Astrodynamics
, Volume 5 (2) – Dec 2, 2020

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Astrodynamics Vol. 5, No. 2, 109{120, 2021 https://doi.org/10.1007/s42064-020-0092-7 Limits of drag augmentation at spacecraft end-of-mission and a mitigation strategy Emma Kerr, Malcolm Macdonald (B) University of Strathclyde, Glasgow G1 1XJ, UK ABSTRACT KEYWORDS An increasing number of objects are being launched into low-Earth orbit. Consequently, drag augmentation to avoid the possibility of future in-orbit collisions space object removal techniques are volume receiving attention. As one of the most developed techniques, drag augmentation is area-time-product increasingly being considered as an option for end-of-mission removal of objects from low- space debris Earth orbit. This paper highlights a common misconception around drag augmentation: liability although it can be used to reduce de-orbit time, when used inappropriately it can increase Learned Hand formula the volume swept by an object and, thus, increase the occurrence risk of collision with calculus of negligence another space object. Knowingly ignoring this increased risk of collisions could leave spacecraft operators, and consequently their responsible state party, open to liability Research Article risk. By investigating the volume swept and de-orbit lifetime, a strategy of delayed Received: 6 April 2020 deployment is proposed as a compromise between reducing volume swept and time to Accepted: 11 August 2020 de-orbit. However, this increases system complexity and, likely, cost. © The Author(s) 2020 1 Introduction such, the prudency of space debris mitigation standards and regulations means space actors are increasingly im- In January 2007, China conducted a direct-ascent anti- plementing end-of-mission disposal plans to be, and be satellite test, destroying the 750 kg Chinese weather satel- seen as, responsible and sustainable actors. lite FY-1C (COSPAR identi cation 1999-025A) at an No international treaty exists to speci cally deal with altitude of 865 km using a kinetic kill vehicle traveling in the issue of space debris. However, both the Outer Space the opposite direction [1]. Whilst not the rst, nor most Treaty and the Liability Convention address liability is- recent such test in space, the altitude was higher than sues by creating a fault-based liability for damage caused prior Russian and US tests, and a more recent Indian test, in space [5{7]. In addition, organizations, such as the creating a prolonged and dispersed debris cloud that has Inter-Agency Space Debris Coordination Committee and had a signi cant impact on the space debris environment the International Organization for Standardization (ISO), in low-Earth orbit (LEO). In February 2009, the defunct have developed best-practice guidelines [8,9]. These guide- Cosmos-2251 (COSPAR identi cation 1993-036A) and lines de ne two protected regions: LEO (de ned as the active Iridium-33 (COSPAR identi cation 1997-051C) region below 2000 km altitude, which is the area of in- satellites collided at an altitude of 789 km [2], the rst terest herein) and geosynchronous Earth orbit (de ned observed hypervelocity collision between two arti cial as the segment of the spherical shell from 200 km below satellites, leading to further growth in the LEO debris to 200 km above the geostationary altitude, approxi- population. These two events have signi cantly increased mately 35,786 km, and from 15 to 15 of latitude). awareness of the challenge presented by space sustain- Both organizations focus on two major areas of space ability. Meanwhile, the number of spacecraft launched debris mitigation. They discuss avoiding both the inten- per year has recently and rapidly increased. This trend tional release of debris during nominal operations and is a result of the increased use of standardized, small and micro-satellite, platforms such as the CubeSat [3, 4]. As unplanned spacecraft break-up. Secondly, they discuss B Malcolm.macdonald.102@strath.ac.uk 110 E. Kerr, M. Macdonald the post-mission disposal of spacecraft, which is the area likely to be catastrophically damaged than if it collides of interest herein. Best-practice guidelines currently re- with the main body of a spacecraft, and that lm is commend that post-mission disposal should result in per- unlikely to fragment into many parts. This logic is applied manent removal from the LEO-protected region within in Refs. [15, 22] where the analysis seeks to minimize the 25 years of decommissioning. further generation of debris rather than the total collision Although debris mitigation guidelines specify a time risk. This suggests that the drag sail surface area should period within which spacecraft should be removed, the be neglected from the ATP, that is, the volume swept method of removing spacecraft is not speci ed. Many analysis. However, fault liability results from any collision de-orbit concepts exist [10]. However, very few of these no matter the impact and as such the onus should be concepts are currently viable. One viable technique is to minimize the collision risk and to do no harm, rather drag augmentation, commonly referred as a drag sail; it than trying to minimize further damage, which implies requires the introduction of a large projected area per- the concept of an allowable collision. Similar arguments pendicular to the velocity vector to increase the eect are explicitly made elsewhere in the literature in favor of atmospheric friction (colloquially termed atmospheric of allowable collisions [23], rather than seeking to do drag), thus increasing the instantaneous area for possible no