2.12666E−01 8.9621E−02 Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 273 ◦ ◦ boundaries of the angles were set as: x (−90 ,0 ), 5 JAXA’s JATOPS tool: The backup ◦ ◦ ◦ ◦ α (0 ,30 ), and δ (0 ,90 ); solution of the optNEAR tool b) TCM2 maneuver settings: As part of the ΔV planning at COI, TCM1, TCM2, V was set to 0.01 km/s. The lower and the upper max and HRM, the optNEAR tool was used as the main ◦ ◦ boundaries of the angles were set as: x (−90 ,0 ), solution for planning the ΔV command, which was to ◦ ◦ ◦ ◦ α (−90 ,0 ), and δ (−180 ,0 ). be executed on board the spacecraft. However, it was further verified that JAXA’s trajectory optimisation 4.3 Brake velocity maneuver at HRM and tool, JATOPS [11], could retrieve the same solution HPK maneuver as the optNEAR tool, once the nominal states at the Planning for the ΔV maneuver at HRM included both COI, TCM1, TCM2, and HRM epochs were computed a brake velocity maneuver at HP on 2018/12/29 and by optNEAR. The difference between optNEAR and a HPK maneuver for BOX-A operation maintenance, JATOPS is in the ability to design the ayu trajectory until 2018/12/31. The first ΔV aimed to simply stop in a single shooting. OptNEAR implements a semi- the spacecraft at the HP arrival point (HRM). The HPK analytical method that uses the weak stability boundary maneuver required designing in the Hill coordinates, as theory to design the first guess trajectory in one pass for the ayu conjunction trajectory. The same shooting (the ayu trajectory). Once optNEAR has successfully method described in Soldini et al. [6, 7] was used provided the first guess (the ayu solution), JATOPS can but with the following initial guess: H =25km 0 then be used as a validation tool for the ΔV s computed (maximum altitude), α = 188 (in-plane angle in the 0 with optNEAR. For further details on the JATOPS tool, x–y coordinates), and v = 0 km/s (out of plane Hill z refer to Tsuda et al. [11]. velocity). The lower and upper boundaries of the Figure 7 shows that the JATOPS tool could be used optimum parameters were as follows: 20 km <H < for high altitude operations as it finds the same solutions ◦ ◦ 30 km, 180 <α< 270 ,and −0.00001 km/s <v < z as the optNEAR tool [11]. Therefore, our ΔV planning 0.00001 km/s. Once the HPK maintenance arc was strategy was to use the optNEAR tool as a baseline for designed in the Hill reference frame, the solution was the computation of the ΔV commands and to rely on refined in the optNEAR tool; V was set to 0.0002 max theJATOPStoolasaback-upsolution. TheJATOPS km/s and the lower and upper boundaries of the angles tool was selected as a back-up solution for the optNEAR ◦ ◦ ◦ ◦ ◦ were set as follows: x (−90 ,0 ), α (0 ,30 ), and δ (90 , tool and the following procedure to retrieve the nominal 180 ). Figure 6 shows the nominal HPK arc trajectory trajectory with JATOPS was confirmed [11]: designed with the optNEAR tool, if the HRM point is (1) The ayu trajectory was divided into three trajectory in its nominal location of 20 km altitude. legs: COI-TCM1 (Leg1), TCM1-TCM2 (Leg2), and Fig. 7 The conjunction trajectory as seen from the HP frame: a Fig. 6 Example of the HPK trajectory arc in the HP reference comparison between the solutions obtained between the optNEAR frame, from 2018/12/29 to 2018/12/31. (red line) and the JATOPS (black line) tools. 274 S. Soldini, H. Takeuchi, S. Taniguchi, et al. TCM2-HRM (Leg3). navigation and operation planning and their results (2) Each leg derived a two-impulse trajectory, using are presented here. The ΔV planning started on states derived by the optNEAR tool from the output 2018/11/22 after two days of data measurements. .way file as the boundary conditions. The initial downlink of the telemetry data started on (3) It was confirmed that the JATOPS tool was a good 2018/11/21. back-upinextremecaseswhena ΔV was required (a) Once the downlink of the AIT and Doppler data to safely return back to HP. was concluded, the navigation teams performed an (4) The JATOPS tool does not have the capability estimate of the spacecraft’s position and velocity. to instantaneously derive the entire nominal ayu The navigation team’s estimates at COI are shown conjunction orbit from COI to HRM, as with the in Table 4. Those estimates were compared with the optNEAR tool. nominal case, as shown in the first row of Table 4. From those estimates, the corresponding ΔV swere computed, as shown in Table 5. 6 Post mission operation To select the best estimate of the spacecraft’s In this section, each of the four maneuvers performed state from the JAXA and Fujitsu solutions, the ΔV s during the solar conjunction phase are presented. The in Table 5 were cross evaluated with the different solar conjunction operation was planned as described in solutions in Table 4. The solutionswerethus Section 2 and in Fig. 3. For each operation planning propagated with goNEAR. (Fig. 3), first the results of the OD teams were analyzed. From this analysis, the solution from Fujitsu was Once the most reliable estimate of the spacecraft’s selected for the ΔV planning as it was shown to position and velocity was selected by the flight dynamic be the most conservative solution in the presence of (FD) and OD teams, planning of the ΔV resulted in the uncertainties in the navigation. delivery of the .way file from the FD team to the attitude (b) After having selected the estimate from the OD’s orbit control system (AOCS) team. The ΔV was thus Fujitsu team, the FD team prepared the ΔV given as a sequence of commands to the spacecraft. planning at COI. Figure 8 shows the .way file After the ΔV was executed on board the spacecraft, prepared on 2018/11/22 for the following day’s its velocity (2-way Doppler) and acceleration (ACMs) operation. The .way file was the input for the AOCS were measured to estimate the actual ΔV performed. team, where the ΔV was computed in a body-fixed The actual and the planned ΔVswerethuscompared frame. Figure 8 shows the estimated states at each to evaluate the performance of the operation. In case epoch and the corresponding ΔV s. of large discrepancies between ΔV s, it was possible to (c) The error between the planned and the actual ΔV correct the maneuver within the same communication was of 98.78% in ΔV , 93.53% in ΔV ,and X Y B B pass. At the end of the operation, the measured ΔV was 98.53% in ΔV , asshowninthereportof Fig. 9. used for the trajectory design of the next trajectory leg. Figure 9 shows the measured and planned ΔV sfor the main (M) and trim (T) maneuvers for each axis 6.1 Conjunction orbit insertion (COI) direction. The accuracy in the maneuvers in term maneuver: 2018/11/23 of absolute and relative errors are also provided. On 2018/11/23, the Hayabusa2 spacecraft performed Due to uncertainties in the ΔV at COI, it was the conjunction orbit insertion maneuver. The concluded that at least one TCM was required on Table 4 Nominal state vector at COI and estimated states by Fujitsu (OPNAV1/NAV3 in Fig. 3), JAXA (OPNAV2/NAV3 in Fig. 3), and HPNAV (NAV1 in Fig. 3) State x y z v v v HP HP HP x y z HP HP HP estimate (km) (km) (km) (mm/s) (mm/s) (mm/s) Nominal 0 0200 0 0 OD’s Fujitsu −0.0115 −0.1428 20.0692 −1.7101 1.2674 −17.9384 −0.0458 −0.1197 19.9301 −2.1938 1.4375 −17.9382 OD’s JAXA HPNAV 0.0425 −0.1217 19.7622 −1.7098 1.7039 −18.0709 Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 275 Fig. 8 Planned ΔV at COI in .way file format. Table 5 Nominal ΔV ,OD’s Fujitsu ΔV (OPNAV1/NAV3 in small position error of the spacecraft. For this Fig. 3), and OD’s JAXA ΔV (OPNAV2/NAV3 in Fig. 3) reason, no contingency ΔV was required at COI. State ΔV ΔV ΔV X Y Z HP HP HP It was also expected that the major ΔV at TCM1 estimate (cm/s) (cm/s) (cm/s) would have been in the Z component. Nominal 1.9844 −0.1637 12.2624 Figure 10 shows the planned trajectory for the OD’s Fujitsu 2.1548 −0.2906 14.0497 selected solution (OD’s Fujitsu is shown in black). OD’s JAXA 2.2060 −0.3080 14.0625 The red trajectory leg is the predicted trajectory from COI to TCM1, when the actual ΔV from theresultreportinFig. 9 wasused. Thegreen trajectory is the new solution from TCM1 to HRM, designed with the optNEAR tool. Fig. 9 Results of the COI operation on 2018/11/23: planned and measured ΔV report. 2018/11/30 before deep conjunction. Errors in the Fig. 10 Planned trajectory OD Fujitsu solution (black), actual ΔV lower than 4 mm/s were considered acceptable, trajectory from COI to TCM1 after COI operation (red), and new asconcludedinSoldini et al. [6, 7], where it was planned trajectory between TCM1 to HRM (green). The black shown that those errors resulted in a negligibly dot represents the Ryugu coordinates. HP reference frame. 276 S. Soldini, H. Takeuchi, S. Taniguchi, et al. 6.2 Trajectory correction maneuver 1 The OD’s JAXA team’s .way file was the input for (TCM1): 2018/11/30 the AOCS team and the ΔV was computed in a body-fixed frame. The first trajectory correction maneuver (TCM1) was (c) In the case of TCM1, the ΔV and ΔV were performed on 2018/11/30 before the spacecraft entered X Y cancelled, resulting in an error after 24 days of 1 the deep solar conjunction phase, with the SEP angle km in X at TCM2, as shown in Fig. 13. An equal to 3 . The TCM1 allowed corrections in the HP increase in the noise of the Doppler signal already trajectory after the actual operation at COI. The ΔV at TCM1 was registered, as shown in Fig. 12. The at TCM1 was planned on 2018/11/29 after the initial noise is evident by looking at the fluctuation in the downlink of the telemetry data on 2018/11/28. vertical axis of Fig. 12, which represents the double (a) The estimates of the spacecraft’s position and error between the measured and planned speed of velocity on 2018/11/29 are shown in Table 6. the spacecraft. This fluctuation is in the order of As with COI, the solutions were crosschecked with the size of the maneuvers (mm/s) and is usually a the nominal case designed after the COI maneuver straight line, when the Sun corona is out of the way (the green trajectory in Fig. 10). The ΔV s of the communication link. The report in Fig. 14 correspondence with the estimated solutions are shows that the error in the ΔV was 99.21%, shown in Table 7. As with the COI maneuver Z resulting in a perfectly executed operation. Between planning, the ΔV sin Table 7 were cross evaluated TCM1 and TCM2, only pre-scheduled attitude with the different solutions in Table 6 and the maintenance maneuvers were performed (every solutions were propagated with goNEAR. From this 1–2 days). It was decided to avoid desaturation of analysis, the solution from JAXA was selected for the reaction wheels in deep conjunction to prevent the ΔV planning at TCM1. errors to the planned trajectory between TCM1 and (b) Figure 11 shows the .way file prepared on the TCM2. 2018/11/29 for the TCM1 operation (2018/11/30). Table 6 Nominal state vector at TCM1 and estimated states by Fujitsu (OPNAV1/NAV3 in Fig. 3), JAXA (OPNAV2/NAV3 in Fig. 3), andHPNAV (NAV1inFig. 3) State x y z v v v HP HP HP x y z HP HP HP estimate (km) (km) (km) (mm/s) (mm/s) (mm/s) Nominal 5.6589 −0.0395 75.1693 1.0321 1.1463 67.1665 OD’s Fujitsu 5.6086 −0.3308 75.0280 0.5944 0.6297 67.0149 OD’s JAXA 5.6395 −0.3308 74.7831 0.8847 0.6304 67.0185 HPNAV 5.8616 −0.4094 74.8879 0.9457 0.6333 68.0690 Fig. 11 Planned ΔV at TCM1 in .way file format. Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 277 Table 7 Nominal ΔV ,OD’s Fujitsu ΔV (OPNAV1/NAV3 in Fig. 3), and OD’s JAXA ΔV (OPNAV2/NAV3 in Fig. 3) State ΔV ΔV ΔV X Y Z HP HP HP estimate (cm/s) (cm/s) (cm/s) Nominal 0.0230 −0.0573 0.3460 OD’s Fujitsu 0.0752 0.0039 0.3674 OD’s JAXA 0.0492 0.0042 0.3793 Fig. 14 Results of the TCM1 operation on 2018/11/30: planned and measured ΔV report. estimating the state vector on 2018/12/11 is shown in Fig. 15, in gray. Compared to the propagated trajectory after executing the actual ΔV at TCM1, a displacement in position of 2 km in the X direction HP at TCM2 was noticed. It was verified that the 0.5 mm/s correction not given at TCM1 in the X-axis was one of the causes of this expected position displacement at TCM2. Moreover, the trajectory between TCM1 and TCM2, designed with the optNEAR tool, assumed that the spacecraft was always Earth-pointing. However, Fig. 12 Doppler signal on 2018/11/30. Horizontal axis: attitude maneuvers were scheduled every 3 days, which reception time in UTC. Vertical axis: the double difference resulted in an error in the pointing accuracy of 1 ; between measured and planned value of the spacecraft’s speed. consequently, the effect on the SRP acceleration was weaker. A smaller effect on the SRP acceleration caused adriftin the X-axis direction away from the asteroid, as shown in Fig. 16. It was verified that propagating the planned trajectory with a reflective coefficient, C ,of 5% less than the nominal value would have compensated fortheerrorinthe X position, shown by the purple HP line in Fig. 16. Furthermore, it is possible that non- linearities affected our solution after 21 days. Therefore, a TCM2 maneuver was needed immediately after deep conjunction on 2018/12/25. The error in the attitude is also thought to be the reason why the asteroid was not in the FOV of the ONC- T camera on 2018/12/15–17, as shown in Fig. 17.Figure Fig. 13 Planned trajectory OD JAXA solution (black), actual trajectoryfromTCM1toTCM2aftertheTCM1operation (red), 17(b) shows that the state of the spacecraft could not and new planned trajectory between TCM2 to HRM (green). The be estimated with the ONC-T camera as Ryugu was out black dot represents the Ryugu coordinates. HP reference frame. of the camera’s FOV, as determined from the images taken. Figure 18 shows the angle between Ryugu and 6.3 Deep conjunction epoch: 2018/12/11 the spacecraft each day after 2018/12/11; it can be seen During the deep conjunction epoch on 2018/12/11, that when the error of 1 in the attitude was included beacon operations were performed to test the Ka-band in the analysis, Ryugu was not in the FOV of the ONC- capability and estimate the state vector of Hayabusa2 T on either day, as shown in Fig. 18(b). Due to the [15]; refer to the green dot in Fig. 1 for the deep geometry of the ayu trajectory, when the attitude error conjunction epoch. The propagated trajectory after was not taken into account it is possible to notice that 278 S. Soldini, H. Takeuchi, S. Taniguchi, et al. Fig. 15 Estimated trajectory in deep conjunction after beacon operation. Ryugu was not in the ONC-T’s FOV on 2018/15/17, as shown in Fig. 18(a). The observation campaign was started on 2018/12/21 to verify that the Z altitude was within the expected HP values. From the Doppler signal in Fig. 19,it was verified that the spacecraft’s velocity had changed sign (Fig. 19(b)), and that the spacecraft was returning to lower altitudes (Fig. 19(a)). The altitude of the spacecraft was approximately 82 km as planned in Fig. 19(a), and was decreasing towards the HP position altitude. 