harm, and overlook the regulatory consequence of collisions. Such concepts have received notable attention, fault liability. However, this type of analysis can provide with various funding bodies and licensing authorities complementary insights to those presented herein. The (state parties) supporting technology and ight demon- level of liability resulting from a collision is a consequence strationse [11{18], as well as in the specialist and popular of the level of damage. Therefore, this study focuses solely mediae [19{21]. on the risk of any collision occurrence and, hence, the Prior studies of the application of drag augmentation operators being liable for the consequences. In particular, lack a full analysis of the implications of increasing pro- it does not aim to address the consequences of a collision jected area on collision risk, focusing principally on time nor the level of liability incurred. The concept of a to de-orbit and assuming a direct correlation with colli- population weighted volume swept is introduced to better sion risk. For example, in Ref. [15], the eect of the solar determine the collision risk, but the resulting liability cycle on de-orbit time is presented; however the eect from a collision is beyond the scope of this study. on volume swept is not. Meanwhile, in Refs. [15, 22], The typical assumption is that the less time an object the eect of increasing the projected area is brie y con- is on-orbit, the lower the collision risk, and as such in- sidered through what is termed the area-time-product creasing the area of a spacecraft will always be bene cial. (ATP), which is equivalent to volume swept, with both This assumption will be shown to be misguided. Rather, only considering results where deployment coincides with by increasing the area of a spacecraft at the end of its solar maximum; concluding that ATP and hence risk is mission an operator could on-occasion be argued at fault, reduced. This is shown in this paper to be correct, but to and hence liable for any subsequent on-orbit collision. also be a best-case analysis when the eect of the solar cycle on volume swept is presented, closing a gap in the 2 Method literature. Although by no means the sole metrics, the simplest The volume swept and de-orbit lifetime (total time spent metrics available to quantify the collision risk are the in orbit after spacecraft operations cease) are dependent amount of time an object spends on-orbit, and how large on the mass and projected area of a spacecraft. Using a a volume it sweeps through in that time. Practically, both validated general perturbations method for orbit lifetime the time to deorbit and the volume swept are metrics for analysis, the relationship between mass, projected area, the probability of collision occurrence. A third metric volume swept, and orbit lifetime can be demonstrated. for risk could also be considered: the composition of the In this study, the general perturbation method developed by Kerr and Macdonald is further developed [24]. This object. Such a metric attempts to capture the probable method was validated using historical two-line element result of a collision, thus focusing on the risk that the collision poses to the space environment. For example, if data for twenty-one spacecraft with drag coecients, an object collides with the thin lm of a drag sail it is less surface areas, masses, and so forth taken from referenced Limits of drag augmentation at spacecraft end-of-mission and a mitigation strategy 111 Table 1 Algorithm used to calculate volume swept Number Step 1 Calculate the orbital lifetime using Eq. (1) or (3), as appropriate. 2 Calculate orbit period hence and semi-major axis after one revolution. 3 Calculate the distance travelled along the orbital path in that single revolution by approximating it as a closed elliptical orbit, with an average semi-major axis, a = (a a )=2. 0 1 4 Repeat steps 1{3 until de-orbit is complete, de ned herein as an altitude of 65 km as per Ref. [24]. 5 Calculate the sum of the distances calculated in step 3 and multiply that sum by the projected area to attain the total volume swept. a T 0 f 3 sources. Where a speci c value could not be sourced HT m 0 H T = 1 e (3) through reference, the recommended ISO value or method 2 a FSC 0 0 D to estimate a value was applied [25]. This validation Here, subscript 0 denotes initial state, while subscript f found the method gave an average orbit lifetime error denotes nal state. To calculate volume swept, the full of 3.5% 3.25% [24]. It showed a better performance deorbit phase should be split into individual orbital rev- compared to third party tools: Systems Tool Kit from olutions, allowing the calculation of distance travelled. Analytical Graphics , General Mission Analysis Tool Using Eqs. (1){(3), the volume swept can be calculated from NASA , and Semi-Analytical Tool for End of Life using the algorithm in Table 1. Analysis (STELA) from CNES . Kerr and Macdonald Introducing a large surface area is frequently held to found STELA to be the most eective among the third- be bene cial as it lowers the orbit lifetime, and hence col- party tools, with an average orbit lifetime error of 6.63% lision risk. However, using the volume swept as a metric 7.00% [24]. The Kerr{Macdonald method includes for collision risk it can be shown that this presumed re- the eect of the solar activity cycle, thus capturing the duction in risk is not always the case. If the time-variant time variance of the atmosphere required herein. As nature of the Earth's atmosphere is ignored, the volume per Refs. [24], the orbit lifetime of a low eccentricity swept is found to be directly proportional to mass and (e < 0:02) satellite is calculated as independent of the area projected to the atmosphere. Meanwhile, the orbit lifetime is not independent as it e H 11 a e 0 0 0 = 1 5 + (1) is inversely proportional to the projected area. Thus, 2B a 20 H the larger the spacecraft projected area, the shorter the where e is eccentricity, a is semi-major axis, and H is lifetime, whilst volume swept remains constant. With scale height. B is calculated as the assumption of a time-invariant atmosphere, as has h i 2 FSC a e a e D 0 0 0 0 0 been widely applied in such prior studies, using volume B = a e I exp (2) 0 0 0 1 T m H H swept and orbit lifetime as the measure of collision risk where T is the orbit period, F is a factor considering the means drag augmentation is always bene cial in terms rotation of the atmosphere, S is the projected area of of debris mitigation measures. However, the Earth's at- the spacecraft in the instantaneous direction of travel, mosphere is highly dynamic and time-variant, and the C is the drag coecient of the spacecraft, m is the eect of these variations must not be neglected [7]. To demonstrate the eect of the variation in mass and pro- mass of the spacecraft, is the atmospheric mass density, jected area over a de-orbit, these parameters are varied and I is the integrated form of the modi ed Bessel between 1 and 1000 kg, and 0.01 and 50 m , respec- function [24]. Alternatively, if an orbit is approximately tively. Two atmospheric models were also considered. circular (e < 0:001, as validated in Ref. [24]), the orbit The rst uses a spherically-symmetrical, time-invariant lifetime can, with no loss in accuracy, be obtained as atmosphere model with average solar activity developed in Ref. [24]. The second includes time-variance in that STK can be downloaded from http://www.agi.com/products/ stk/. atmosphere model by incorporating the model of the GMAT can be downloaded from http://gmatcentral.org/. solar activity cycle developed in Ref. [24]. The resultant STELA can be downloaded from https://logiciels.cnes.fr/ content/stela. volumes swept are shown in Fig. 1. The orbit used is cir- 112 E. Kerr, M. Macdonald lifetime alone. It is of note that in this study it is as- 4000 sumed that the drag augmentation device is deployed to the required size, the nature and operations of this device are not considered and the device could be, for example, a drag sail, or balloon type device. Of note, Ref. [26] ad- dresses the likelihood of achieving aerodynamic stability 0 0 1000 1000 0 with a drag sail. 500 500 40 40 2 2 Given the large variation introduced by the start date m (kg) S (m ) m (kg) S (m ) 0 60 0 60 (a) (b) during the solar cycle, a new de-orbit scheme is imme- Fig. 1 Volume swept vs. mass (m) and projected area (S). diately apparent; taking advantage of the periods where Single surface in (a) shows the time-invariant atmosphere a low volume swept occurs. By delaying deployment of case. A total of 11 surfaces in (b) demonstrate a time-variant the large surface area of a drag device to coincide with atmosphere case; each surface created using a dierent start date at 1-year intervals through the solar activity cycle. a period of high solar activity, and hence high drag, the volume swept by an object and its orbit lifetime can be cular with 65 inclination and 400 km altitude, with orbit optimized. However, the engineering implementation of decay having occurred at 65 km. Figure 1(a) shows the this method, for example, maintaining compliance with time-invariant atmosphere, and Fig. 1(b) shows a series of spacecraft paci cation guidelines, is beyond the scope of dierent start dates at 1-year intervals through the solar this study. The volume swept with the \delayed deploy- activity cycle, and thus 11 surfaces are presented. The so- ment" of a drag augmentation device can be calculated lar activity cycle is the approximately 11-year variation in with a few minor additions to the algorithm presented the amount of radiation that impacts Earth's atmosphere in Table 1, as shown in Table 2. Further details of this from the Sun. Increased radiation heats the atmosphere scenario is discussed in the Results section. causing expansion, thus increasing atmospheric density End-of-mission is used in this paper to denote the at a given altitude [7]. Atmospheric density at altitudes point at which the spacecraft has completed its prin- of 100{1000 km during solar activity maximum can vary cipal purpose, its mission; this can occur as a planned by up to two orders of magnitude from the minimum event or due to an anomaly on-board the spacecraft. solar activity conditions [7]. Including this variation in At end-of-mission, the spacecraft is, wherever possible, atmospheric density means that spacecraft orbit lifetime, decommissioned, within the context of this paper this and hence volume swept, become dependent on the date will ideally include paci cation of the spacecraft as per at which de-orbit begins, as can be seen in Fig. 1. As shown in Fig. 1(b), for the same mass and area, large best-practice guidelines to avoid an unplanned spacecraft break-up [8, 9], and triggering of the drag augmenta- dierences can exist in the volume swept by a spacecraft depending on the start date through the solar activity tion device, which may deploy immediately or at some cycle. This variation is not captured by considering orbit planned time in the future. The de-orbit phase is de ned Table 2 Algorithm used to calculate volume swept with \delayed deployment" of a drag augmentation device Number Step 1 Calculate the orbital lifetime using Eq. (1) or (3), as appropriate. 