6.4 Trajectory correction maneuver 2 (TCM2): 2018/12/25 After 21 days of blackout in the communication link, the first telemetry data from the spacecraft was downloaded Fig. 16 Estimating the equivalent error in C . on 2018/12/22. The second TCM2 maneuver was scheduled for the 2018/12/25 after the planning on 2018/12/24. (a) The estimates of the spacecraft’s position and velocity on 2018/12/24 are shown in Table 8. The solutions for the COI and TCM1 operations planning were crosschecked with the nominal case, designed after the TCM1 maneuver (the green trajectory in Fig. 13) was executed. The ΔV s corresponding to the estimate solutions are shown in Table 9.The ΔV sinTable 9 were cross evaluated with the different solutions in Table 8 and the solutions were propagated with goNEAR. From this analysis, the solution from Fujitsu was selected for Fig. 17 Post estimation 2018/12/21: ONC-T images. the ΔV planning at TCM2. Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 279 Fig. 18 ONC-T angle FOV as function of the days from deep conjunction: the blue area shows during which epochs Ryugu is not in the FOV of ONC-T. Table 8 Nominal state vector at TCM2 and estimated states by Fujitsu (OPNAV1/NAV3 in Fig. 3), JAXA (OPNAV2/NAV3 in Fig. 3), andHPNAV (NAV1inFig. 3) State x y z v v v HP HP HP x y z HP HP HP estimate (km) (km) (km) (mm/s) (mm/s) (mm/s) Nominal 5.3185 −1.2411 55.0592 −0.6931 0.2238 −8.8516 OD’s Fujitsu 6.6334 −1.8447 56.8919 −0.6281 0.1917 −8.6760 OD’s JAXA 6.5968 −1.8250 56.8739 −0.6252 0.1940 −8.6823 HPNAV 6.4577 −1.7198 56.8581 −0.8764 0.2514 −8.7487 Table 9 Nominal ΔV ,OD’s Fujitsu ΔV (OPNAV1/NAV3 in Fig. 3), and OD’s JAXA ΔV (OPNAV2/NAV3 in Fig. 3) State ΔV ΔV ΔV X Y Z HP HP HP estimate (cm/s) (cm/s) (cm/s) Nominal −3.0005 0.5207 1.5554 OD’s Fujitsu −7.0870 2.6334 −5.8566 OD’s JAXA −7.0163 2.5521 −5.7345 (b) Figure 20 shows the .way file prepared on 2018/12/24 for the TCM2 operation (2018/12/25). TheOD’sFujitsuteam.wayfilewastheinputfor the AOCS team and the ΔV was computed in a body-fixed frame. (c) As a consequence of cancelling the ΔV and ΔV at X X TCM1, the TCM2 in each X, Y ,and Z component was performed, as shown in Fig. 20.As expected, the larger ΔV was given in the X direction, as at TCM1 (Fig. 11). The ΔV of 0.5 mm/s wasnotperformed, resultinginanexpected1km displacement in X at TCM2. The error between the planned and the actual ΔV at TCM2 was Fig. 19 Doppler measurements on 2018/12/21. 105.89% in ΔV , 100.21% in ΔV , and 93.48% in X Y B B 280 S. Soldini, H. Takeuchi, S. Taniguchi, et al. Fig. 20 Planned ΔV at TCM2 in .way file format. ΔV , as shown in the report of Fig. 21. Figure 22 Figure 23 shows the results after the operation shows the X–Z and Y –Z components of the ayu by comparing the planned trajectory with the actual trajectory in the HP frame at TCM2, displayed in predicted trajectory, in black and red, respectively. the control room. 6.5 Home recovery maneuver and home position keeping: 2018/12/29 On 2019/12/29, the last conjunction operation was performed. As explained in Section 4.3,two ΔV swere combined into one maneuver; a HPK maneuver (BOX-A operation keeping until 2018/12/31) together with the HRM ΔV . (a) Table 10 shows the estimates of the spacecraft’s position and velocity on 2018/12/30. As for the previous operations, the solutions were crosschecked with the nominal case, designed after the TCM2 maneuver (Fig. 23) was executed. The ΔV s Fig. 21 Results of the TCM2 operation on 2018/12/25: planned and measured ΔV report. Fig. 23 Planned trajectory OD Fujitsu solution (black), actual trajectory after TCM2 operation (red), and BOX-A operation Fig. 22 Planned ayu trajectory displayed on the screen of the (gray). The black dot represents the Ryugu coordinates. HP reference frame. ISAS’s control room on 2018/12/25. Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 281 Table 10 Nominal state vector at HRM and estimated states by Fujitsu (OPNAV1/NAV3 in Fig. 3), JAXA (OPNAV2/NAV3 in Fig. 3), andHPNAV (NAV1inFig. 3) State x y z v v v HP HP HP x y z HP HP HP estimate (km) (km) (km) (mm/s) (mm/s) (mm/s) Nominal −0.0993 −0.0217 20.3407 0.7 0.1 11.5 OD’s Fujitsu −0.6307 −0.0807 19.9176 3.3 0.4 14.0 OD’s JAXA −0.5825 −0.0923 19.7616 3.0 0.5 14.9 HPNAV −0.6572 −0.0527 19.8053 3.4 0.3 14.6 corresponding to the estimate solutions are shown in showninFig. 25.Figure 25 shows the planned Table 11.The ΔV sin Table 11 were cross evaluated and actual predicted trajectory after the HRM with the different solutions in Table 10 and the maneuver. solutions were propagated with goNEAR. From this The lower ΔV given is due to a decrease in pressure analysis, the solution from Fujitsu was selected for in the fuel tank, which required adjustment after the the ΔV planning at HRM. conjunction operation, as shown in Fig. 25. The error (b) Figure 24 shows the .way file prepared on between the planned and the actual ΔV at HRM was 2018/12/30 for the combined HRM and HPK 89.29% in ΔV , 92.15% in ΔV , and 97.43% in X Y B B maneuvers (2018/12/31). The OD’s Fujitsu team ΔV , as shown in the report of Fig. 26. Therefore, on .way file was the input for the AOCS team and the 2018/12/31 a BOX-A operation was performed to bring ΔV was computed in a body-fixed frame. the spacecraft back to 20 km. 2018/12/29 marked the (c) The HRM ΔV accounts for the brake velocity ΔV end of the superior solar conjunction phase and the start at HRM plus the HPK ΔV to target the center ofthesecondhalfoftheRyuguproximityoperations. of BOX-A operation on 2018/12/31. A lower ΔV 6.6 Summary of the solar conjunction executionof3mm/sinboththe X and Y directions operation was experienced, which allowed braking velocity in the Z direction but not the lateral direction, as In this section, the results of the COI (2018/11/23), TCM1 (2018/11/30), TCM2 (2018/12/25), and HRM Table 11 Nominal ΔV ,OD’sFujitsu ΔV (OPNAV1/NAV3 in (2018/12/29) operations are shown. The deterministic Fig. 3), and OD’s JAXA ΔV (OPNAV2/NAV3 in Fig. 3) ΔV was computed for each trajectory leg, using the State ΔV ΔV ΔV X Y Z HP HP HP optNEAR tool. The comparison between the planned estimate (cm/s) (cm/s) (cm/s) Nominal 0.2650 −0.0610 1.3410 trajectory after the OD campaign and the actual ΔV OD’s Fujitsu 0.3090 −0.0560 1.3750 trajectory after the mission operation are shown for OD’s JAXA 0.3020 −0.0550 1.3800 COI (Fig. 10), TCM1 (Fig. 13), TCM2 (Fig. 23), and Fig. 24 Planned ΔV at HRM (including HPK) in .way file format. 282 S. Soldini, H. Takeuchi, S. Taniguchi, et al. HRM (Fig. 25). In Figs. 10, 13, 23,and 25,the trajectory in black is the planned trajectory, while the one in red is the propagated trajectory after measuring the actual ΔV . The deterministic ΔV was computed using optNEAR in J2000EQ and then given in the HP and spacecraft’s body-fixed reference frames, as shown in Table 12. As previously mentioned, ΔV slower than 1 mm/s was neglected while ΔV faster than 10 cm/s wasexecutedtwo timesasmainandtrim ΔV s, as shown in Table 13. Table 13 shows the effects on the ΔV of truncation of up to 4 digits of the ΔV command. Fig. 25 Planned trajectory OD Fujitsu solution (black) and Evidently, both TCM1 and TCM2 did not require a the actual trajectory after HRM operation (red). The edges of trim ΔV , while the Z direction required main and trim BOX-A are marked in gray. The black dot represents the Ryugu coordinates. HP reference frame. ΔV s for both COI and HRM. The planned trim ΔV was usually rescheduled during the mission operation to compensate for the error of the main ΔV.In Table 13, the actual measurements are the ACMs for the X and Y ΔV s and 2-way Doppler for the Z ΔV . 7 Conclusions In this article, the Hayabusa2’s low energy conjunction (ayu) trajectory, executed in late 2018, was presented. As a result of the operation, the optNEAR tool was validated in real time and was used for the validation of JAXA’s JATOPS trajectory design tool at high altitude operations. The spacecraft reached a maximum distance of 109 km from Ryugu on 2018/12/11 and Fig. 26 Results of the HRM (including HPK) operation on returned to home position (20 km from Ryugu) on 2018/12/29: planned and measured ΔV report. 2018/12/29 after 21 days of uncontrolled orbital motion. Table 12 Designed deterministic ΔV in HP and body-fixed frames Maneuver ΔV ΔV ΔV ΔV ΔV ΔV X Y Z X Y Z HP HP HP B B B COI (cm/s) 2.154758 −0.290556 14.049689 −2.071104 0.595609 14.052644 TCM1 (cm/s) 0.049176 0.004165 0.379261 −0.048507 0.005917 0.379325 TCM2 (cm/s) −0.708705 0.263339 −0.585655 −0.719433 0.234432 −0.584859 HRM (cm/s) 3.092521 −0.560379 13.753272 3.111279 −0.530874 13.750199 Table 13 Planned and actual executed ΔV in the body-fixed frame ΔV ΔV ΔV ΔV ΔV ΔV X Y Z X Y Z B B B B B B Maneuver (planned) (planned) (planned) (actual) (actual) (actual) COI (main) (cm/s) −2.0700 0.5900 10.0000 −2.0448 0.54918 9.4530 COI (trim) (cm/s) 0.0000 0.0000 4.5970 0.0000 0.0000 4.3900 TCM1 (main) (cm/s) 0.0000 0.0000 0.3800 0.0000 0.0000 0.3770 TCM1 (trim) (cm/s) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 TCM2 (main) (cm/s) −0.7206 0.2310 −0.5892 −0.7631 0.2315 −0.5508 TCM2 (trim) (cm/s) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 HRM (main) (cm/s) 3.0900 −0.5600 10.0000 2.7700 −0.4880 9.3370 HRM (trim) (cm/s) 0.0000 0.0000 4.4100 0.0000 0.0000 4.0600 Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 283 Due to the error in the attitude maintenance in deep A.2 Partial derivatives of the 3rd body conjunction, Ryugu was not in the FOV of the ONC-T perturbations camera on 2019/12/15, while it was consistently in the The partial derivatives of the 3rd body perturbation are FOV of ONC-W1. On 2018/12/11 (deep conjunction), derived as a beacon operation was performed for radio science ⎡ ⎤ ∂F ∂F ∂F 4p 4p 4p μ 3(x−d ) j j j Pj x purposes to test the Ka-band capability under solar − 1 − 3 2 ∂x ∂y ∂z Δ Δ ⎢ ⎥ ⎢ ⎥ corona noise. The total expenditure in the ΔV was, as ∂F ∂F ∂F ⎢ 5p 5p 5p j j j 3(x−d )(y−d ) ⎢ ⎥ x y = ⎢ Pj 5 ⎢ ⎥ ∂x ∂y ∂z Δ desired, less than 0.36 m/s. Based on the observation ⎣ ⎣ ⎦ ∂F ∂F ∂F 6p 6p 6p 3(x−d )(z−d ) j j j x z data collected during the solar conjunction, the orbit of Pj 5 ∂x ∂y ∂z Ryugu was recalculated. This updated orbit was used 3(x−d )(y−d ) 3(x−d )(z−d ) x y x z after returning to the HP position (HRM) to resume μ μ Pj 5 Pj 5 Δ Δ the home position at an altitude of 20 km above the μ 3(y−d ) Pj y 3(y−d )(z−d ) ⎥ z z asteroid surface. It was confirmed that using this new − 1 − μ 3 2 Pj 5 ⎥ Δ Δ Δ orbit of Ryugu achieves and maintains a more stable   ⎦ 3(y−d )(z−d ) μ 3(z−d ) y z Pj z μ − 1 − Pj 5 3 2 home position. Δ Δ Δ (23) A.3 Partial derivatives of solar radiation Appendix A: Partial derivatives of the pressure perturbation optNEAR’s linearized equations The cannonball model assumes that the Hayabusa2 The partial derivatives including the gravity of Ryugu, spacecraft is Sun-pointing. This is not exact during the 3rd body, and the SRB perturbations are given by the conjunction phase when Hayabusa2 is kept Earth- the following equation: pointing. Therefore, the equations for a flat surface are ⎡ ⎤ ⎡ ⎤ ∂F ∂F ∂F ∂F ∂F ∂F 4 4 4 4r 4r 4r more appropriate and used here. The partial derivatives ∂x ∂y ∂z ∂x ∂y ∂z ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ of Eq. (4) are given by rearranging Eq. (4) as follows: ∂F ∂F ∂F ∂F ∂F ∂F 5 5 5 5r 5r 5r ⎢ ⎥ =⎢ ⎥ + ∂x ∂y ∂z ∂x ∂y ∂z ⎣ ⎦ ⎣ ⎦ K(1 − ) r · r Earth ls ∂F ∂F ∂F ∂F ∂F ∂F 6 6 6 6r 6r 6r a = − r SRP ls ∂x ∂y ∂z ∂x ∂y ∂z r r Earth ls ⎡ ⎤ ⎡ ⎤ ∂F ∂F ∂F 4p 4p 4p j j j ∂F ∂F ∂F 4SRP 4SRP 4SRP 2K (r · r ) Earth ls ∂x ∂y ∂z ∂x ∂y ∂z − r (24) ⎢ ⎥ Earth NP j 3 4 ⎢ ⎥ ⎢ ⎥ r r ∂F ∂F ∂F ⎢ ⎥ Earth ls 5p 5p 5p j j j ∂F ∂F ∂F ⎢ ⎥ 5SRP 5SRP 5SRP +⎢ ⎥ ⎢ ⎥ ∂x ∂y ∂z ∂x ∂y ∂z ⎣ ⎦ ⎣ ⎦ with j=1 ∂F ∂F ∂F ∂F ∂F ∂F P A 6p 6p 6p 6SRP 6SRP 6SRP j j j 0 ∂x ∂y ∂z K = AU (25) ∂x ∂y ∂z c m (21) Note that: ⎧ ⎫ ⎧ ⎫ A.1 Partial derivatives of the Ryugu’s gravity ⎪ ⎪ ⎪ ⎪ X X − X E S ⎪ ⎪ ⎪ ⎪ ⎨ ⎬ ⎨ ⎬ The partial derivatives of Ryugu’s gravity are given by r = Y and r = Y − Y (26) Earth E ls S ⎪ ⎪ ⎪ ⎪ ⎡ ⎤ ⎪ ⎪ ⎪ ⎪ ⎩ ⎭ ⎩ ⎭ ∂F ∂F ∂F 4r 4r 4r Z Z − Z E S ∂x ∂y ∂z ⎢ ⎥ ⎢ ⎥ ∂F ∂F ∂F 5r 5r 5r ⎢ ⎥ = Thederivativesof thetwotermsinEq.(24)are ∂x ∂y ∂z ⎣ ⎦ derived by components and it was distinguished between ∂F ∂F ∂F 6r 6r 6r ∂x ∂y ∂z the 1st term of Eq. (24)and2ndtermofEq.(24). The ⎡ ⎤ μ 3xy partial derivatives of SRP are a 3x 3xz − 1 − μ μ 3 2 a 5 a 5 r r r r ⎢ ⎥ ⎡ ⎤ ∂F ∂F ∂F ⎢ ⎥ 4SRP 4SRP 4SRP ⎡ ⎤ 3xy μ 3y 3yz ⎢ a ⎥ ∂x ∂y ∂z μ − 1 − μ a a a a 5 3 2 a 5 1xx 1xy 1xz ⎢ r r r r ⎥ ⎢ ⎥ K(1−) ⎢ ⎥ ⎢ ⎥ ⎣   ⎦ ∂F ∂F ∂F 5SRP 5SRP 5SRP 2 = − ⎢ ⎥ ⎣ a a a ⎦ 1yx 1yy 1yz 3xz 3yz μ 3z a ∂x ∂y ∂z μ μ − 1 − ⎣ ⎦ r a 5 a 5 3 2 Earth r r r r a a a ∂F ∂F ∂F 1zx 1zy 1zz 6SRP 6SRP 6SRP (22) ∂x ∂y ∂z 284 S. Soldini, H. Takeuchi, S. Taniguchi, et al. ⎡ ⎤ ∂a Z (Y − Y ) 1y E S a a a 2xx 2xy 2xz = a = − + 1yz ⎢ ⎥ 4 ∂z r 2K ⎢ ⎥ ls − ⎢ a a a ⎥ 2yx 2yy 2yz r ⎣ ⎦ r · r (Y − Y )(Z − Z) Earth Earth ls S S 4 (34) a a a 2zx 2zy 2zz r ls (27) Derivative of the z-component This formulation was written for flat surface Earth- ∂a X (Z − Z) 1z E S = a = − + pointing, and therefore the norm is a function of the 1zx ∂x r ls Earth–asteroid line, for simplicity. The two terms of r · r (Z − Z)(X − X) Earth ls S S Eq. (27) are derived by components as 4 (35) ls 1) 1st term ∂a Y (Z − Z) r · r X (X −X)+Y (Y −Y )+Z (Z −Z) 1z E S Earth ls E S E S E S = a = − + r = · 1zy ls 4 4 2 2 2 2 ∂y r [(X −X) +(Y −Y ) +(Z −Z) ] ls ls S S S r · r (Z − Z)(Y − Y ) ⎧ ⎫ Earth ls S S 4 (36) ⎪ ⎪ 6 X − X ⎪ S ⎪ ⎨ ⎬ ls Y − Y = a (28) ⎪ ⎪ ⎪ ⎪ ⎩ ⎭ ∂a X (X −X)+Y (Y −Y )+2Z (Z −Z) 1z E S E S E S Z − Z =a =− + 1zz ∂z r ls Derivatives of the x-component r · r (Z −Z) Earth ls S 4 (37) ∂a 2X (X −X)+Y (Y −Y )+Z (Z −Z) ls 1x E S E S E S =a =− + 1xx ∂x r ls 2) 2nd term r · r (X −X) Earth ls S 4 (29) 2 (r · r ) Earth ls ls r = Earth ls ⎧ ⎫ ⎪ X ⎪ ∂a Y (X − X) 1x E S E ⎪ ⎪ ⎨ ⎬ = a = − + 1xy [X (X −X)+Y (Y −Y )+Z (Z −Z)] E S E S E S ∂y r =a ls Y E 2 2 2 2 ⎪ ⎪ [(X −X) +(Y −Y ) +(Z −Z) ] S S S ⎪ ⎪ ⎩ ⎭ r · r (X − X)(Y − Y ) Earth ls S S 4 (30) ls (38) Partial derivatives of ∂a Z (X − X) 1x E S = a = − + 1xz 4 2 ∂z r ∂ (r · r ) r · r ∂(r · r ) Earth ls Earth ls Earth ls ls =2 − 4 4 ∂r r r ∂r ls ls r · r (X − X)(Z − Z) Earth ls S S 4 (31) 6 2 4 (r · r ) ∂r Earth ls ls ls (39) r ∂r ls Derivative of the y-component where ⎧ ⎫ ∂a X (Y − Y ) ⎪ X ⎪ 1y E S ⎪ ⎪ = a = − + ⎨ ⎬ 1yx ∂(r · r ) Earth ls ∂x r ls = − Y (40) ∂r ⎪ ⎪ r · r (Y − Y )(X − X) ⎪ ⎪ Earth ls S S ⎩ ⎭ 4 (32) ls and ⎧ ⎫ ∂a X (X −X)+2Y (Y −Y )+Z (Z −Z) 1y E S E S E S ⎪ ⎪ X − X ⎪ ⎪ =a =− + ⎨ ⎬ 1yy 4 ∂r ∂y r 2 2 2 ls ls =−4 (X −X) +(Y −Y ) +(Z −Z) Y − Y S S S S ∂r ⎪ ⎪ ⎪ ⎪ r · r (Y −Y ) ⎩ ⎭ Earth ls S Z − Z 4 (33) ls (41) Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 285 therefore [2] Lauretta, D., Balram-Knutson, S., Beshore, E., Boynton, ⎧ ⎫ W., dAubigny, C., DellaG-iustina, D., Enos, H., Gholish, ⎪ ⎪ ⎪ E ⎪ ⎨ ⎬ 2 D., Hergenrother, C., Howell, E., et al. Osiris-REx: ∂ (r · r ) r · r Earth ls Earth ls = − 2 Y + E Sample return from asteroid (101955) bennu. Space 4 4 ⎪ ⎪ ∂r r r ⎪ ⎪ ls ls ⎩ ⎭ Science Reviews, 2017, 212: 925–984. [3] Tsuda, Y., Yoshikawa, M., Abe, M., Minamino, H., ⎧ ⎫ ⎪ X − X ⎪ Nakazawa, S. System design of the Hayabusa2—Asteroid ⎪ ⎪ ⎨ ⎬ (r · r ) Earth ls sample return mission to 1999 JU3. Acta Astronautica, 4 (42) Y − Y r ⎪ ⎪ 2013, 91: 356–362. ls ⎪ ⎪ ⎩ ⎭ Z − Z [4] Morley, T., Budnik, F. Effects on spacecraft radiometric data at superior solar conjunction. In: Proceedings Finally of the 20th International Symposium on Space Flight ⎡ ⎤ ⎡ ⎧ ⎫ Dynamics, 2007: 24–28 ⎪ ⎪ a a a X 2xx 2xy 2xz E ⎪ ⎪ ⎨ ⎬ ⎢ ⎥ ⎢ [5] Yoshikawa, M., Yano, H., Kawaguchi, J., Fujiwara, r · r Earth ls ⎢ ⎥ ⎢ = −2 + a a a Y 2yx 2yy 2yz E ⎣ ⎦ ⎣ 4 A., Abe, M., Iwata, T., Tanaka, S., Mori, O., r ⎪ ⎪ ls ⎪ ⎪ ⎩ ⎭ a a a Z 2zx 2zy 2zz E Yoshimitsu, T., Takagi, Y., et al. Technologies for future ⎧ ⎫ asteroid exploration: What we learned from Hayabusa ⎪ ⎪ X −X ⎪ ⎪ ⎨ ⎬ mission. In: Proceedings of Spacecraft Reconnaissance (r · r ) Earth ls 4 Y −Y · of Asteroid and Comet Interiors, 2006: 3038. ⎪ ⎪ ⎪ ⎪ ls ⎩ ⎭ [6] Soldini, S., Yamaguchi, T., Tsuda, Y., Saiki, T., Z −Z Nakazawa, S. Hayabusa2’s superior solar conjunction phase: Trajectory design, guidance and navigation. Space (43) X Y Z E E E Science Reviews, 2020, https://doi.org/10.1007/s112-14- A.4 Partial derivatives of solar radiation 020-00371-5. [7] Soldini, S., Yamaguchi, T., Tsuda, Y., Saiki, T. pressure perturbation (Sun-pointing) Hayabusa2 mission solar conjunction trajectory for For a cannonball model, the partial derivatives of the hovering satellite: Design, navigation and post-operation SRP perturbation are quite simple and they are given evaluation. In: Proceedings of the 29th AAS/AIAA Space by Flight Mechanics Meeting, 2019: AAS 19-241. [8] Uesugi, K., Matsuo, H., Kawaguchi, J., Hayashi, T. ⎡ ⎤ ∂F ∂F ∂F 4SRP 4SRP 4SRP Japanese first double lunar swingby mission “Hiten”. ∂x ∂y ∂z ⎢ ⎥ Acta Astronautica, 1991, 25(7): 347–355. ⎢ ⎥ ∂F ∂F ∂F 5SRP 5SRP 5SRP [9] Belbruno, E., Miller, A. A ballistic lunar capture ⎢ ⎥ = ∂x ∂y ∂z ⎣ ⎦ trajectory for the Japanese spacecraft Hiten. Jet ∂F ∂F ∂F 6SRP 6SRP 6SRP Propulsion Laboratory IOM 312/90.41371-EAB, 1990. ∂x ∂y ∂z [10] Koon, W. S., Lo, M. W., Marsden, J. E., Ross, S. D. ⎡ ⎤ K 3x 3xy 3xz 1 − −K −K 3 2 5 5 Dynamical systems, the three-body problem and space r r r r ⎢ ⎥ ⎢ ⎥ mission design. Equadiff 99, 2000: 1167–1181. 3xy 3y 3yz ⎢ ⎥ −K 1 − −K (44) 5 3 2 5 [11] Tsuda, Y., Takeuchi H., Ogawa, N. O. G., Kikuchi, ⎢ r r r r ⎥ ⎣ ⎦ S., Oki, Y., Ishiguro, M., Kuroda, D., Urakawa S., O. 3yz 3xz K 3z −K −K 1 − 5 5 3 2 r r r r S., Hayabusa2 project team. Rendezvous to asteroid with highly uncertain ephemeris: Hayabusa2’s ryugu- with P C A approach operation result. Astrodynamics, 2020, 4: 137– 0 r sc K = AU (45) c m sc [12] Tsuda,Y.,Ono,G.,Saiki,T.,Mimasu,Y.,Ogawa,N., Terui, F. Solar radiation pressure-assisted fuel-free Sun References tracking and its application to Hayabusa2. Journal of Spacecraft and Rockets, 2017, 54(6): 1284–1293. [1] Watanabe, S., Hirabayashi, M., Hirata, N., Noguchi, [13] Ono,G.,Tsuda,Y.,Akatsuka,K.,Saiki,T.,Mimasu, R., Shimaki, Y., Ikeda, H., Tatsumi, E., Yoshikawa, M., Y., Ogawa, N., Terui, F. Generalized attitude model Kikuchi, S., Yabuta, H., et al. Hayabusa2 observations for momentum-biased solar sail spacecraft. Journal of of the top-shape carbonaceous asteroid 162173 Ryugu. Guidance, Control, and Dynamics, 2016, 39(7): 1491– Science, 2019, 364(6437): 268–272. 1500. 286 S. Soldini, H. Takeuchi, S. Taniguchi, et al. [14] Tsuda, Y., Saiki, T., Funase, R., Mimasu, Y. the lead of the orbit determination of Hayabusa2. His current research interest is developing the deep space multi-objects Generalized attitude model for spinning solar sail orbit determination system. E-mail: takeuchi@jaxa.jp. spacecraft. Journal of Guidance, Control, and Dynamics, 2013, 36(4): 967–974. [15] Takeuchi, H., Yoshikawa, K., Tokei, Y., Oki, Y., Kikuchi, Sho Taniguchi completed his master’s S., Ikeda, H., Soldini, S., Ogawa, N., Mimasu, Y., course in mechanical engineering at Ono, G., et al. The deep-space multi-object orbit Ibaraki University in 1995. He joined determination system and its application to Hayabusa2’s Fujitsu in 1999, and engaged in tracking asteroid proximity operations. Astrodynamics, 2020, and tracking services at JAXA in 2005. 4(4): 377–392. In 2009, he was engaged in deep space [16] Soldini, S., Takanao, S., Ikeda, H., Wada, K., Yuichi, T., orbit determination work at the Science Hirata, N., Hirata, N. A generalised methodology for System Solution Division of the TC analytic construction of 1:1 resonances around irregular Solution Business Unit, Fujitsu Limited. He is also a regular bodies: Application to the asteroid Ryugu’s ejecta member of the Japanese Society of Astronautics. E-mail: dynamics. Planetary and Space Science, 2020, 180: taniguchi.sho@jp.fujitsu.com. [17] Montenbruck, O., Gill, E. Satellite Orbits Model, Shota Kikuchi received his Ph.D. degree Methods and Applications. New York: Springer-Verlag in aeronautics and astronautics from the Berlin Heidelberg, 2000. University of Tokyo in 2018. From 2015 to 2017, he had served as a visiting scholar Stefania Soldini received her Ph.D. at Purdue University and NASA Jet degree in October 2016 from the University Propulsion Laboratory. He is currently of Southampton, UK. She is an assistant a postdoctoral research associate at professor in space engineering in the JAXA and is engaged in the Hayabusa2 University of Liverpool, UK. Since 2020, asteroid sample-return mission as a system engineer. His she has been the PI of the “3D printed primary research interests lie in the field of astrodynamics, self-folding origami solar sail” project particularly in dynamics around small bodies. E-mail: funded by the CEII/EPSRC Network+ kikuchi.shota@jaxa.jp. (https://www.youtube.com/ watch?v=U5IhFIxZxZI&t=6s) in collaboration with Japan Aerospace Exploration Agency (JAXA) and Oxford Space Systems, UK. She is also a Yuto Takei received his Ph.D. degree member of the Hayabusa2 Joint Science Team (HJST) in engineering from Tokyo Institute as astrodynamics Co-I and member of the ESA’s HERA of Technology, Japan in 2015. He and NASA’s DART group. She was the PI of the“Hayabusa2” is a researcher at the Research and superior solar conjunction mission phase in late 2018. She Development Directorate and JAXA. He worked at the JAXA’s Institute of Space and Astronautical is involved in the Hayabusa2 project as Science (ISAS) from 2016 to 2019, after completing one-year a systems engineer. His research interests JSPS post-doc research fellowship at the same institute. include astrodynamics, spacecraft system, Her research interests are astrodynamics, guidance, space robotics, and deep space exploration. E-mail: navigation & control (GNC) for asteroids proximity takei.yuto@jaxa.jp. operations, ejecta particles dynamics, planetary defence, solar sail technology, additive manufacturing, and AI. E-mail: Go Ono is a researcher at JAXA. He stefania.soldini@liverpool.ac.uk. graduated with his master degree in engineering from the University of Bath Hiroshi Takeuchi received his Ph.D. in 2011 and with his Ph.D. degree in degree of science (physics and applied aerospace engineering from the University physics) from Waseda University in of Tokyo in 2014. He joined JAXA in 2000. In 2006, he started working at 2015 and has been working on guidance, ISAS/JAXA as a member of deep space navigation, and control systems of JAXA’s orbit determination group. He was a deep space missions such as Hayabusa2 and MMX. His visiting researcher of the NASA Jet Propulsion Laboratory in 2012–2013. He current research interests are astrodynamics and deep space is currently an associate professor of ISAS/JAXA and is also exploration. E-mail: ono.go@jaxa.jp. Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 287 Takanao Saiki received his Ph.D. degree has been a research engineer at ISAS and JAXA. Her in aeronautics and astronautics from the current research interests include astrodynamics, mission University of Tokyo, Japan in 2005. He design, robotics, spacecraft systems and operation. E-mail: is an assistant professor at ISAS, JAXA. naoko.ogawa@isas.jaxa.jp. He is now involved in the Hayabusa2 project. He was a chief developer of the Yuya Mimasu is a researcher at impact system and he is currently a project JAXA. He graduated with his Ph.D. engineer. His research interests include degree in aerospace engineering from astrodynamics, spacecraft system, and deep space exploration. Kyushu University. After graduation, Email: saiki.takanao@jaxa.jp. he joined JAXA and has been working on the guidance, navigation, and control subsystem of Hayabusa2, which is JAXA’s Yuichi Tsuda received his Ph.D. degree asteroid sample-return mission. His in aeronautics and astronautics from research interests are astrodynamics and mission analysis University of Tokyo in 2003 and joined around small bodies. Email: mimasu.yuya@jaxa.jp. JAXA in 2003 as a research associate. He had been a visiting scholar of the Atsushi Fujii is a researcher at Department of Aerospace Engineering, Hayabusa2 Project Team, ISAS, JAXA. University of Michigan and Department He received his bachelor of engineering of Aerospace Engineering Sciences, from Saitama University, Japan. He University of Colorado Boulder in 2008–2009. He was involves in Hayabusa2 project as a ground a deputy lead of the IKAROS project, the world’s first system engineer. interplanetary solar sail mission. He is currently a professor of ISAS/JAXA and is the project manager of Hayabusa2, an asteroid sample-return mission. His research interests Satoru Nakazawa received his Ph.D. are astrodynamics, spacecraft system, and deep space degree in science from Nagoya University, exploration. E-mail: tsuda.yuichi@jaxa.jp. Japan in 1999. He is an assistant professor at ISAS and JAXA. He is now involved in Fuyuto Terui received his Ph.D. degree the Hayabusa2 project. He is the deputy in aerospace engineering from University manager of the project team. His research of Osaka Prefecture in 1989. He has interests include planetary science, been a staff member of Space Technology spacecraft system engineering, and deep Research Center of National Aerospace space exploration. Email: nakazawa.satoru@jaxa.jp. Laboratory (NAL) of Japan since 1989. He had been a visiting scholar of the Kent Yoshikawa received his bachelor’s University of Cambridge, Engineering and master’s degrees in engineering from Department, Control Group between 1994 and 1995. After Tokyo Institute of Technology in 2013 and the reorganization of space agencies in Japan, he has 2015, respectively. From 2015, he started been a staff member of JAXA since 2003 and is now a workingasanengineerinthe Research function manager of the Hayabusa2 project as well as and Development Directorate, JAXA. a representative of attitude and orbit control system of His current research interests include Hayabusa2 spacecraft. His main research fields include astrodynamics, GNC, planetary robotics, robust control and image-based guidance, and navigation and and planetary exploration. Email: yoshikawa.kento@jaxa.jp. control of a spacecraft such as debris removal space robot and the asteroid exploration probe. E-mail: terui.fuyuto@jaxa.jp. Yusuke Oki is a researcher at JAXA. He graduated with a master degree in astronautics from the University of Tokyo Naoko Ogawa received her B.E., M.E. and Ph.D. degrees in mathematical in 2016, and with a Ph.D. degree in engineering and information physics in astronautics from the University of Tokyo 2000, 2002 and 2005, respectively, from in 2019. He joined JAXA in 2019, and the University of Tokyo, Japan. From has been working on system design and 2004 to 2008 she has been a research orbit design of spacecrafts. His current fellow of the Japan Society for the research interests are astrodynamics, concurrent design, and Promotion of Science. Since 2008, she deep space exploration. E-mail: oki.yusuke@jaxa.jp. 288 S. Soldini, H. Takeuchi, S. Taniguchi, et al. Chikako Hirose has worked at JAXA navigation and control for interplanetary spacecraft. E-mail: since 2004. She is currently a senior Yamaguchi.Tomohiro@ce.MitsubishiElectric.co.jp. engineer and has had involvement in over 20 missions in flight dynamics field. She joined Makoto Yoshikawa is an associate the Hayabusa2 team since 2018 after she professor in ISAS, JAXA. He is the finished her research at NASA as a visiting mission manager of Hayabusa2 project. researcher for one year. Prior to that, she He got his Ph.D. degree in astronomy from demonstrated her leadership in Venus orbit the University of Tokyo in 1989. After insertion of the Japanese first planet orbiter, Akatsuki. She working as a researcher of JSPS (Japan obtainedhermasterdegreeinphysics fromOchanomizu Society for the Promotion of Science), University in 2004. E-mail: hirose.chikako@jaxa.jp. he worked at former Communication Research Laboratory from 1991 as senior researcher. He Hirotaka Sawada received his B.E. and joined ISAS as associate professor in 1998. His research field M.E. degrees from the Tokyo Institute is celestial mechanics, and he was involved in many space missions such as GEOTAIL, HALCA, Nozomi, Hayabusa, of Technology, Japan in 1998 and 2001, Akatsuki, and IKAROS. He is now also working for planetary respectively. He received his Ph.D. degree defense issues. E-mail: yoshikawa.makoto@jaxa.jp. from the Tokyo Institute of Technology, Japan in 2004. He is an associate senior Open Access This article is licensed under a Creative engineer of JAXA. He is currently involved Commons Attribution 4.0 International License, which in the Martian Moons Exploration (MMX) permits use, sharing, adaptation, distribution and reproduc- project. His specialized field of research includes space tion in any medium or format, as long as you give appropriate robotics, dynamics, and control of space systems. E-mail: credit to the original author(s) and the source, provide a link sawada.hirotaka@jaxa.jp. to the Creative Commons licence, and indicate if changes were made. Tomohiro Yamaguchi is a system The images or other third party material in this article are engineer of Mitsubishi Electric Cor- included in the article’s Creative Commons licence, unless poration. He received his Ph.D. degree indicated otherwise in a credit line to the material. If material from the Graduate University for is not included in the article’s Creative Commons licence and Advanced Studies, Japan in 2012. His your intended use is not permitted by statutory regulation or career includes system design, mission exceeds the permitted use, you will need to obtain permission analysis, and operations for interplanetary directly from the copyright holder. spacecrafts in both agencies and industry. To view a copy of this licence, visit His current research interests are system design and guidance, http://creativecommons.org/licenses/by/4.0/. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Astrodynamics Springer Journals