2 Calculate orbital period and hence semi-major axis after one revolution. 3 Calculate the distance travelled along the orbital path in that single revolution by approximating it as a closed elliptical orbit, with an average semi-major axis, a = (a a )=2. 0 1 4 Repeat steps 1{3 until de-orbit is complete, de ned herein as an altitude of 65 km as per Ref. [24]. 5 Calculate the sum of the distances calculated in step 3 prior to deployment of drag augmentation device and multiply that sum by the projected area of the spacecraft alone to attain the total volume swept prior to deployment. 6 Calculate the sum of the distances calculated in step 3 after deployment of drag augmentation device and multiply that sum by the projected area of the spacecraft with the device deployed to attain the volume swept after deployment. 7 Calculate the total volume swept over the orbit lifetime by summing the volumes swept prior-to and after deployment of drag augmentation device as calculated in steps 5 and 6. Volume swept (km ) Volume swept (km ) Limits of drag augmentation at spacecraft end-of-mission and a mitigation strategy 113 as beginning when the spacecraft is fully decommissioned UKube-1 has a drag augmentation device of projected and passivated. End-of-life is de ned as the point at area 10 m on-board. The rst hypothetical case assumes which the spacecraft no longer exists, due to re-entry this device is deployed immediately at end-of-mission, in the Earth's atmosphere, taken within this article as while the second considers what happens when the de- 65 km altitude. ployment is delayed in order to coincide with the subse- Principal results are presented for a hypothetical sce- quent period of high solar activity. Figure 2(a) shows the nario involving UKube-1 (COSPAR identi cation 2014- orbit lifetime for each case, and Fig. 2(b) shows volume 037F), a three-unit, or 3U CubeSat with three deployable swept during each de-orbit scenario. Note that the anal- solar panels that has a mass of 3.98 kg. As of Septem- ysis in Fig. 2 is for start epochs spaced evenly through an ber 9, 2016, UKube-1 has been inactive and believed average solar cycle. Hence, it is not linked to the above to be tumbling randomly [27], hence at end-of-mission end-of-mission epoch for UKube-1, providing an indica- as de ned herein. On this date, the spacecraft had a tive in-sight rather than a prediction. It is noted that the semi-major axis of 7006.23 km, eccentricity of 0.0003369, current solar activity cycle is nearly over. Predicting the and inclination of 98.4032 [28]. Note that the spacecraft behavior of the subsequent cycle is extremely dicult; mass is a measured quantity, and the semi-major axis, a cycle behavior can, currently, only be accurately pre- eccentricity, and inclination are taken from orbit track- dicted once it has begun, and even then, estimates can ing data, and as such each are speci ed to the level of vary vastly due to the chaotic nature of the solar cycle. detail available. If UKube-1 is considered randomly tum- Therefore, an average cycle is used when predicting orbit bling its projected area is calculated using the method of area-averaging outlined in the ISO standard for orbit No deployment lifetime estimation [25], found to be 0.0628 m . The Immediate deployment Delayed deployment drag coecient of spacecraft is also based on the ISO standard for orbit lifetime estimation, giving an assumed drag coecient of 2.2 [25]. Secondary results are presented in the discussion sec- tion for CanX-7 (COSPAR identi cation 2016-059F), a 3U CubeSat (34 cm 10 cm 10 cm) of mass 3.5 kg, with a drag sail of eective area of 2 m deployed on 2 May 3, 2017 [29]. The initial epoch of the CanX-7 case study is May 4, 2017, when the spacecraft had a semi- 0 2 4 6 8 10 major axis of 7059.3238 km, eccentricity of 0.0030913, Solar cycle start year (a) and inclination of 98.1796 [28]. Once again, the mass is a referenced value, while the semi-major axis, eccentricity No deployment and inclination are taken from orbit tracking data, and Immediate deployment Delayed deployment as such are speci ed to the level of detail available. If 150 CanX-7 is considered randomly tumbling, without the drag sail deployed, its projected area is calculated to be 0.039 m . The drag sail is assumed to stabilize the atti- tude of spacecraft such that it projects the sail eective area to the atmosphere [29]. 3 Results 0 2 4 6 8 10 To demonstrate the eect of a time varying atmosphere Solar cycle start year (b) the UKube-1 spacecraft is used as a case study. Along- Fig. 2 UKube-1 de-orbit characteristics: (a) time and (b) side an analysis of the likely behavior of UKube-1, two volume swept, as aected by de-orbit start epoch through hypothetical cases are considered, both assuming that solar cycle. Volume swept (km ) Total deorbit time (year) 114 E. Kerr, M. Macdonald lifetime beyond the current cycle. This does introduce spacecraft decays naturally due to atmospheric friction uncertainties on the order of magnitudes, providing an on the tumbling spacecraft's projected area alone until indicative insight rather than a prediction. Until solar the appropriate deployment date, at which time the drag cycle modelling becomes more accurate using an averaged augmentation device is deployed. The appropriate date cycle is the only prudent approach. The average cycle is mission speci c. Thus, the likely volume swept can used herein was statistically derived from previous cycles be calculated using a Monte Carlo analysis with the de- and has a mean of 140 sfu. Further, the atmospheric ployment date during the solar cycle as the variable. In density model used can have a signi cant impact on the comparison to the \immediate deployment" case, except orbit lifetime and, hence, volume swept. Herein, the ana- for the period around solar maximum, the de-orbit time lytical model developed by Kerr and Macdonald based on increases, but the volume swept is considerably reduced. JB2008 is used [24]. JB2008 is the model recommended As shown in Fig. 2(a), both the \immediate deployment" in the 2012 Committee on Space Research International and \delayed deployment" cases decrease or maintain the Reference Atmosphere for total atmospheric mass den- de-orbit lifetime, compared to the \no deployment" case. sity calculation [30]. Kerr and Macdonald developed an It is also noted in this gure that the time for delayed interpolated form of JB2008 and a density index allowing deployment signi cantly increases at approximately year direct incorporation of solar activity [24]. seven of the solar cycle as this is the latest point that In Fig. 2, \no deployment" denotes the case of decaying the deployment can be made within the cycle, beyond naturally due to atmospheric friction assuming random this point deployment must be delayed until after the tumbling with no de-orbit device. \Immediate deploy- next solar minimum. Resulting in a step-change in de- ment" and \delayed deployment" denote the hypothetical orbit time. It is concluded that delayed deployment is a cases of a 10 m drag augmentation device. The solar satisfactory compromise. activity cycle start years of zero and ve correspond to As the method is semi-analytical, see Table 2, the the average solar activity cycle minimum and maximum identi ed trends will be mathematically consistent with respectively. reduced duration and/or altitude variation case studies. Figure 2 shows that the date during the solar activity For example, considering only the period between two cycle, at which de-orbit begins, has a signi cant eect on altitude bands rather than until de-orbit is complete, this both the de-orbit lifetime and the volume swept during means that the identi ed trends will be consistent through de-orbit. A minimum in both can be observed approxi- regions of dense debris, as well as regions of sparse debris. mately 3{5 years into the solar activity cycle, just prior However, considering the current space object population to the maximum of the solar activity cycle. Figure 2(b) can provide further insight. Figure 3 shows a histogram has been truncated to highlight the detail. However, in of the percentage of regularly tracked objects from the the full gure it could be seen that if deployment occurs current catalogue in 100 km altitude bins . at approximately year 4, the volume swept is an order of It can be seen in Fig. 3 that around 60% of the cata- magnitude lower than if deployment occurred at the solar logued objects are at altitudes in the range 700{1000 km. activity cycle minimum (year 0/year 11). Thus, while Ideally, an object would spend as little time, and sweep as orbit lifetime is always reduced, often drastically, by in- little volume as possible in these highly populated regions troducing a drag augmentation device, the volume swept during the de-orbit phase. By calculating the volume is often increased. Drag augmentation should therefore swept by a spacecraft in each region, a weighted metric is only be used during, or just prior to, the maximum of proposed that considers the volume swept through more a solar activity cycle. However, end-of-mission cannot populated regions as a greater risk than the same volume always be predicted or guaranteed to coincide with this swept in a region with a lower percentage population of period. Therefore, when using a drag augmentation de- objects. This allows operators to consider this increased vice, it should be capable of delaying deployment from risk during initial mission design. Figure 4 shows the the end-of-mission and spacecraft decommissioning to volume swept by UKube-1 in each region, (a) without ensure that deployment coincides with the maximum and (b) with a drag sail deployed. of the upcoming solar activity cycle. Hence, the third As given in the Space-Track TLE catalogue, obtained from www. case considered, explicitly detailed in Table 2, where the space-track.org on July 06, 2020. Limits of drag augmentation at spacecraft end-of-mission and a mitigation strategy 115 altitude, consequently less volume is swept in the 600{ 700 km region than in the 500{600 km region. Note that a similar rational explains the dierent shape of the line in Fig. 4(a) for the 600{700 km region in comparison to other altitude bins. This is primarily driven by the orbit lifetime and initial altitude; with de-orbit beginning at or just after a solar maximum and failing to complete prior to solar minimum, resulting in an increased volume being swept until solar activity again increases. The peak of this initial altitude bin is displaced as the spacecraft only 0 200 400 600 800 1000 1200 1400 1600 1800 2000 transits, approximately, the bottom quarter of it. Altitude bin (km) Fig. 3 Population of objects in LEO separated into 100 km Using the population density in each region, a weighted altitude bins. volume swept is calculated as P + N VS = VS (4) PW Total VS 100–200 km 200–300 km where VS is the population weighted volume swept, PW 300–400 km 400–500 km VS is the volume swept, P is the number of objects 500–600 km 600–700 km in the region of interest, and N is the total number of objects. This formulation provides a concise means to 50 represent the local density of objects in