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Abstract

Astrodynamics Vol. 4, No. 4, 265–288, 2020 https://doi.org/10.1007/s42064-020-0076-7 Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 1,2 2 3 2 2 Stefania Soldini (), Hiroshi Takeuchi , Sho Taniguchi , Shota Kikuchi ,Yuto Takei ,Go 2 3 3 2 2 2 Ono , Masaya Nakano , Takafumi Ohnishi , Takanao Saiki , Yuichi Tsuda , Fuyuto Terui , 2 2 2 2 2 Naoko Ogawa , Yuya Mimasu , Tadateru Takahashi , Atsushi Fujii , Satoru Nakazawa , 2 2 2 2 2,4 Kent Yoshikawa , Yusuke Oki ,Chikako Hirose , Hirotaka Sawada , Tomohiro Yamaguchi , and Makoto Yoshikawa 1. Department of Mechanical, Materials and Aerospace Engineering, University of Liverpool, Liverpool L69 3BX, UK 2. Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara 252-5210, Japan 3. Fujitsu Limited, Tokyo 105-7123, Japan 4. Mitsubishi Electric Corporation, Tokyo 100-8310, Japan ABSTRACT KEYWORDS In late 2018, the asteroid Ryugu was in the Sun’s shadow during the superior solar conjunction superior solar conjunction phase. As the Sun–Earth–Ryugu angle decreased to below 3 , the Hayabusa2 spacecraft Hayabusa2 experienced 21 days of planned blackout in the Earth–probe communication link. This Ryugu was the first time a spacecraft had experienced solar conjunction while hovering around a hovering satellite minor body. For the safety of the spacecraft, a low energy transfer trajectory named Ayu mission operations was designed in the Hill reference frame to increase its altitude from 20 to 110 km. The trajectory was planned with the newly developed optNEAR tool and validated with real Research Article time data. This article shows the results of the conjunction operation, from planning to Received: 18 Januany 2020 flight data. Accepted: 26 March 2020 © The Author(s) 2020 Contrary to NASA’s OSIRIS-REx mission [2], the 1 Introduction Hayabusa2 spacecraft did not orbit Ryugu, but instead The Hayabusa2 mission was a Japanese robotic mission hovered at a relative distance of 20 km from its center, to Ryugu [1]. Since rendezvousing with Ryugu less than known as the home position (HP) point [3]. Navigation one year ago, Hayabusa2 has set a new first for Japan by was performed in the HP frame, with the z-axis aligned successfully performing the first ever impact experiment with the asteroid–Earth line. Hayabusa2 typically on an asteroid (April 2019). The impact experiment was operates at around 20 km altitude in +z ,known HP executed after successful completion of another critical as controlled BOX-A [3]. To maintain Hayabusa2’s operation: the touchdown operation for sampling position in BOX-A, a ΔV command was sent to Ryugu’s surface (February 2018). The first touchdown the spacecraft every 1–2 days. A decrease in the was followed by a second successful touchdown at the Sun–Earth–probe (SEP) angle below 3 caused a location of the small carry-on impactor’s (SCI) artificial substantial increase in data noise in the Doppler crater site in July 2019. After entering the Sun’s measurements [4], thus making it difficult to correctly shadow in late 2018 with the start of the superior solar send commands to the spacecraft. JAXA’s previous conjunction phase, Hayabusa2 successfully deployed two Hayabusa mission experienced solar conjunction during rovers (September 2018) and a lander (October 2018). the transfer phase [5], when it was placed in a In November 2019, Hayabusa2 completed its exploration heliocentric orbit towards Itokawa. It was the first time phase and began its return journey towards the Earth. that a spacecraft experienced superior solar conjunction stefania.soldini@liverpool.ac.uk 266 S. Soldini, H. Takeuchi, S. Taniguchi, et al. Nomenclature AIT asteroid image tracking AOCS attitude orbit control system AU astronomic unit COI conjunction orbit insertion FD flight dynamics FOV field of view GCP-NAV ground control point navigation goNEAR gravitational orbits near earth asteroid regions HGA highgainantenna HP home position (20 km from Ryugu) HPNAV home position NAVigation HRM home position recovery maneuver JATOPS JAXA approach trajectory optimizer with stochastic constraints OD orbit determination optNEAR optimum trajectory near Earth asteroid regions RCS reaction control system SEP Sun–Earth–probe SRP solar radiation pressure TCM trajectory control maneuver ToF time of flight UTC universal coordinated time while in the hovering phase. This condition lasted 21 free mode (ballistic capture). As a first approximation, days for Hayabusa2, making the standard 1–2 days the conjunction trajectory was designed in the Hill HP maintenance operation infeasible. As a 20 km frame of the Sun–asteroid system and the solution altitude is usually artificially maintained, it was too was then refined in the full-ephemeris problem [6, 7]. risky to leave the spacecraft uncontrolled in proximity The time of flight (ToF) of the flown ayu conjunction to Ryugu. To prevent a close approach with the trajectory was around 38 days, with two deterministic asteroid, or an undesired escape from Ryugu’s sphere of ΔV designed at the conjunction orbit insertion (COI) influence, the optimum trajectory near-Earth asteroid point (home position (HP) before the conjunction) and regions (optNEAR) tool was developed for the design of at the home position recovery (HRM) point (HP after a low energy transfer trajectory for hovering satellites. the conjunction). Two trajectory correction maneuvers The trajectory was designed in the Hill frame and (TCMs) were scheduled before and after the deep due to its fish-like shape was named “ayu” (Japanese conjunction phase. The trajectory designed with the sweetfish) trajectory [6, 7]. For the case of Hayabusa2, optNEAR tool was validated in real time operations the ayu trajectory was designed to reach an altitude and used for testing the JAXA’s trajectory design of 110 km in deep conjunction (minimum SEP angle). JATOPS (JAXA approach trajectory optimizer with Only two deterministic maneuvers were required, with a stochastic constraints) tool for high altitude operations. ΔV budget of less than 1 m/s. The shooting method The results of the post-flight operations are presented developed in optNEAR takes advantage of the natural here. dynamics of the asteroid–Sun system, knowing that in the Hill problem the spacecraft motion is opposed by the 2 Solar conjunction mission design and solar radiation pressure (SRP) acceleration, for a fixed operation planning initial energy level. This principle was previously used by JAXA’s Hiten mission [8], for the design of a recovery The ayu conjunction trajectory was designed in the trajectory in the patched Sun–Earth and Earth–Moon Hill reference frame, as shown in Soldini et al. [6, 7]. systems [9]. The ayu trajectory aimed to direct the Thedynamicsofthemotherspacecraft waswritten spacecraft towards the zero velocity curves of the Hill in a rotating reference frame, where the system was problem (boundary of possible motion), where the centered on Ryugu and the Sun, and the asteroid was maximum altitude of 110 km was reached and the return placed along the x-axis. The Sun was in the negative to a 20 km altitude could therefore be executed in fuel- x coordinates. Depending on how the initial energy of Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 267 the spacecraft (state vector) was set, it was possible [6, 7]. As a result of an uncertainty analysis in the to distinguish regions of motion where the spacecraft deterministic maneuvers at COI and HRM, Soldini et dynamics was not permitted [10]. This information was al. concluded that at least two stochastic TCMs were used to increase the spacecraft’s altitude from 20 km to a required [6, 7], as shownbytheredpointin Fig. 1. safety altitude during deep conjunction. On 2018/12/11, The conjunction operation required four maneuvers the spacecraft reached the deep conjunction position to be performed. The solution in the Hill reference located at the boundary of the permitted motion, as frame was the first guess solution. The trajectory was seen in the Hill reference frame. In deep conjunction, then refined and recomputed in the full ephemeries the SEP angle was at its minimum value of 0.4 . planetary equations via the use of NASA’s SPICE The conjunction operation started and ended when toolkit, interfaced with the optNEAR tool. the SEP angle was equal to 5 and the gravity constant Table 1 shows the epochs of the Hayabusa2’s superior 3 2 of Ryugu, μ ,was set to 30 m /s ,as in Soldini et al. [6,7]. solar conjunction operations as afunctionoftheSEP Figure 1 shows the nominal conjunction trajectory as angle. The overall solar conjunction phase lasted for seen from the Hill reference frame and HP reference 37 days and for 21 days the spacecraft was kept free frame (Figs. 1(a) and 1(b)). The trajectory’s fish-like from on ground control, while in deep conjunction. Note shape in the Hill coordinates can be seen in Fig. 1(a). that on 2018/12/28, it was decided to modify the ΔV The z-axis of the HP reference frame was along the planning at HRM (last line in Table 1) and the home Earth-asteroid line pointing towards the Earth. The position keeping (HPK) maneuver for hovering position Sun–asteroid line belonged to the positive coordinates maintenance (20 km from Ryugu along the z axis) HP of the x–z plane and the y axis was given such that the was merged with the HRM maneuver. HP frame was a right-handed coordinate system. Figure In Soldini et al. [6, 7], it was demonstrated that 1(b) shows that the ayu trajectory was a periodic orbit the ayu conjunction trajectory allowed a low fuel when placed in the HP reference frame. Indeed, COI expenditure and Ryugu was always in the field of view and HRM share the same coordinates in this frame. (FOV) of Hayabusa2’s wide angle navigation camera Figure 1 also shows the epochs of the TCMs (red points) and the deep conjunction epoch (green point). Table 1 Scheduled maneuvers for the Hayabusa2’s superior solar conjunction The ayu conjunction trajectory requires two deterministic maneuvers: before and after the superior Maneuver Epoch (UTC) SEP angle ( ) COI 2018/11/23 5 solar conjunction at the COI point and the HRM, TCM1 2018/11/30 3 respectively (Fig. 1)[6, 7]. The total contribution of TCM2 2018/12/25 4 the two deterministic ΔV maneuvers at COI and HRM HRM+HPK 2018/12/29 5 computed with the optNEAR tool was 0.2359 m/s Fig. 1 Design of the solar conjunction ayu trajectory as seen in the Hill reference frame (a) and HP reference frame (b). 268 S. Soldini, H. Takeuchi, S. Taniguchi, et al. ONC-W1 (60 ). Figure 2 shows the ayu trajectory in deep conjunction. A radio science experiment 3 2 for μ =32m /s and for a conjunction maneuver was carried out during the deep conjunction epoch starting at a SEP angle of 6 . Figure 2(a) shows (the green point in Fig. 1) for testing the Ka- thetrajectorybyforward (black) and backward (green) band capability for retrieving telemetry data to integration from the deep conjunction point (-H), as estimate the spacecraft’s position and velocity. The shown by the green point in Fig. 1. The geometry of the spacecraft remained in deep conjunction for 21 days camera was verified when the spacecraft was kept Earth- with no commands sent from Earth. pointing (∼ Sun-pointing in deep conjunction). Figure (3) Recovery phase: TCM2 (2018/12/22)–HRM 2(b) shows the angle between the x-axis direction and (2018/12/29). The recovery phase required a thespacecraft–Ryuguline(halfofthecameraFOV). second TCM2 maneuver when the SEP angle was The asteroid was always in the FOV of the ONC-W1 4 .The HRM was performed when the SEP angles camera and in some cases was within the ONC-T camera was 5 . FOV (6 ). (4) Home position keeping: HPK (2018/12/29). At the For the solar conjunction mission planning, four main HRM epoch, a ΔV for HPK maintenance was added phases were defined and the epoch of the maneuvers are with the scope of bringing the spacecraft to 20 km giveninTable 1: altitude on 2018/12/31. (1) Preparation phase: COI (2018/11/23)–TCM1 2.1 Maneuver operation (2018/11/30). During the preparation phase, the spacecraft performed a 180 slew maneuver around The conjunction orbit took into account the solar the z -axis to ensure the correct orientation of HP radiation pressure perturbation and was designed to the 12 thrusters after the deep conjunction phase stay in the +z region without any deterministic HP (flip of the HP frame). The COI maneuver was maneuvers between COI and HRM. The maximum performed when the SEP angle was 5 and TCM1 distance from Ryugu was 109 km on 2018/12/11 (deep was performed when the SEP angle was 3 . conjunction epoch, green point in Fig. 1). The COI (2) Deep conjunction phase: TCM1 (2018/12/01)– and HRM ΔV s were 2 cm/s in x and 12 cm/s in HP TCM2 (2018/12/21). When the spacecraft was in y . The maneuvers were calculated based on the HP deep conjunction (SEP angle < 3 ), the spacecraft results of the orbit determination (OD) team, who did not perform any orbit maneuvers, only attitude made use of radiometric data and ONC-W1’s asteroid maintenance. Beacon operations were carried out image tracking (AIT) data to estimate the state of to monitor the status of the spacecraft while the spacecraft. The AIT data was verified using the Fig. 2 The left panel shows the two arcs of the conjunction trajectory from deep conjunction to COI (green line) and from deep conjunction to HRM (black line). The right panel shows that Ryugu is always in the ONC-W1 camera FOV (60 ) and in some cases in theFOV oftheONC-Tcamera (6 ). Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 269 raw ONC-W1 images. Each maneuver was supported onboard camera-based asteroid direction determination via 2 days of navigation campaign. The minimum (asteroid image tracking-AIT) were combined [6, 7, 11]. ΔV threshold for the reaction control system (RCS) To guarantee a precise relative navigation, three was 1 mm/s and any maneuver below 1 mm/s was techniques were run in parallel. These are shown in cancelled. If the planned ΔV was above 10 cm/s than Fig. 3, Phase (2): (a) NAV1, called HPNAV (home the maneuver was divided into main and trim ΔV s. The position navigation), a hybrid navigation technique that ΔV was measured by the 2-way Doppler, while the combines radiometric (RARR) and optical navigation HP ΔV was measured by the accelerometers (ACMs). (ONC-T camera) techniques. It is a method for x,y HP The trim, ΔV , was also used as a minor correction of the finding the position and speed of the spacecraft, using main ΔV during the same pass (contingency case). The the direction to the image center and attitude data Hayabusa2 spacecraft was kept Earth-pointing during [11]. (b) NAV2, called GCP-NAV (ground control the conjunction phase, for radio-science purposes. The point navigation), a technique of finding the position spacecraft made use of the star trackers to maintain and speed of the spacecraft by observing features on its attitude. The attitude maneuvers were scheduled the asteroid surface [11]. (c) NAV3, a full asteroid– every three days to keep the high gain antenna (HGA) spacecraft simultaneous orbit determination technique Earth-pointing. Every attitude slew was below 3 .The (Fujitsu team and JAXA team) [11]. Earth moved at a rate of about 0.75 ( )/day and the Once the results of the navigation were validated, half-band-width of the HGA was 1.2 . Note that it was the ΔV planning phase started (Phase (3) in Fig. 3). verified that Ryugu was always visible from ONC-W1 The optNEAR tool was used as the main baseline for (60 FOV). During the entire sequence, the SEP angle the ΔV planning, which is the subject of this article. was below 2 . The JATOPS tool, which was used during the approach Figure 3 shows a schematic representation of the phase, now became the backup solution for the solar operation planing. Similar to Hayabuas2’s approach conjunction phase [11]. Theresultsof theguidanceare phase [11], the operation planning for the solar givenina.way fileformattobeusedasinputstothe conjunction phase can be divided into: Phase (1), spacecraft operation (Phase (4) in Fig. 3). onboard image-based optical measurements (before Finally, the spacecraft operation phase consisted of 7:00 UTC in Fig. 3); Phase (2), radio-optical hybrid transforming the .way file, ΔV , from the HP reference navigation (7:00–13:00 UTC in Fig. 3); Phase (3), frame to the spacecraft’s asteroid fixed frame [6, 7]and guidance (13:00–16:00 UTC in Fig. 3); and Phase (4), sending the command to the spacecraft. The operation spacecraft operation (from 16:00 UTC in Fig. 3). planning and the results of the mission operations The operation planning started two days before the are presented in this article. The mission operation maneuver planning, known as the observation campaign, process described here was followed for each of the four by downloading the telemetry from the spacecraft; scheduled maneuvers at COI, TCM1, TCM2, and HRM Phase (1) in Fig. 3. The range-rate (RARR) and the epochs described in Table 1. 2.2 Attitude maintenance The Hayabusa2 team considered three options for the attitude maintenance of the spacecraft during deep conjunction: 1) Safe mode (spinning). This method is safe as the spacecraft is passively stabilized. Only range and rangeratearepossibleinthismode. However, its major drawback is it requires fuel and time to de-spin the spacecraft and progress to three-axis stabilisation. 2) Hayabusa2 acting as a solar sail. This mode makes use of 1 reaction wheel control [12, 13]. The Fig. 3 Mission operation plan for each of the four scheduled conjunction maneuvers. spacecraft is passively stabilized using the SRP 270 S. Soldini, H. Takeuchi, S. Taniguchi, et al. torque. The passive stabilisation makes this method or written more compactly: very safe to use. This method was inspired by X = F (X,t) (2) JAXA’s IKAROS mission [14] and the Hayabusa2 spacecraft tested this method during cruise mode 3 2 where μ is the gravity constant of Ryugu (30 m /s ). [12]. However, the major disadvantage of this The 3rd body acceleration is given by method is that the HGA can’t be used when the Δ d spacecraft is in “solar sail” mode as the spacecraft a = −μ + (3) Pj Pj 3 3 Δ d would need to be maintained as Sun-pointing, not Earth-pointing [13]. with Δ = r − d,where r is the spacecraft’s position 3) Hayabusa2 is kept Earth-pointing during deep vector from Ryugu and d is the position vector of the conjunction. The spacecraft makes use of the perturbing body (Pj) from Ryugu. Note that when star trackers to maintain its attitude. Attitude the optNEAR tool calls the NASA’s SPICE Toolkit, maneuvers are required during deep conjunction, the ephemeris are downloaded from a reference frame which makes this method less safe than both options centered on the solar system barycenter (SSB), and 1) and 2). However, the HGA can be used without therefore the vector d is given by the position vector of any difficulties. the planet in SSB coordinates minus the position vector Since the Hayabusa2 team selected option 3) for radio- of Ryugu in SSB coordinates. For a non-diffusive Earth- science purposes (testing of the Ka-band capability tracking flat surface, the SRP acceleration is in deep conjunction) [15], attitude maneuvers were P A AU r 0 ls scheduled every three days to maintain the HGA as a = − cos θ (1 − ) +2 cos θn ˆ SRP c m r r ls ls Earth-pointing. (4) where the Sun–line direction (r ) is given by considering ls the distance of the spacecraft from Ryugu minus the 3 n-body propagator in J2000EQ distance of the Sun from Ryugu. The normal vector (n ˆ) coordinates centered at Ryugu to Hayabusa2’s solar panels is kept Earth-pointing, thus (J2000EQ-Ry): optNEAR tool Earth n ˆ = (5) The optNEAR tool is a trajectory optimizer that make Earth use of an n-body propagator written in J2000 equatorial and coordinates, with the reference frame centered on Ryugu r · r ls Earth cos θ = (6) (J2000EQ-Ry). The optNEAR’s propagator (known as r r ls Earth goNEAR [6, 16]) was written in python language and r is the Ryugu–Earth distance where the vector Earth makes use of NASA’s SPICE Toolkit package to import is pointing toward the Earth. In Eq. (4), A is the the ephemeris of Ryugu, all the planets, the Earth, spacecraft’s reflective area, assumed as 13.276 m (i.e., Moon, and Sun. The effect of the SRP acceleration was the solar panels), the spacecraft’s mass, m, is 580 kg, also taken into account. In this case, the spacecraft was 2 P is the solar flux of 1366 W/m , c is the speed of considered as Earth-pointing and the flat plate model light of 2.99792458 × 10 m/s, and  is the reflectivity was used for the SRP acceleration [17]. The n-body of the spacecraft, assumed to be 0.321. Note that planetary equations are given by = C − 1,with C being the reflectivity coefficient of r r ⎡ ⎤ ⎧ ⎫ ⎡ ⎤ the spacecraft ( =0 complete absorption and  =1 X F ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎢ ⎥ complete specular reflection). A very simple way to ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎢ ⎥ Y F ⎪ ⎪ ⎢ ⎥ 2 demonstrate the relationship between  and C is to ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎢ ⎥ ⎨ ⎬ ⎢ ⎥ ˙ Z ⎢ ⎥ Z F consider that ρ +ρ +ρ =1,with ρ being the specular ⎢ ⎥ s a d s ⎢ ⎥ =⎢ NP ⎥ = μ j ⎢ ⎥ ⎪ ¨ ⎪ ⎢ − X + a | + a | ⎥ reflectivity coefficient, ρ the absorption coefficient, and 3 P x SRP x a ⎪ X ⎪ r j=1 ⎢ F ⎥ ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎢ ⎥ ρ the diffusive coefficient. If the diffusion term is ⎪ ⎪ NP ⎢ ⎥ d μ j ¨ a ⎪ ⎪ ⎢ ⎥ Y − Y + a | + a | F ⎪ ⎪ 3 P y SRP y 5 j ⎣ ⎦ r j=1 ⎪ ⎪ ⎣ ⎦ ⎪ ⎪ neglected (ρ =0), it is possible to write that ρ =1−ρ d a s ⎩ ⎭ NP μ j Z a F − Z + a | + a | and also that C =1+ ρ . ρ and ρ were renamed here 3 P z SRP z r s s a j=1 j (1) as  and C , respectively. The linearized equations of r Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 271 Eq. (1) are conjunction. To achieve high accuracy in the final error x˙ (t)= A(t)x(t) (7) position at HP, a constrained optimization was used such that: where the matrix of the linearized equation can be min |ΔV | (12) derived as x,α,δ ⎡ ⎤ with 0 0 0 100 V = V cos δ cos α ⎢ ⎥ x ⎢ ⎥ 0 0 0 010 ⎢ ⎥ V = V cos δ sin α (13) ⎢ ⎥ y ⎢ 0 0 0 001 ⎥ ⎢ ⎥ V = V sin δ A = ⎢ ⎥ (8) ∂F ∂F ∂F 4 4 4 ⎢ ⎥ ∂x ∂y ∂z ⎢ ⎥ 2 2 2 ⎢ ⎥ where V = V (1 + sin x) and ΔV = V + V + V , ∂F ∂F ∂F max 5 5 5 x y z ⎢ ⎥ ∂x ∂y ∂z ⎣ ⎦ subject to the following constraints: ∂F ∂F ∂F 6 6 6 ∂x ∂y ∂z |x(t ) − x ¯|− toll = 0 The derivatives in Eq. (8) were computed analytically (14) |y(t ) − y¯|− toll = 0 and their equations are given in Appendix A. To relate |z(t ) − z¯|− toll = 0 astate toaspecificepoch, t, from an initial state, t , the state transition matrix is needed: The toll is usually set to 0.1 m. Note that the ∂X(t) minimization of ΔV is reduced to finding three angles, Φ(t, t )= (9) ∂X(t ) α (in-plane angle), δ (out-of-plane angle), and x (e.g., V = V ,with x =0 ). At t , after the ODE max 1 that it is numerically computed as integration of Eq. (1), the final desired position of Φ(t, t )= A(t)Φ(t, t ) (10) the spacecraft was to be equal to the nominal state 0 0 r¯ =[0, 0, 20 km], in HP coordinates, at the end of the HP with Φ(t ,t )= I. Therefore, 0 0 conjunction epoch (2018/12/29 in Table 1). Note that the ODE integration was performed in the J2000EQ- δx(t)= Φ(t, t )δx(t ) (11) 0 0 Ry reference frame, and therefore a transformation was The computation of the STM can be done by deriving required to move r¯ into J2000EQ-Ry coordinates (r¯), HP the analytic expression of the linearized equations as shown in Soldini et al. [6, 7]. matrix A and by solving Eq. (10) numerically, together 4.1 Deterministic ΔV maneuver at COI: with the equations of motion in Eq. (3). The derivatives Refinement of the Hill trajectory in the in Appendix A were tested by comparing the analytical n-body dynamics derivatives with the numerical derivatives. At the beginning of the conjunction phase (COI epoch in Table 1), the shooting method (optNEAR tool) 4 optNAER’s single shooting method described made use of the ayu conjunction trajectory for the ΔV planning designed in the Hill coordinates [6, 7]. The ayu The shooting methods developed in the optNEAR tool trajectory designed in Refs. [6,7] was therefore the first were used for the ΔV planning during Hayabusa2’s guess for the two-boundary value problem in the full superior solar conjunction operation. The aim was ephemeris model (goNEAR tool [6,16]) where the initial to minimize the overall ΔV budget required to place (COI) and final (HRM) positions were fixed. In Fig. 4, the spacecraft in the ayu conjunction trajectory. The the black line is the un-optimized trajectory (goNEAR operation aimed to depart from the hovering location propagator), while the red trajectory is optimized with at HP and return to HP after the spacecraft left the the optNEAR tool. The magenta point is the location of Sun’s shadow. optNEAR’s shooting method aimed to the HP at HRM (2018/12/29 in Table 1). Tables 2 and minimize the ΔV maneuver such that following the 3 show the ΔV designed at COI and HRM in the HP integration of the non-linear dynamics in Eq. (1), the and J2000EQ-Ry coordinates, respectively. Each table spacecraft returned to HP at the end of the solar shows the epoch of the maneuver in UTC and the ΔV is 272 S. Soldini, H. Takeuchi, S. Taniguchi, et al. Fig. 5 Shooting method: reference trajectory (solid line) and perturbed trajectory (dashed line). in the system of Eq. (15)is Φ (t ,t )δr + Φ (t ,t )δv = 0 (16) 11 1 0 0 12 1 0 0 so that −1 δv = −Φ (t ,t )Φ (t ,t )δr (17) Fig. 4 Conjunction trajectory optimized (red) with the n-body 0 1 0 11 1 0 0 optimizer (optNEAR tool) and the propagated trajectory in black (goNEAR tool) as seen from Ryugu, Eq. (1). with Φ (t ,t ) as 11 1 0 ⎡ ⎤ Φ Φ Φ 11 12 13 given for each axis direction in HP coordinates (Table 2) ⎢ ⎥ ⎢ ⎥ Φ (t ,t )= (18) Φ Φ Φ and in J2000 coordinates (Table 3). Note that due to 11 1 0 21 22 23 ⎣ ⎦ the mounting direction of the thrusters a ΔV margin Φ Φ Φ 31 32 33 (t ,t ) 1 0 (Table 2) was added to include thrust losses in the y HP and Φ (t ,t ) as direction [6, 7]. ThesettingsusedintheoptNEARtool 12 1 0 ⎡ ⎤ for the COI maneuver planning were V =0.0004 max Φ Φ Φ 14 15 16 km/s. The lower and the upper boundaries of the angles ⎢ ⎥ ⎢ ⎥ ◦ ◦ ◦ ◦ ◦ ◦ Φ (t ,t )= Φ Φ Φ (19) 12 1 0 24 25 26 were set as: x (−90 ,0 ), α (0 ,30 ), and δ (0 ,90 ). ⎣ ⎦ Φ Φ Φ 34 35 36 (t ,t ) 1 0 4.2 Trajectory correction maneuvers: TCM1 and TCM2 The initial state is therefore After COI, every initial state guess at the TCM epoch x = δx + x ¯ 0 0 0 (20) t (time of maneuver) can be found analytically through v = δv + v¯ 0 0 0 the state transition matrix: and is used as the initial guess for the shooting method δr Φ Φ δr 1 11 12 0 = (15) in optNEAR. The settings used for the optNEAR tool δv Φ Φ δv 1 21 22 0 t ,t 1 0 at TCMs are with the objective of bringing the final position state to a) TCM1 maneuver settings: V was set to 0.002 km/s. The lower and the upper zero, as shown in Fig. 5(b) (δr =0). The first equation 0 max 3 2 ◦ Table 2 ΔV in HP reference frame for the Earth-pointing spacecraft (μ =32m /s and SEP = 5 ) ΔV (HP) Epoch UTC ΔV (HP) ΔV (HP) x ◦ z cos(75 ) (ET) (date) (m/s) (m/s) (m/s) COI 596,203,269.18 2018/11/23 T00:00 1.891E−02 −6.0322E−03 1.175E−01 HRM 599,313,669.18 2018/12/29 T00:00 −1.8058E−02 1.5744E−02 −1.1549E−01 Total 3.6977E−02 2.177E−02 2.3299E−01 3 2 ◦ Table 3 ΔV in J2000 reference frame for the Earth-pointing spacecraft (μ =32m /s and SEP = 5 ) Epoch UTC ΔV (J2000) ΔV (J2000) ΔV (J2000) x y z (ET) (date) (m/s) (m/s) (m/s) COI 596,203,269.18 2018/11/23 T00:00 3.1793E−02 1.05487E−01 4.50463E−02 HRM 599,313,669.18 2018/12/29 T00:00 1.4375E−02 1.07179E−01 4.4575E−02 Total 4.6168E−02 2.12666E−01 8.9621E−02 Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 273 ◦ ◦ boundaries of the angles were set as: x (−90 ,0 ), 5 JAXA’s JATOPS tool: The backup ◦ ◦ ◦ ◦ α (0 ,30 ), and δ (0 ,90 ); solution of the optNEAR tool b) TCM2 maneuver settings: As part of the ΔV planning at COI, TCM1, TCM2, V was set to 0.01 km/s. The lower and the upper max and HRM, the optNEAR tool was used as the main ◦ ◦ boundaries of the angles were set as: x (−90 ,0 ), solution for planning the ΔV command, which was to ◦ ◦ ◦ ◦ α (−90 ,0 ), and δ (−180 ,0 ). be executed on board the spacecraft. However, it was further verified that JAXA’s trajectory optimisation 4.3 Brake velocity maneuver at HRM and tool, JATOPS [11], could retrieve the same solution HPK maneuver as the optNEAR tool, once the nominal states at the Planning for the ΔV maneuver at HRM included both COI, TCM1, TCM2, and HRM