a given region of space, providing a means of assessing collision risk. Figure 5 shows the volume swept by UKube-1 with and 0 1 2 3 4 5 6 7 8 9 10 11 Solar cycle start year without the population weighting, denoted by \integrated (a) 200 risk". Total VS No deployment 160 100–200 km Immediate deployment 200–300 km Integrated risk no deployment 140 300–400 km Integrated risk immediate deployment 400–500 km 160 500–600 km 600–700 km 140 0 1 2 3 4 5 6 7 8 9 10 11 Solar cycle start year (b) 0 0 1 2 3 4 5 6 7 8 9 10 11 Fig. 4 Volume swept by UKube-1 during deorbit in dierent Solar cycle start year regions: (a) without and (b) with 10 m drag sail deployed, Fig. 5 Volume swept by UKube-1 (with and without inte- as aected by deorbit start date through solar cycle. grated risk) during de-orbit as aected by de-orbit start date through solar cycle. UKube-1 has a relatively low initial altitude so it spends no time in the highly populated regions, between 700 and It can be seen in Fig. 5 that the volume swept in both 1000 km. With the exception of the rst altitude bin, cases with the integrated risk is higher, as expected. UKube-1 will sweep less volume in each successive bin as However, the volume swept is not signi cantly altered altitude loss accelerates due to the increasing atmospheric in either case. This is primarily due to the low initial drag force. The volume swept in the rst altitude bin is altitude of UKube-1, aording it a safer de-orbit overall. dependent on the initial altitude within that bin. UKube- Figures 4 and 5 have been reproduced in Figs. 6 and 7, 1 began the de-orbit phase at approximately 628 km using the hypothetical case of UKube-1 having an initial 3 3 Percentage of spacecraft (%) Volume swept (km ) Volume swept (km ) Volume swept (km ) 116 E. Kerr, M. Macdonald higher initial altitude, that if the spacecraft deploys the drag sail at the least opportune moment during the solar Total VS 500–600 km 100–200 km 600–700 km activity cycle (around 8{9 years through the solar activity 200–300 km 700–800 km 300–400 km 800–900 km cycle) that the eect of the weighting is greater than if 400–500 km the solar activity cycle is exploited (with sail deployment occurring at 3{5 years). This indicates that the worst- 600 case scenario introduces more risk than can be determined by than volume swept alone, as the larger volume is being swept out of the most populated regions. Furthermore, the ideal deployment window (speci cally, the window 0 1 2 3 4 5 6 7 8 9 10 11 Solar cycle start year when the immediate deployment volume swept is less (a) 1800 than the no deployment volume swept) is reduced, and Total VS thus the possibility of a random failure occurring at an 100–200 km 200–300 km inopportune moment is increased. Thus, reinforcing the 1400 300–400 km 400–500 km 500–600 km argument for a delayed deployment capability. 600–700 km 700–800 km 800–900 km 4 Discussion Several major consequences of delayed deployment should be considered. First, increasing the time to deorbit po- tentially increases the risk of an unplanned break-up. The challenge of designing a sub-system that must re- 0 1 2 3 4 5 6 7 8 9 10 11 Solar cycle start year main idle for up to eight years, after end-of-mission, then (b) Fig. 6 Volume swept by UKube-1 (initial altitude 900 km) assuredly activate and deploy a drag augmentation device during deorbit in dierent regions: (a) without and (b) with from a tumbling spacecraft will also potentially increase 10 m drag sail deployed, as aected by deorbit start date the failure risk rate and/or system complexity, and hence through solar cycle. likely cost. The lack of complexity and low sub-system cost are the current attractors of the drag augmenta- tion concept. The outcome of any collision should also be considered. Although the volume swept is increased by the introduction of a drag augmentation device, a collision with the thin lm of the sail area is less likely to cause catastrophic damage. Therefore, although the collision risk increases, a directly proportional increase in liability risk cannot be assumed as this would require a No deployment Immediate deployment Integrated risk no deployment statistical analysis of the space object population coupled Integrated risk immediate deployment with the probability of the object being de-orbited, with 0 1 2 3 4 5 6 7 8 9 10 11 Solar cycle start year and without a drag augmentation device, having a con- Fig. 7 UKube-1 (initial altitude 900 km) volume swept, junction with another space object from that population. with and without integrated risk, during de-orbit as aected However, in not implementing the delayed deployment by de-orbit start date through solar cycle. method operators tacitly accept the potential for an in- altitude of 900 km to show the result of passing through crease in volume swept and hence the increased risk of a a more populated region. collision occurrence, catastrophic or not. It can be seen in Figs. 6 and 7 that the impact of the Noting that on-orbit liability is fault-based, a terres- weighting is more prominent for a case with a higher trial analogy can be made. In 1947, the United States initial altitude. In comparing the untruncated versions of America Court of Appeals for the Second Circuit pro- of Figs. 5 and 7, it could be more clearly seen for the posed a test to determine the standard of care for the tort 3 3 3 Volume swept (km ) Volume swept (km ) Volume swept (km ) Limits of drag augmentation at spacecraft end-of-mission and a mitigation strategy 117 of negligence, this was the rst-time calculus was used to determine liability. The judgment was written by Judge