epochs were computed a brake velocity maneuver at HP on 2018/12/29 and by optNEAR. The difference between optNEAR and a HPK maneuver for BOX-A operation maintenance, JATOPS is in the ability to design the ayu trajectory until 2018/12/31. The first ΔV aimed to simply stop in a single shooting. OptNEAR implements a semi- the spacecraft at the HP arrival point (HRM). The HPK analytical method that uses the weak stability boundary maneuver required designing in the Hill coordinates, as theory to design the first guess trajectory in one pass for the ayu conjunction trajectory. The same shooting (the ayu trajectory). Once optNEAR has successfully method described in Soldini et al. [6, 7] was used provided the first guess (the ayu solution), JATOPS can but with the following initial guess: H =25km 0 then be used as a validation tool for the ΔV s computed (maximum altitude), α = 188 (in-plane angle in the 0 with optNEAR. For further details on the JATOPS tool, x–y coordinates), and v = 0 km/s (out of plane Hill z refer to Tsuda et al. [11]. velocity). The lower and upper boundaries of the Figure 7 shows that the JATOPS tool could be used optimum parameters were as follows: 20 km <H < for high altitude operations as it finds the same solutions ◦ ◦ 30 km, 180 <α< 270 ,and −0.00001 km/s <v < z as the optNEAR tool [11]. Therefore, our ΔV planning 0.00001 km/s. Once the HPK maintenance arc was strategy was to use the optNEAR tool as a baseline for designed in the Hill reference frame, the solution was the computation of the ΔV commands and to rely on refined in the optNEAR tool; V was set to 0.0002 max theJATOPStoolasaback-upsolution. TheJATOPS km/s and the lower and upper boundaries of the angles tool was selected as a back-up solution for the optNEAR ◦ ◦ ◦ ◦ ◦ were set as follows: x (−90 ,0 ), α (0 ,30 ), and δ (90 , tool and the following procedure to retrieve the nominal 180 ). Figure 6 shows the nominal HPK arc trajectory trajectory with JATOPS was confirmed [11]: designed with the optNEAR tool, if the HRM point is (1) The ayu trajectory was divided into three trajectory in its nominal location of 20 km altitude. legs: COI-TCM1 (Leg1), TCM1-TCM2 (Leg2), and Fig. 7 The conjunction trajectory as seen from the HP frame: a Fig. 6 Example of the HPK trajectory arc in the HP reference comparison between the solutions obtained between the optNEAR frame, from 2018/12/29 to 2018/12/31. (red line) and the JATOPS (black line) tools. 274 S. Soldini, H. Takeuchi, S. Taniguchi, et al. TCM2-HRM (Leg3). navigation and operation planning and their results (2) Each leg derived a two-impulse trajectory, using are presented here. The ΔV planning started on states derived by the optNEAR tool from the output 2018/11/22 after two days of data measurements. .way file as the boundary conditions. The initial downlink of the telemetry data started on (3) It was confirmed that the JATOPS tool was a good 2018/11/21. back-upinextremecaseswhena ΔV was required (a) Once the downlink of the AIT and Doppler data to safely return back to HP. was concluded, the navigation teams performed an (4) The JATOPS tool does not have the capability estimate of the spacecraft’s position and velocity. to instantaneously derive the entire nominal ayu The navigation team’s estimates at COI are shown conjunction orbit from COI to HRM, as with the in Table 4. Those estimates were compared with the optNEAR tool. nominal case, as shown in the first row of Table 4. From those estimates, the corresponding ΔV swere computed, as shown in Table 5. 6 Post mission operation To select the best estimate of the spacecraft’s In this section, each of the four maneuvers performed state from the JAXA and Fujitsu solutions, the ΔV s during the solar conjunction phase are presented. The in Table 5 were cross evaluated with the different solar conjunction operation was planned as described in solutions in Table 4. The solutionswerethus Section 2 and in Fig. 3. For each operation planning propagated with goNEAR. (Fig. 3), first the results of the OD teams were analyzed. From this analysis, the solution from Fujitsu was Once the most reliable estimate of the spacecraft’s selected for the ΔV planning as it was shown to position and velocity was selected by the flight dynamic be the most conservative solution in the presence of (FD) and OD teams, planning of the ΔV resulted in the uncertainties in the navigation. delivery of the .way file from the FD team to the attitude (b) After having selected the estimate from the OD’s orbit control system (AOCS) team. The ΔV was thus Fujitsu team, the FD team prepared the ΔV given as a sequence of commands to the spacecraft. planning at COI. Figure 8 shows the .way file After the ΔV was executed on board the spacecraft, prepared on 2018/11/22 for the following day’s its velocity (2-way Doppler) and acceleration (ACMs) operation. The .way file was the input for the AOCS were measured to estimate the actual ΔV performed. team, where the ΔV was computed in a body-fixed The actual and the planned ΔVswerethuscompared frame. Figure 8 shows the estimated states at each to evaluate the performance of the operation. In case epoch and the corresponding ΔV s. of large discrepancies between ΔV s, it was possible to (c) The error between the planned and the actual ΔV correct the maneuver within the same communication was of 98.78% in ΔV , 93.53% in ΔV ,and X Y B B pass. At the end of the operation, the measured ΔV was 98.53% in ΔV , asshowninthereportof Fig. 9. used for the trajectory design of the next trajectory leg. Figure 9 shows the measured and planned ΔV sfor the main (M) and trim (T) maneuvers for each axis 6.1 Conjunction orbit insertion (COI) direction. The accuracy in the maneuvers in term maneuver: 2018/11/23 of absolute and relative errors are also provided. On 2018/11/23, the Hayabusa2 spacecraft performed Due to uncertainties in the ΔV at COI, it was the conjunction orbit insertion maneuver. The concluded that at least one TCM was required on Table 4 Nominal state vector at COI and estimated states by Fujitsu (OPNAV1/NAV3 in Fig. 3), JAXA (OPNAV2/NAV3 in Fig. 3), and HPNAV (NAV1 in Fig. 3) State x y z v v v HP HP HP x y z HP HP HP estimate (km) (km) (km) (mm/s) (mm/s) (mm/s) Nominal 0 0200 0 0 OD’s Fujitsu −0.0115 −0.1428 20.0692 −1.7101 1.2674 −17.9384 −0.0458 −0.1197 19.9301 −2.1938 1.4375 −17.9382 OD’s JAXA HPNAV 0.0425 −0.1217 19.7622 −1.7098 1.7039 −18.0709 Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 275 Fig. 8 Planned ΔV at COI in .way file format. Table 5 Nominal ΔV ,OD’s Fujitsu ΔV (OPNAV1/NAV3 in small position error of the spacecraft. For this Fig. 3), and OD’s JAXA ΔV (OPNAV2/NAV3 in Fig. 3) reason, no contingency ΔV was required at COI. State ΔV ΔV ΔV X Y Z HP HP HP It was also expected that the major ΔV at TCM1 estimate (cm/s) (cm/s) (cm/s) would have been in the Z component. Nominal 1.9844 −0.1637 12.2624 Figure 10 shows the planned trajectory for the OD’s Fujitsu 2.1548 −0.2906 14.0497 selected solution (OD’s Fujitsu is shown in black). OD’s JAXA 2.2060 −0.3080 14.0625 The red trajectory leg is the predicted trajectory from COI to TCM1, when the actual ΔV from theresultreportinFig. 9 wasused. Thegreen trajectory is the new solution from TCM1 to HRM, designed with the optNEAR tool. Fig. 9 Results of the COI operation on 2018/11/23: planned and measured ΔV report. 2018/11/30 before deep conjunction. Errors in the Fig. 10 Planned trajectory OD Fujitsu solution (black), actual ΔV lower than 4 mm/s were considered acceptable, trajectory from COI to TCM1 after COI operation (red), and new asconcludedinSoldini et al. [6, 7], where it was planned trajectory between TCM1 to HRM (green). The black shown that those errors resulted in a negligibly dot represents the Ryugu coordinates. HP reference frame. 276 S. Soldini, H. Takeuchi, S. Taniguchi, et al. 6.2 Trajectory correction maneuver 1 The OD’s JAXA team’s .way file was the input for (TCM1): 2018/11/30 the AOCS team and the ΔV was computed in a body-fixed frame. The first trajectory correction maneuver (TCM1) was (c) In the case of TCM1, the ΔV and ΔV were performed on 2018/11/30 before the spacecraft entered X Y cancelled, resulting in an error after 24 days of 1 the deep solar conjunction phase, with the SEP angle km in X at TCM2, as shown in Fig. 13. An equal to 3 . The TCM1 allowed corrections in the HP increase in the noise of the Doppler signal already trajectory after the actual operation at COI. The ΔV at TCM1 was registered, as shown in Fig. 12. The at TCM1 was planned on 2018/11/29 after the initial noise is evident by looking at the fluctuation in the downlink of the telemetry data on 2018/11/28. vertical axis of Fig. 12, which represents the double (a) The estimates of the spacecraft’s position and error between the measured and planned speed of velocity on 2018/11/29 are shown in Table 6. the spacecraft. This fluctuation is in the order of As with COI, the solutions were crosschecked with the size of the maneuvers (mm/s) and is usually a the nominal case designed after the COI maneuver straight line, when the Sun corona is out of the way (the green trajectory in Fig. 10). The ΔV s of the communication link. The report in Fig. 14 correspondence with the estimated solutions are shows that the error in the ΔV was 99.21%, shown in Table 7. As with the COI maneuver Z resulting in a perfectly executed operation. Between planning, the ΔV sin Table 7 were cross evaluated TCM1 and TCM2, only pre-scheduled attitude with the different solutions in Table 6 and the maintenance maneuvers were performed (every solutions were propagated with goNEAR. From this 1–2 days). It was decided to avoid desaturation of analysis, the solution from JAXA was selected for the reaction wheels in deep conjunction to prevent the ΔV planning at TCM1. errors to the planned trajectory between TCM1 and (b) Figure 11 shows the .way file prepared on the TCM2. 2018/11/29 for the TCM1 operation (2018/11/30). Table 6 Nominal state vector at TCM1 and estimated states by Fujitsu (OPNAV1/NAV3 in Fig. 3), JAXA (OPNAV2/NAV3 in Fig. 3), andHPNAV (NAV1inFig. 3) State x y z v v v HP HP HP x y z HP HP HP estimate (km) (km) (km) (mm/s) (mm/s) (mm/s) Nominal 5.6589 −0.0395 75.1693 1.0321 1.1463 67.1665 OD’s Fujitsu 5.6086 −0.3308 75.0280 0.5944 0.6297 67.0149 OD’s JAXA 5.6395 −0.3308 74.7831 0.8847 0.6304 67.0185 HPNAV 5.8616 −0.4094 74.8879 0.9457 0.6333 68.0690 Fig. 11 Planned ΔV at TCM1 in .way file format. Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 277 Table 7 Nominal ΔV ,OD’s Fujitsu ΔV (OPNAV1/NAV3 in Fig. 3), and OD’s JAXA ΔV (OPNAV2/NAV3 in Fig. 3) State ΔV ΔV ΔV X Y Z HP HP HP estimate (cm/s) (cm/s) (cm/s) Nominal 0.0230 −0.0573 0.3460 OD’s Fujitsu 0.0752 0.0039 0.3674 OD’s JAXA 0.0492 0.0042 0.3793 Fig. 14 Results of the TCM1 operation on 2018/11/30: planned and measured ΔV report. estimating the state vector on 2018/12/11 is shown in Fig. 15, in gray. Compared to the propagated trajectory after executing the actual ΔV at TCM1, a displacement in position of 2 km in the X direction HP at TCM2 was noticed. It was verified that the 0.5 mm/s correction not given at TCM1 in the X-axis was one of the causes of this expected position displacement at TCM2. Moreover, the trajectory between TCM1 and TCM2, designed with the optNEAR tool, assumed that the spacecraft was always Earth-pointing. However, Fig. 12 Doppler signal on 2018/11/30. Horizontal axis: attitude maneuvers were scheduled every 3 days, which reception time in UTC. Vertical axis: the double difference resulted in an error in the pointing accuracy of 1 ; between measured and planned value of the spacecraft’s speed. consequently, the effect on the SRP acceleration was weaker. A smaller effect on the SRP acceleration caused adriftin the X-axis direction away from the asteroid, as shown in Fig. 16. It was verified that propagating the planned trajectory with a reflective coefficient, C ,of 5% less than the nominal value would have compensated fortheerrorinthe X position, shown by the purple HP line in Fig. 16. Furthermore, it is possible that non- linearities affected our solution after 21 days. Therefore, a TCM2 maneuver was needed immediately after deep conjunction on 2018/12/25. The error in the attitude is also thought to be the reason why the asteroid was not in the FOV of the ONC- T camera on 2018/12/15–17, as shown in Fig. 17.Figure Fig. 13 Planned trajectory OD JAXA solution (black), actual trajectoryfromTCM1toTCM2aftertheTCM1operation (red), 17(b) shows that the state of the spacecraft could not and new planned trajectory between TCM2 to HRM (green). The be estimated with the ONC-T camera as Ryugu was out black dot represents the Ryugu coordinates. HP reference frame. of the camera’s FOV, as determined from the images taken. Figure 18 shows the angle between Ryugu and 6.3 Deep conjunction epoch: 2018/12/11 the spacecraft each day after 2018/12/11; it can be seen During the deep conjunction epoch on 2018/12/11, that when the error of 1 in the attitude was included beacon operations were performed to test the Ka-band in the analysis, Ryugu was not in the FOV of the ONC- capability and estimate the state vector of Hayabusa2 T on either day, as shown in Fig. 18(b). Due to the [15]; refer to the green dot in Fig. 1 for the deep geometry of the ayu trajectory, when the attitude error conjunction epoch. The propagated trajectory after was not taken into account it is possible to notice that 278 S. Soldini, H. Takeuchi, S. Taniguchi, et al. Fig. 15 Estimated trajectory in deep conjunction after beacon operation. Ryugu was not in the ONC-T’s FOV on 2018/15/17, as shown in Fig. 18(a). The observation campaign was started on 2018/12/21 to verify that the Z altitude was within the expected HP values. From the Doppler signal in Fig. 19,it was verified that the spacecraft’s velocity had changed sign (Fig. 19(b)), and that the spacecraft was returning to lower altitudes (Fig. 19(a)). The altitude of the spacecraft was approximately 82 km as planned in Fig. 19(a), and was decreasing towards the HP position altitude. 6.4 Trajectory correction maneuver 2 (TCM2): 2018/12/25 After 21 days of blackout in the communication link, the first telemetry data from the spacecraft was downloaded Fig. 16 Estimating the equivalent error in C . on 2018/12/22. The second TCM2 maneuver was scheduled for the 2018/12/25 after the planning on 2018/12/24. (a) The estimates of the spacecraft’s position and velocity on 2018/12/24 are shown in Table 8. The solutions for the COI and TCM1 operations planning were crosschecked with the nominal case, designed after the TCM1 maneuver (the green trajectory in Fig. 13) was executed. The ΔV s corresponding to the estimate solutions are shown in Table 9.The ΔV sinTable 9 were cross evaluated with the different solutions in Table 8 and the solutions were propagated with goNEAR. From this analysis, the solution from Fujitsu was selected for Fig. 17 Post estimation 2018/12/21: ONC-T images. the ΔV planning at TCM2. Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 279 Fig. 18 ONC-T angle FOV as function of the days from deep conjunction: the blue area shows during which epochs Ryugu is not in the FOV of ONC-T. Table 8 Nominal state vector at TCM2 and estimated states by Fujitsu (OPNAV1/NAV3 in Fig. 3), JAXA (OPNAV2/NAV3 in Fig. 3), andHPNAV (NAV1inFig. 3) State x y z v v v HP HP HP x y z HP HP HP estimate (km) (km) (km) (mm/s) (mm/s) (mm/s) Nominal 5.3185 −1.2411 55.0592 −0.6931 0.2238 −8.8516 OD’s Fujitsu 6.6334 −1.8447 56.8919 −0.6281 0.1917 −8.6760 OD’s JAXA 6.5968 −1.8250 56.8739 −0.6252 0.1940 −8.6823 HPNAV 6.4577 −1.7198 56.8581 −0.8764 0.2514 −8.7487 Table 9 Nominal ΔV ,OD’s Fujitsu ΔV (OPNAV1/NAV3 in Fig. 3), and OD’s JAXA ΔV (OPNAV2/NAV3 in Fig. 3) State ΔV ΔV ΔV X Y Z HP HP HP estimate (cm/s) (cm/s) (cm/s) Nominal −3.0005 0.5207 1.5554 OD’s Fujitsu −7.0870 2.6334 −5.8566 OD’s JAXA −7.0163 2.5521 −5.7345 (b) Figure 20 shows the .way file prepared on 2018/12/24 for the TCM2 operation (2018/12/25). TheOD’sFujitsuteam.wayfilewastheinputfor the AOCS team and the ΔV was computed in a body-fixed frame. (c) As a consequence of cancelling the ΔV and ΔV at X X TCM1, the TCM2 in each X, Y ,and Z component was performed, as shown in Fig. 20.As expected, the larger ΔV was given in the X direction, as at TCM1 (Fig. 11). The ΔV of 0.5 mm/s wasnotperformed, resultinginanexpected1km displacement in X at TCM2. The error between the planned and the actual ΔV at TCM2 was Fig. 19 Doppler measurements on 2018/12/21. 105.89% in ΔV , 100.21% in ΔV , and 93.48% in X Y B B 280 S. Soldini, H. Takeuchi, S. Taniguchi, et al. Fig. 20 Planned ΔV at TCM2 in .way file format. ΔV , as shown in the report of Fig. 21. Figure 22 Figure 23 shows the results after the operation shows the X–Z and Y –Z components of the ayu by comparing the planned trajectory with the actual trajectory in the HP frame at TCM2, displayed in predicted trajectory, in black and red, respectively. the control room. 6.5 Home recovery maneuver and home position keeping: 2018/12/29 On 2019/12/29, the last conjunction operation was performed. As explained in Section 4.3,two ΔV swere combined into one maneuver; a HPK maneuver (BOX-A operation keeping until 2018/12/31) together with the HRM ΔV . (a) Table 10 shows the estimates of the spacecraft’s position and velocity on 2018/12/30. As for the previous operations, the solutions were crosschecked with the nominal case, designed after the TCM2 maneuver (Fig. 23) was executed. The ΔV s Fig. 21 Results of the TCM2 operation on 2018/12/25: planned and measured ΔV report. Fig. 23 Planned trajectory OD Fujitsu solution (black), actual trajectory after TCM2 operation (red), and BOX-A operation Fig. 22 Planned ayu trajectory displayed on the screen of the (gray). The black dot represents the Ryugu coordinates. HP reference frame. ISAS’s control room on 2018/12/25. Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 281 Table 10 Nominal state vector at HRM and estimated states by Fujitsu (OPNAV1/NAV3 in Fig. 3), JAXA (OPNAV2/NAV3 in Fig. 3), andHPNAV (NAV1inFig. 3) State x y z v v v HP HP HP x y z HP HP HP estimate (km) (km) (km) (mm/s) (mm/s) (mm/s) Nominal −0.0993 −0.0217 20.3407 0.7 0.1 11.5 OD’s Fujitsu −0.6307 −0.0807 19.9176 3.3 0.4 14.0 OD’s JAXA −0.5825 −0.0923 19.7616 3.0 0.5 14.9 HPNAV −0.6572 −0.0527 19.8053 3.4 0.3 14.6 corresponding to the estimate solutions are shown in showninFig. 25.Figure 25 shows the planned Table 11.The ΔV sin Table 11 were cross evaluated and actual predicted trajectory after the HRM with the different solutions in Table 10 and the maneuver. solutions were propagated with goNEAR. From this The lower ΔV given is due to a decrease in pressure analysis, the solution from Fujitsu was selected for in the fuel tank, which required adjustment after the the ΔV planning at HRM. conjunction operation, as shown in Fig. 25. The error (b) Figure 24 shows the .way file prepared on between the planned and the actual ΔV at HRM was 2018/12/30 for the combined HRM and HPK 89.29% in ΔV , 92.15% in ΔV , and 97.43% in X Y B B maneuvers (2018/12/31). The OD’s Fujitsu team ΔV , as shown in the report of Fig. 26. Therefore, on .way file was the input for the AOCS team and the 2018/12/31 a BOX-A operation was performed to bring ΔV was computed in a body-fixed frame. the spacecraft back to 20 km. 2018/12/29 marked the (c) The HRM ΔV accounts for the brake velocity ΔV end of the superior solar conjunction phase and the start at HRM plus the HPK ΔV to target the center ofthesecondhalfoftheRyuguproximityoperations. of BOX-A operation on 2018/12/31. A lower ΔV 6.6 Summary of the solar conjunction executionof3mm/sinboththe X and Y directions operation was experienced, which allowed braking velocity in the Z direction but not the lateral direction, as In this section, the results of the COI (2018/11/23), TCM1 (2018/11/30), TCM2 (2018/12/25), and HRM Table 11 Nominal ΔV ,OD’sFujitsu ΔV (OPNAV1/NAV3 in (2018/12/29) operations are shown. The deterministic Fig. 3), and OD’s JAXA ΔV (OPNAV2/NAV3 in Fig. 3) ΔV was computed for each trajectory leg, using the State ΔV ΔV ΔV X Y Z HP HP HP optNEAR tool. The comparison between the planned estimate (cm/s) (cm/s) (cm/s) Nominal 0.2650 −0.0610 1.3410 trajectory after the OD campaign and the actual ΔV OD’s Fujitsu 0.3090 −0.0560 1.3750 trajectory after the mission operation are shown for OD’s JAXA 0.3020 −0.0550 1.3800 COI (Fig. 10), TCM1 (Fig. 13), TCM2 (Fig. 23), and Fig. 24 Planned ΔV at HRM (including HPK) in .way file format. 282 S. Soldini, H. Takeuchi, S. Taniguchi, et al. HRM (Fig. 25). In Figs. 10, 13, 23,and 25,the trajectory in black is the planned trajectory, while the one in red is the propagated trajectory after measuring the actual ΔV . The deterministic ΔV was computed using optNEAR in J2000EQ and then given in the HP and spacecraft’s body-fixed reference frames, as shown in Table 12. As previously mentioned, ΔV slower than 1 mm/s was neglected while ΔV faster than 10 cm/s wasexecutedtwo timesasmainandtrim ΔV s, as shown in Table 13. Table 13 shows the effects on the ΔV of truncation of up to 4 digits of the ΔV command. Fig. 25 Planned trajectory OD Fujitsu solution (black) and Evidently, both TCM1 and TCM2 did not require a the actual trajectory after HRM operation (red). The edges of trim ΔV , while the Z direction required main and trim BOX-A are marked in gray. The black dot represents the Ryugu coordinates. HP reference frame. ΔV s for both COI and HRM. The planned trim ΔV was usually rescheduled during the mission operation to compensate for the error of the main ΔV.In Table 13, the actual measurements are the ACMs for the X and Y ΔV s and 2-way Doppler for the Z ΔV . 7 Conclusions In this article, the Hayabusa2’s low energy conjunction (ayu) trajectory, executed in late 2018, was presented. As a result of the operation, the optNEAR tool was validated in real time and was used for the validation of JAXA’s JATOPS trajectory design tool at high altitude operations. The spacecraft reached a maximum distance of 109 km from Ryugu on 2018/12/11 and Fig. 26 Results of the HRM (including HPK) operation on returned to home position (20 km from Ryugu) on 2018/12/29: planned and measured ΔV report. 2018/12/29 after 21 days of uncontrolled orbital motion. Table 12 Designed deterministic ΔV in HP and body-fixed frames Maneuver ΔV ΔV ΔV ΔV ΔV ΔV X Y Z X Y Z HP HP HP B B B COI (cm/s) 2.154758 −0.290556 14.049689 −2.071104 0.595609 14.052644 TCM1 (cm/s) 0.049176 0.004165 0.379261 −0.048507 0.005917 0.379325 TCM2 (cm/s) −0.708705 0.263339 −0.585655 −0.719433 0.234432 −0.584859 HRM (cm/s) 3.092521 −0.560379 13.753272 3.111279 −0.530874 13.750199 Table 13 Planned and actual executed ΔV in the body-fixed frame ΔV ΔV ΔV ΔV ΔV ΔV X Y Z X Y Z B B B B B B Maneuver (planned) (planned) (planned) (actual) (actual) (actual) COI (main) (cm/s) −2.0700 0.5900 10.0000 −2.0448 0.54918 9.4530 COI (trim) (cm/s) 0.0000 0.0000 4.5970 0.0000 0.0000 4.3900 TCM1 (main) (cm/s) 0.0000 0.0000 0.3800 0.0000 0.0000 0.3770 TCM1 (trim) (cm/s) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 TCM2 (main) (cm/s) −0.7206 0.2310 −0.5892 −0.7631 0.2315 −0.5508 TCM2 (trim) (cm/s) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 HRM (main) (cm/s) 3.0900 −0.5600 10.0000 2.7700 −0.4880 9.3370 HRM (trim) (cm/s) 0.0000 0.0000 4.4100 0.0000 0.0000 4.0600 Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 283 Due to the error in the attitude maintenance in deep A.2 Partial derivatives of the 3rd body conjunction, Ryugu was not in the FOV of the ONC-T perturbations camera on 2019/12/15, while it was consistently in the The partial derivatives of the 3rd body perturbation are FOV of ONC-W1. On 2018/12/11 (deep conjunction), derived as a beacon operation was performed for radio science ⎡ ⎤ ∂F ∂F ∂F 4p 4p 4p μ 3(x−d ) j j j Pj x purposes to test the Ka-band capability under solar − 1 − 3 2 ∂x ∂y ∂z Δ Δ ⎢ ⎥ ⎢ ⎥ corona noise. The total expenditure in the ΔV was, as ∂F ∂F ∂F ⎢ 5p 5p 5p j j j 3(x−d )(y−d ) ⎢ ⎥ x y = ⎢ Pj 5 ⎢ ⎥ ∂x ∂y ∂z Δ desired, less than 0.36 m/s. Based on the observation ⎣ ⎣ ⎦ ∂F ∂F ∂F 6p 6p 6p 3(x−d )(z−d ) j j j x z data collected during the solar conjunction, the orbit of Pj 5 ∂x ∂y ∂z Ryugu was recalculated. This updated orbit was used 3(x−d )(y−d ) 3(x−d )(z−d ) x y x z after returning to the HP position (HRM) to resume μ μ Pj 5 Pj 5 Δ Δ the home position at an altitude of 20 km above the μ 3(y−d ) Pj y 3(y−d )(z−d ) ⎥ z z asteroid surface. It was confirmed that using this new − 1 − μ 3 2 Pj 5 ⎥ Δ Δ Δ orbit of Ryugu achieves and maintains a more stable   ⎦ 3(y−d )(z−d ) μ 3(z−d ) y z Pj z μ − 1 − Pj 5 3 2 home position. Δ Δ Δ (23) A.3 Partial derivatives of solar radiation Appendix A: Partial derivatives of the pressure perturbation optNEAR’s linearized equations The cannonball model assumes that the Hayabusa2 The partial derivatives including the gravity of Ryugu, spacecraft is Sun-pointing. This is not exact during the 3rd body, and the SRB perturbations are given by the conjunction phase when Hayabusa2 is kept Earth- the following equation: pointing. Therefore, the equations for a flat surface are ⎡ ⎤ ⎡ ⎤ ∂F ∂F ∂F ∂F ∂F ∂F 4 4 4 4r 4r 4r more appropriate and used here. The partial derivatives ∂x ∂y ∂z ∂x ∂y ∂z ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ of Eq. (4) are given by rearranging Eq. (4) as follows: ∂F ∂F ∂F ∂F ∂F ∂F 5 5 5 5r 5r 5r ⎢ ⎥ =⎢ ⎥ + ∂x ∂y ∂z ∂x ∂y ∂z ⎣ ⎦ ⎣ ⎦ K(1 − ) r · r Earth ls ∂F ∂F ∂F ∂F ∂F ∂F 6 6 6 6r 6r 6r a = − r SRP ls ∂x ∂y ∂z ∂x ∂y ∂z r r Earth ls ⎡ ⎤ ⎡ ⎤ ∂F ∂F ∂F 4p 4p 4p j j j ∂F ∂F ∂F 4SRP 4SRP 4SRP 2K (r · r ) Earth ls ∂x ∂y ∂z ∂x ∂y ∂z − r (24) ⎢ ⎥ Earth NP j 3 4 ⎢ ⎥ ⎢ ⎥ r r ∂F ∂F ∂F ⎢ ⎥ Earth ls 5p 5p 5p j j j ∂F ∂F ∂F ⎢ ⎥ 5SRP 5SRP 5SRP +⎢ ⎥ ⎢ ⎥ ∂x ∂y ∂z ∂x ∂y ∂z ⎣ ⎦ ⎣ ⎦ with j=1 ∂F ∂F ∂F ∂F ∂F ∂F P A 6p 6p 6p 6SRP 6SRP 6SRP j j j 0 ∂x ∂y ∂z K = AU (25) ∂x ∂y ∂z c m (21) Note that: ⎧ ⎫ ⎧ ⎫ A.1 Partial derivatives of the Ryugu’s gravity ⎪ ⎪ ⎪ ⎪ X X − X E S ⎪ ⎪ ⎪ ⎪ ⎨ ⎬ ⎨ ⎬ The partial derivatives of Ryugu’s gravity are given by r = Y and r = Y − Y (26) Earth E ls S ⎪ ⎪ ⎪ ⎪ ⎡ ⎤ ⎪ ⎪ ⎪ ⎪ ⎩ ⎭ ⎩ ⎭ ∂F ∂F ∂F 4r 4r 4r Z Z − Z E S ∂x ∂y ∂z ⎢ ⎥ ⎢ ⎥ ∂F ∂F ∂F 5r 5r 5r ⎢ ⎥ = Thederivativesof thetwotermsinEq.(24)are ∂x ∂y ∂z ⎣ ⎦ derived by components and it was distinguished between ∂F ∂F ∂F 6r 6r 6r ∂x ∂y ∂z the 1st term of Eq. (24)and2ndtermofEq.(24). The ⎡ ⎤ μ 3xy partial derivatives of SRP are a 3x 3xz − 1 − μ μ 3 2 a 5 a 5 r r r r ⎢ ⎥ ⎡ ⎤ ∂F ∂F ∂F ⎢ ⎥ 4SRP 4SRP 4SRP ⎡ ⎤ 3xy μ 3y 3yz ⎢ a ⎥ ∂x ∂y ∂z μ − 1 − μ a a a a 5 3 2 a 5 1xx 1xy 1xz ⎢ r r r r ⎥ ⎢ ⎥ K(1−) ⎢ ⎥ ⎢ ⎥ ⎣   ⎦ ∂F ∂F ∂F 5SRP 5SRP 5SRP 2 = − ⎢ ⎥ ⎣ a a a ⎦ 1yx 1yy 1yz 3xz 3yz μ 3z a ∂x ∂y ∂z μ μ − 1 − ⎣ ⎦ r a 5 a 5 3 2 Earth r r r r a a a ∂F ∂F ∂F 1zx 1zy 1zz 6SRP 6SRP 6SRP (22) ∂x ∂y ∂z 284 S. Soldini, H. Takeuchi, S. Taniguchi, et al. ⎡ ⎤ ∂a Z (Y − Y ) 1y E S a a a 2xx 2xy 2xz = a = − + 1yz ⎢ ⎥ 4 ∂z r 2K ⎢ ⎥ ls − ⎢ a a a ⎥ 2yx 2yy 2yz r ⎣ ⎦ r · r (Y − Y )(Z − Z) Earth Earth ls S S 4 (34) a a a 2zx 2zy 2zz r ls (27) Derivative of the z-component This formulation was written for flat surface Earth- ∂a X (Z − Z) 1z E S = a = − + pointing, and therefore the norm is a function of the 1zx ∂x r ls Earth–asteroid line, for simplicity. The two terms of r · r (Z − Z)(X − X) Earth ls S S Eq. (27) are derived by components as 4 (35) ls 1) 1st term ∂a Y (Z − Z) r · r X (X −X)+Y (Y −Y )+Z (Z −Z) 1z E S Earth ls E S E S E S = a = − + r = · 1zy ls 4 4 2 2 2 2 ∂y r [(X −X) +(Y −Y ) +(Z −Z) ] ls ls S S S r · r (Z − Z)(Y − Y ) ⎧ ⎫ Earth ls S S 4 (36) ⎪ ⎪ 6 X − X ⎪ S ⎪ ⎨ ⎬ ls Y − Y = a (28) ⎪ ⎪ ⎪ ⎪ ⎩ ⎭ ∂a X (X −X)+Y (Y −Y )+2Z (Z −Z) 1z E S E S E S Z − Z =a =− + 1zz ∂z r ls Derivatives of the x-component r · r (Z −Z) Earth ls S 4 (37) ∂a 2X (X −X)+Y (Y −Y )+Z (Z −Z) ls 1x E S E S E S =a =− + 1xx ∂x r ls 2) 2nd term r · r (X −X) Earth ls S 4 (29) 2 (r · r ) Earth ls ls r = Earth ls ⎧ ⎫ ⎪ X ⎪ ∂a Y (X − X) 1x E S E ⎪ ⎪ ⎨ ⎬ = a = − + 1xy [X (X −X)+Y (Y −Y )+Z (Z −Z)] E S E S E S ∂y r =a ls Y E 2 2 2 2 ⎪ ⎪ [(X −X) +(Y −Y ) +(Z −Z) ] S S S ⎪ ⎪ ⎩ ⎭ r · r (X − X)(Y − Y ) Earth ls S S 4 (30) ls (38) Partial derivatives of ∂a Z (X − X) 1x E S = a = − + 1xz 4 2 ∂z r ∂ (r · r ) r · r ∂(r · r ) Earth ls Earth ls Earth ls ls =2 − 4 4 ∂r r r ∂r ls ls r · r (X − X)(Z − Z) Earth ls S S 4 (31) 6 2 4 (r · r ) ∂r Earth ls ls ls (39) r ∂r ls Derivative of the y-component where ⎧ ⎫ ∂a X (Y − Y ) ⎪ X ⎪ 1y E S ⎪ ⎪ = a = − + ⎨ ⎬ 1yx ∂(r · r ) Earth ls ∂x r ls = − Y (40) ∂r ⎪ ⎪ r · r (Y − Y )(X − X) ⎪ ⎪ Earth ls S S ⎩ ⎭ 4 (32) ls and ⎧ ⎫ ∂a X (X −X)+2Y (Y −Y )+Z (Z −Z) 1y E S E S E S ⎪ ⎪ X − X ⎪ ⎪ =a =− + ⎨ ⎬ 1yy 4 ∂r ∂y r 2 2 2 ls ls =−4 (X −X) +(Y −Y ) +(Z −Z) Y − Y S S S S ∂r ⎪ ⎪ ⎪ ⎪ r · r (Y −Y ) ⎩ ⎭ Earth ls S Z − Z 4 (33) ls (41) Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 285 therefore [2] Lauretta, D., Balram-Knutson, S., Beshore, E., Boynton, ⎧ ⎫ W., dAubigny, C., DellaG-iustina, D., Enos, H., Gholish, ⎪ ⎪ ⎪ E ⎪ ⎨ ⎬ 2 D., Hergenrother, C., Howell, E., et al. Osiris-REx: ∂ (r · r ) r · r Earth ls Earth ls = − 2 Y + E Sample return from asteroid (101955) bennu. Space 4 4 ⎪ ⎪ ∂r r r ⎪ ⎪ ls ls ⎩ ⎭ Science Reviews, 2017, 212: 925–984. [3] Tsuda, Y., Yoshikawa, M., Abe, M., Minamino, H., ⎧ ⎫ ⎪ X − X ⎪ Nakazawa, S. System design of the Hayabusa2—Asteroid ⎪ ⎪ ⎨ ⎬ (r · r ) Earth ls sample return mission to 1999 JU3. Acta Astronautica, 4 (42) Y − Y r ⎪ ⎪ 2013, 91: 356–362. ls ⎪ ⎪ ⎩ ⎭ Z − Z [4] Morley, T., Budnik, F. Effects on spacecraft radiometric data at superior solar conjunction. In: Proceedings Finally of the 20th International Symposium on Space Flight ⎡ ⎤ ⎡ ⎧ ⎫ Dynamics, 2007: 24–28 ⎪ ⎪ a a a X 2xx 2xy 2xz E ⎪ ⎪ ⎨ ⎬ ⎢ ⎥ ⎢ [5] Yoshikawa, M., Yano, H., Kawaguchi, J., Fujiwara, r · r Earth ls ⎢ ⎥ ⎢ = −2 + a a a Y 2yx 2yy 2yz E ⎣ ⎦ ⎣ 4 A., Abe, M., Iwata, T., Tanaka, S., Mori, O., r ⎪ ⎪ ls ⎪ ⎪ ⎩ ⎭ a a a Z 2zx 2zy 2zz E Yoshimitsu, T., Takagi, Y., et al. Technologies for future ⎧ ⎫ asteroid exploration: What we learned from Hayabusa ⎪ ⎪ X −X ⎪ ⎪ ⎨ ⎬ mission. In: Proceedings of Spacecraft Reconnaissance (r · r ) Earth ls 4 Y −Y · of Asteroid and Comet Interiors, 2006: 3038. ⎪ ⎪ ⎪ ⎪ ls ⎩ ⎭ [6] Soldini, S., Yamaguchi, T., Tsuda, Y., Saiki, T., Z −Z Nakazawa, S. Hayabusa2’s superior solar conjunction phase: Trajectory design, guidance and navigation. Space (43) X Y Z E E E Science Reviews, 2020, https://doi.org/10.1007/s112-14- A.4 Partial derivatives of solar radiation 020-00371-5. [7] Soldini, S., Yamaguchi, T., Tsuda, Y., Saiki, T. pressure perturbation (Sun-pointing) Hayabusa2 mission solar conjunction trajectory for For a cannonball model, the partial derivatives of the hovering satellite: Design, navigation and post-operation SRP perturbation are quite simple and they are given evaluation. In: Proceedings of the 29th AAS/AIAA Space by Flight Mechanics Meeting, 2019: AAS 19-241. [8] Uesugi, K., Matsuo, H., Kawaguchi, J., Hayashi, T. ⎡ ⎤ ∂F ∂F ∂F 4SRP 4SRP 4SRP Japanese first double lunar swingby mission “Hiten”. ∂x ∂y ∂z ⎢ ⎥ Acta Astronautica, 1991, 25(7): 347–355. ⎢ ⎥ ∂F ∂F ∂F 5SRP 5SRP 5SRP [9] Belbruno, E., Miller, A. A ballistic lunar capture ⎢ ⎥ = ∂x ∂y ∂z ⎣ ⎦ trajectory for the Japanese spacecraft Hiten. Jet ∂F ∂F ∂F 6SRP 6SRP 6SRP Propulsion Laboratory IOM 312/90.41371-EAB, 1990. ∂x ∂y ∂z [10] Koon, W. S., Lo, M. W., Marsden, J. E., Ross, S. D. ⎡ ⎤ K 3x 3xy 3xz 1 − −K −K 3 2 5 5 Dynamical systems, the three-body problem and space r r r r ⎢ ⎥ ⎢ ⎥ mission design. Equadiff 99, 2000: 1167–1181. 