Learned Hand wherein he described what is now termed the calculus of negligence, or the Learned Hand formula, an algebraic formula, B = P L. From this, liability is based on the relation between investment in precaution B and the product of the probability P and magnitude L of resulting harm. Where P L exceeds B, the defendant should be liable, where B is equal to or greater than P L, the defendant should not be held liable [31]. The applica- tion of the Learned Hand formula in outer space has not been much discussed; however by increasing the prob- ability of a collision the Learned Hand formula implies a reckless act, in which case spacecraft operators who inappropriately deploy a drag augmentation device, and hence the State Party that licensed the operation, could be argued liable for any subsequent on-orbit collision. Depending on the outcome of a collision an argument could be made to limit liability, as the introduction of an inappropriately deployed drag augmentation device would have increased the probability, P , but may also have decreased the magnitude of resultant harm, L. This assumes that collision occurred with the sail area rather Fig. 8 CanX-7 deorbit characteristics, (a) time and (b) than the main spacecraft body, resulting in, likely, less volume swept, as aected by de-orbit start epoch through than catastrophic damage. However, as the collision is solar cycle. an unpredictable event, the only responsible path for In comparison to the UKube-1 case study, delayed space actors, and those who license them, is to reduce the probability of any type of collision occurring in the deployment now shows a marked improvement over the rst place. no deployment cases. This is due to the duration of the no deployment case exceeding a single solar cycle, as Of note, the technology demonstration mission CanX- such the delayed deployment provides a much shorter 7 is currently on-orbit and deployed a drag sail in May lifetime. A resultant smaller volume swept is also re- 2017 [29], just ahead of a solar minimum, after the end alised. CanX-7 deployed its drag sail at an inopportune of its operational life. In doing so the operators of CanX- moment, in a non-truncated version of Fig. 8(b) it could 7 have, perhaps unwittingly, increased the on-orbit colli- be seen that during the theoretical average solar cycle sion risk of the spacecraft. Figure 8 recreates the analysis used herein the deployment on May 3, 2017 produces an completed in the prior section for UKube-1, for CanX-7. estimated volume swept of 605 km in comparison to It shows the eect of varying the epoch through the solar the 160 or 98 km produced in the no deployment activity cycle at which de-orbit begins on the de-orbit lifetime and the volume swept during de-orbit. Note that and delayed deployment cases respectively for that date. Ideally, given that CanX-7 was a technology demonstra- once again the analysis in Fig. 8 is for start epochs spaced tor mission primarily designed to demonstrate a drag evenly through an average solar cycle, and is hence not sail, the operators of CanX-7 should have delayed its linked to the actual deployment date. However, note the addition of the vertical line showing the actual deploy- launch for around 6.5 years, and then launched and per- ment epoch of the CanX-7 drag sail. As Fig. 8 assumes formed immediate deployment during November 2023. an average solar cycle it gives only an indicative in-sight This scenario would have produced a total volume swept 3 3 3 rather than a prediction. of 56 km (55 km by the sail and 1 km by the 118 E. Kerr, M. Macdonald spacecraft body) based on the average solar cycle data spacecraft operators who plan to inappropriately deploy used herein. If they had done so CanX-7 would have a drag augmentation device, and hence the State Party swept the least total volume possible, minimizing both that licensed them, could be argued liable for any sub- the risk of a collision occurrence and the risk posed by sequent on-orbit collision. Therefore, it is recommended that collision. that these licensing authorities consider prior, and any It is important to note that the mitigation strategy of future approval to deploy such devices as that State Party delayed deployment is most eective if the drag augmen- could bear international responsibility for any subsequent tation device is of sucient size to cause the spacecraft collision. to de-orbit over one solar activity maximum period. The device may therefore have to be larger than would be Acknowledgements required to de-orbit over the minimum required period The authors thank Dr. Lesley Jane Smith of Leuphana of 25 years given by the debris mitigation guidelines. University of Luneburg for her discussions on the use Finally, one unquanti able risk, not considered herein, of the Learned Hand formula with regard to liability in is that by delaying deployment, and therefore increasing space. This work received funding from the European time on-orbit, an increased on-orbit population could be Union's Horizon 2020 research and innovation program encountered at the time of deployment. Thus, the colli- under grant agreement No. 687295. sion, or integrated risk would also be increased. However, there is no way to accurately predict future populations References and regulatory practice focuses on the current situation, and the eect of any action on existing space actors and [1] Kelso, T. S. Analysis of the 2007 Chinese ASAT test and objects. the impact of its debris on the space environment. In: Proceedings of the 8th Advanced Maui Optical and Space Surveillance Technologies Conference, 2007: 321{330. 