3xy 3y 3yz ⎢ ⎥ −K 1 − −K (44) 5 3 2 5 [11] Tsuda, Y., Takeuchi H., Ogawa, N. O. G., Kikuchi, ⎢ r r r r ⎥ ⎣ ⎦ S., Oki, Y., Ishiguro, M., Kuroda, D., Urakawa S., O. 3yz 3xz K 3z −K −K 1 − 5 5 3 2 r r r r S., Hayabusa2 project team. Rendezvous to asteroid with highly uncertain ephemeris: Hayabusa2’s ryugu- with P C A approach operation result. Astrodynamics, 2020, 4: 137– 0 r sc K = AU (45) c m sc [12] Tsuda,Y.,Ono,G.,Saiki,T.,Mimasu,Y.,Ogawa,N., Terui, F. Solar radiation pressure-assisted fuel-free Sun References tracking and its application to Hayabusa2. Journal of Spacecraft and Rockets, 2017, 54(6): 1284–1293. [1] Watanabe, S., Hirabayashi, M., Hirata, N., Noguchi, [13] Ono,G.,Tsuda,Y.,Akatsuka,K.,Saiki,T.,Mimasu, R., Shimaki, Y., Ikeda, H., Tatsumi, E., Yoshikawa, M., Y., Ogawa, N., Terui, F. Generalized attitude model Kikuchi, S., Yabuta, H., et al. Hayabusa2 observations for momentum-biased solar sail spacecraft. Journal of of the top-shape carbonaceous asteroid 162173 Ryugu. Guidance, Control, and Dynamics, 2016, 39(7): 1491– Science, 2019, 364(6437): 268–272. 1500. 286 S. Soldini, H. Takeuchi, S. Taniguchi, et al. [14] Tsuda, Y., Saiki, T., Funase, R., Mimasu, Y. the lead of the orbit determination of Hayabusa2. His current research interest is developing the deep space multi-objects Generalized attitude model for spinning solar sail orbit determination system. E-mail: takeuchi@jaxa.jp. spacecraft. Journal of Guidance, Control, and Dynamics, 2013, 36(4): 967–974. [15] Takeuchi, H., Yoshikawa, K., Tokei, Y., Oki, Y., Kikuchi, Sho Taniguchi completed his master’s S., Ikeda, H., Soldini, S., Ogawa, N., Mimasu, Y., course in mechanical engineering at Ono, G., et al. The deep-space multi-object orbit Ibaraki University in 1995. He joined determination system and its application to Hayabusa2’s Fujitsu in 1999, and engaged in tracking asteroid proximity operations. Astrodynamics, 2020, and tracking services at JAXA in 2005. 4(4): 377–392. In 2009, he was engaged in deep space [16] Soldini, S., Takanao, S., Ikeda, H., Wada, K., Yuichi, T., orbit determination work at the Science Hirata, N., Hirata, N. A generalised methodology for System Solution Division of the TC analytic construction of 1:1 resonances around irregular Solution Business Unit, Fujitsu Limited. He is also a regular bodies: Application to the asteroid Ryugu’s ejecta member of the Japanese Society of Astronautics. E-mail: dynamics. Planetary and Space Science, 2020, 180: taniguchi.sho@jp.fujitsu.com. [17] Montenbruck, O., Gill, E. Satellite Orbits Model, Shota Kikuchi received his Ph.D. degree Methods and Applications. New York: Springer-Verlag in aeronautics and astronautics from the Berlin Heidelberg, 2000. University of Tokyo in 2018. From 2015 to 2017, he had served as a visiting scholar Stefania Soldini received her Ph.D. at Purdue University and NASA Jet degree in October 2016 from the University Propulsion Laboratory. He is currently of Southampton, UK. She is an assistant a postdoctoral research associate at professor in space engineering in the JAXA and is engaged in the Hayabusa2 University of Liverpool, UK. Since 2020, asteroid sample-return mission as a system engineer. His she has been the PI of the “3D printed primary research interests lie in the field of astrodynamics, self-folding origami solar sail” project particularly in dynamics around small bodies. E-mail: funded by the CEII/EPSRC Network+ kikuchi.shota@jaxa.jp. (https://www.youtube.com/ watch?v=U5IhFIxZxZI&t=6s) in collaboration with Japan Aerospace Exploration Agency (JAXA) and Oxford Space Systems, UK. She is also a Yuto Takei received his Ph.D. degree member of the Hayabusa2 Joint Science Team (HJST) in engineering from Tokyo Institute as astrodynamics Co-I and member of the ESA’s HERA of Technology, Japan in 2015. He and NASA’s DART group. She was the PI of the“Hayabusa2” is a researcher at the Research and superior solar conjunction mission phase in late 2018. She Development Directorate and JAXA. He worked at the JAXA’s Institute of Space and Astronautical is involved in the Hayabusa2 project as Science (ISAS) from 2016 to 2019, after completing one-year a systems engineer. His research interests JSPS post-doc research fellowship at the same institute. include astrodynamics, spacecraft system, Her research interests are astrodynamics, guidance, space robotics, and deep space exploration. E-mail: navigation & control (GNC) for asteroids proximity takei.yuto@jaxa.jp. operations, ejecta particles dynamics, planetary defence, solar sail technology, additive manufacturing, and AI. E-mail: Go Ono is a researcher at JAXA. He stefania.soldini@liverpool.ac.uk. graduated with his master degree in engineering from the University of Bath Hiroshi Takeuchi received his Ph.D. in 2011 and with his Ph.D. degree in degree of science (physics and applied aerospace engineering from the University physics) from Waseda University in of Tokyo in 2014. He joined JAXA in 2000. In 2006, he started working at 2015 and has been working on guidance, ISAS/JAXA as a member of deep space navigation, and control systems of JAXA’s orbit determination group. He was a deep space missions such as Hayabusa2 and MMX. His visiting researcher of the NASA Jet Propulsion Laboratory in 2012–2013. He current research interests are astrodynamics and deep space is currently an associate professor of ISAS/JAXA and is also exploration. E-mail: ono.go@jaxa.jp. Hayabusa2’s superior solar conjunction mission operations: Planning and post-operation results 287 Takanao Saiki received his Ph.D. degree has been a research engineer at ISAS and JAXA. Her in aeronautics and astronautics from the current research interests include astrodynamics, mission University of Tokyo, Japan in 2005. He design, robotics, spacecraft systems and operation. E-mail: is an assistant professor at ISAS, JAXA. naoko.ogawa@isas.jaxa.jp. He is now involved in the Hayabusa2 project. He was a chief developer of the Yuya Mimasu is a researcher at impact system and he is currently a project JAXA. He graduated with his Ph.D. engineer. His research interests include degree in aerospace engineering from astrodynamics, spacecraft system, and deep space exploration. Kyushu University. After graduation, Email: saiki.takanao@jaxa.jp. he joined JAXA and has been working on the guidance, navigation, and control subsystem of Hayabusa2, which is JAXA’s Yuichi Tsuda received his Ph.D. degree asteroid sample-return mission. His in aeronautics and astronautics from research interests are astrodynamics and mission analysis University of Tokyo in 2003 and joined around small bodies. Email: mimasu.yuya@jaxa.jp. JAXA in 2003 as a research associate. He had been a visiting scholar of the Atsushi Fujii is a researcher at Department of Aerospace Engineering, Hayabusa2 Project Team, ISAS, JAXA. University of Michigan and Department He received his bachelor of engineering of Aerospace Engineering Sciences, from Saitama University, Japan. He University of Colorado Boulder in 2008–2009. He was involves in Hayabusa2 project as a ground a deputy lead of the IKAROS project, the world’s first system engineer. interplanetary solar sail mission. He is currently a professor of ISAS/JAXA and is the project manager of Hayabusa2, an asteroid sample-return mission. His research interests Satoru Nakazawa received his Ph.D. are astrodynamics, spacecraft system, and deep space degree in science from Nagoya University, exploration. E-mail: tsuda.yuichi@jaxa.jp. Japan in 1999. He is an assistant professor at ISAS and JAXA. He is now involved in Fuyuto Terui received his Ph.D. degree the Hayabusa2 project. He is the deputy in aerospace engineering from University manager of the project team. His research of Osaka Prefecture in 1989. He has interests include planetary science, been a staff member of Space Technology spacecraft system engineering, and deep Research Center of National Aerospace space exploration. Email: nakazawa.satoru@jaxa.jp. Laboratory (NAL) of Japan since 1989. He had been a visiting scholar of the Kent Yoshikawa received his bachelor’s University of Cambridge, Engineering and master’s degrees in engineering from Department, Control Group between 1994 and 1995. After Tokyo Institute of Technology in 2013 and the reorganization of space agencies in Japan, he has 2015, respectively. From 2015, he started been a staff member of JAXA since 2003 and is now a workingasanengineerinthe Research function manager of the Hayabusa2 project as well as and Development Directorate, JAXA. a representative of attitude and orbit control system of His current research interests include Hayabusa2 spacecraft. His main research fields include astrodynamics, GNC, planetary robotics, robust control and image-based guidance, and navigation and and planetary exploration. Email: yoshikawa.kento@jaxa.jp. control of a spacecraft such as debris removal space robot and the asteroid exploration probe. E-mail: terui.fuyuto@jaxa.jp. Yusuke Oki is a researcher at JAXA. He graduated with a master degree in astronautics from the University of Tokyo Naoko Ogawa received her B.E., M.E. and Ph.D. degrees in mathematical in 2016, and with a Ph.D. degree in engineering and information physics in astronautics from the University of Tokyo 2000, 2002 and 2005, respectively, from in 2019. He joined JAXA in 2019, and the University of Tokyo, Japan. From has been working on system design and 2004 to 2008 she has been a research orbit design of spacecrafts. His current fellow of the Japan Society for the research interests are astrodynamics, concurrent design, and Promotion of Science. Since 2008, she deep space exploration. E-mail: oki.yusuke@jaxa.jp. 288 S. Soldini, H. Takeuchi, S. Taniguchi, et al. Chikako Hirose has worked at JAXA navigation and control for interplanetary spacecraft. E-mail: since 2004. She is currently a senior Yamaguchi.Tomohiro@ce.MitsubishiElectric.co.jp. engineer and has had involvement in over 20 missions in flight dynamics field. She joined Makoto Yoshikawa is an associate the Hayabusa2 team since 2018 after she professor in ISAS, JAXA. He is the finished her research at NASA as a visiting mission manager of Hayabusa2 project. researcher for one year. Prior to that, she He got his Ph.D. degree in astronomy from demonstrated her leadership in Venus orbit the University of Tokyo in 1989. After insertion of the Japanese first planet orbiter, Akatsuki. She working as a researcher of JSPS (Japan obtainedhermasterdegreeinphysics fromOchanomizu Society for the Promotion of Science), University in 2004. E-mail: hirose.chikako@jaxa.jp. he worked at former Communication Research Laboratory from 1991 as senior researcher. He Hirotaka Sawada received his B.E. and joined ISAS as associate professor in 1998. His research field M.E. degrees from the Tokyo Institute is celestial mechanics, and he was involved in many space missions such as GEOTAIL, HALCA, Nozomi, Hayabusa, of Technology, Japan in 1998 and 2001, Akatsuki, and IKAROS. He is now also working for planetary respectively. He received his Ph.D. degree defense issues. E-mail: yoshikawa.makoto@jaxa.jp. from the Tokyo Institute of Technology, Japan in 2004. He is an associate senior Open Access This article is licensed under a Creative engineer of JAXA. He is currently involved Commons Attribution 4.0 International License, which in the Martian Moons Exploration (MMX) permits use, sharing, adaptation, distribution and reproduc- project. His specialized field of research includes space tion in any medium or format, as long as you give appropriate robotics, dynamics, and control of space systems. E-mail: credit to the original author(s) and the source, provide a link sawada.hirotaka@jaxa.jp. to the Creative Commons licence, and indicate if changes were made. Tomohiro Yamaguchi is a system The images or other third party material in this article are engineer of Mitsubishi Electric Cor- included in the article’s Creative Commons licence, unless poration. He received his Ph.D. degree indicated otherwise in a credit line to the material. If material from the Graduate University for is not included in the article’s Creative Commons licence and Advanced Studies, Japan in 2012. His your intended use is not permitted by statutory regulation or career includes system design, mission exceeds the permitted use, you will need to obtain permission analysis, and operations for interplanetary directly from the copyright holder. spacecrafts in both agencies and industry. To view a copy of this licence, visit His current research interests are system design and guidance, http://creativecommons.org/licenses/by/4.0/.

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Published: Nov 2, 2020

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