5 Conclusions [2] Kelso, T. S. Analysis of the Iridium 33-Cosmos 2251 Rather than reduce the risk of an on-orbit collision oc- collision. In: Proceedings of the 19th AIAA/AAS Astro- curring, as is widely held, the orbit removal concept dynamics Specialist Conference, 2009: AAS 09{368. [3] Heidt, H., Puig-Suari, J., Moore, A., Nakasuka, S., known as drag augmentation often increases the risk. Twiggs, R. CubeSat: A new generation of picosatellite This increase is induced by the solar activity cycle, which for education and industry low-cost space experimenta- causes Earth's atmosphere to be time-variant and dy- tion. In: Proceedings of the 14th AIAA/USU Conference namic. Drag augmentation should therefore ideally only on Small Satellites, 2000: SSC01-VIIIb-5. be used during, or just prior to, the maximum of a so- [4] National Academies of Sciences, Engineering, and lar activity cycle. However, end-of-mission cannot be Medicine. Achieving Science with CubeSats: Thinking guaranteed to coincide with this period. Therefore, when inside the Box. Washington, D.C.: National Academies using a drag augmentation device, it should be capable of Press, 2016. delaying deployment from the end-of-mission and space- [5] United Nations Committee on the Peaceful Uses of Outer craft decommissioning for up to eight years and should Space Legal Subcommittee. Treaty on principles gov- erning the activities of states in the exploration and use be able to deploy from a tumbling, otherwise passivated of outer space, including the Moon and other celestial spacecraft. This new requirement likely increases sys- bodies, 1966. tem complexity, and hence cost; the lack of complexity [6] United Nations Committee on the Peaceful Uses of Outer and low-cost being the current attractors of the concept. Space Legal Subcommittee. 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UKube-1: operations and lessons learned. In: In: Proceedings of the 4th International Symposium on Proceedings of the 8th European CubeSat Symposium, Solar Sailing, 2017. [15] Visagie, L., Lappas, V., Erb, S. Drag sails for space [28] Information on http://celestrak.com/ (cited 11 July debris mitigation. Acta Astronautica, 2015, 109: 65{75. 2018). [16] Forshaw, J. L., Aglietti, G. S., Navarathinam, N., Kad- hem, H., Salmon, T., Pisseloup, A., Jore, E., Chabot, [29] Cotton, B., Bennett, I., Zee, R. E. On-orbit results from T., Retat, I., Axthelm, R. et al. RemoveDEBRIS: An the CanX-7 drag sail deorbit mission. In: Proceedings of in-orbit active debris removal demonstration mission. the 31st Annual AIAA/USU Small Satellite Conference, Acta Astronautica, 2016, 127: 448{463. [17] Forshaw, J. L., Aglietti, G. S., Salmon, T., Retat, I., [30] Commitee on Space Research. COSPAR International Roe, M., Burgess, C., Chabot, T., Pisseloup, A., Phipps, Reference Atmosphere, 2012. A., Bernal, C., et al. Final payload test results for the [31] Grossman, P. Z., Cearley, R. W., Cole, D. H. Uncer- RemoveDebris active debris removal mission. Acta As- tainty, insurance and the Learned Hand formula. Law, tronautica 2017, 138: 326{342. Probability and Risk, 2006, 5(1): 1{18. [18] Guglielmo, D., Omar, S., Bevilacqua, R. Drag de-orbit device: A new standard reentry actuator for CubeSats. Journal of Spacecraft and Rockets, 2018, https://doi. Emma Kerr is currently working org/10.2514/1.A34218. as a space safety engineer and [19] Werner, D. Drag sails could counter debris. Aerospace project manager for Deimos Space America, 2017. UK Ltd. She received her Ph.D. [20] Information on http://news.bbc.co.uk/1/hi/8590103.stm degree in aerospace engineering from (cited 11 July 2018). the University of Strathclyde, UK, [21] Information on https://www.bbc.co.uk/news/science- where she also worked as a research environment-43584070 (cited 11 July 2018). assistant. Following her Ph.D. degree, [22] Ahmadloo, H., Zhang, J. De-orbiting collision risk as- Emma worked as a post-doctoral fellow for the Space sessment and detailed orbital simulation of LEO space Environment Research Centre based at RMIT University, debris removal drag sail. In: Proceedings of the 9th Australia, specialising in space weather and atmospheric Asian-Paci c Conference on Aerospace and Science/the density eects on orbit propagation. 120 E. Kerr, M. Macdonald Malcolm Macdonald is professor mons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in and chair of applied space technology at University of Strathclyde, working any medium or format, as long as you give appropriate credit at the interface between academia, in- to the original author(s) and the source, provide a link to dustry, and government. His work the Creative Commons licence, and indicate if changes were made. aims to enable and develop new space- derived services through advancing a The images or other third party material in this article are range of new technologies, challenging included in the article's Creative Commons licence, unless conventional ideas, and working at the interface between indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and disciplines to advance new concepts in the exploration and exploitation of space. He is a fellow of the Royal Aero- your intended use is not permitted by statutory regulation or nautical Society, and an associate fellow of the AIAA. exceeds the permitted use, you will need to obtain permission E-mail: Malcolm.macdonald.102@strath.ac.uk. directly from the copyright holder. To view a copy of this licence, visit http:// Open Access This article is licensed under a Creative Com- creativecommons.org/licenses/by/4.0/.

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