AC5 Collision prob v5

0339-EX-PL-2013 Text Documents

Aerospace Corporation, THE

2013-11-19ELS_143114

AeroCube 5 Drag Enhancement Device • In order to comply with the 25-year LEO de-orbit requirement, a passive electrodynamic tether is deployed from AC5 bus. – Orbit decays y faster due to electrodynamic y force – Increase in surface area also increases orbit decay rate (atmospheric drag) • The tether has an end mass plate for stabilization. stabilization The electrodynamic forces should passively stabilize the spacecraft and deployed tether system in a gravity gradient configuration. – Device provided by a commercial company Tethers Unlimited Inc. – Total device mass = 85 grams – Tether tape dimensions (12 m length, 75 mm wide) – End plate dimensions (100 mm x 83 mm x 6.5 mm) – Deployed two years after spacecraft operations are complete A-110513-1 1

AeroCube 5.0 Case Descriptions Case 1 • 4 intact cases were considered: C Case 2 1. AeroCube body only (assumes average tumble configuration) • Assumes tether is not deployed. ram direction 2. AeroCube and tether device deployed (assumes gravity gradient stabilization) • Tether system is fully deployed and in a gravity gradient nadir stabile orientation until reentry. Case 3 3. AeroCube and tether device deployed (gravity gradient stabilization with libration of the tether of ~30 degrees from nadir) • Tether system deployed but uncertainty in the stabilization 30 degrees effects ff t – Assumption taken from conversations with Nestor Voronka ram direction and Rob Hoyt of Tethers Unlimited 4. AeroCube and tether device deployed (alignment with nadir velocity vector with libration of the tether of ~30 degrees from the velocity vector ) • A different orientation to determine the range of lifetimes. Case 4 ram direction 30 degrees A-110513-1 2

AeroCube 5.0 Initial Conditions • Area estimation: The AeroCube 5 satellite core body is 10.26 x 10.26 x 17.02 cm – Case 1: AeroCube body (assuming tumble) area = 0.023 m2 – Case 2: AeroCube body + tether system (gravity gradient alignment) with = 0.596 m2 – Case 3: AeroCube body + tether system (gravity gradient alignment with 30 degree libration about nadir)= 0.559 m2 – Case 4: AeroCube body + tether system (velocity vector alignment with 30 degree libration about ram direction) = 0.314 m2 – All areas with tether take into account twist twist. • Ref. Noord, J.L., West, B., Gilchrist, B., “Electrodynamic Tape Tether Performance with Varying Tether Widths at Low Earth Altitudes.”, AIAA, 39th Aerospace Sciences Meeting & Exhibit, Reno, NV, 2001 • Mass estimate: 2.08 kg – Includes cubesat + tether drag device • Atmospheric Assumption: Considered 50th percentile (nominal) level of solar flux (F10.7 ) and geomagnetic index (Ap) – U Usedd NASA Marshall M h ll SSpace Fli Flight ht C Center t monthly thl predictions di ti (b (based d on NOAA data) d t ) from f October 2013 to 2030; for years after 2030, repeated last 11-years (2019-2030) of Marshall predicted data • Initial orbit (provided by David Hinkley) o – 469 x 972 km perigee/apogee altitude, altitude 120 Inclination, Inclination Epoch: December 1 1, 2013 A-110513-1 3

AeroCube 5.0 Initial Conditions (cont’d) • NASA Standard 8719.14A requires consideration of the case in which the tether is severed at the half-way point (assumed here to occur right after deployment) • Severed tether half attached to AC5 – Area estimation: • Case 2: AeroCube body + half tether (gravity gradient alignment) with = 0.309 0 309 m2 • Case 3: AeroCube body + half tether (gravity gradient alignment with 30 degree libration about nadir)= 0.290 m2 • Case 4: AeroCube body + half tether (velocity vector alignment with 30 degree libration about ram direction) = 0 161 m2 0.161 – Mass estimate: 2.004 kg • Includes cubesat + half tether • Severed tether half attached to end plate – Area estimation: • Case 2: End plate+ half tether (gravity gradient alignment) with = 0.287 m2 • Case 3: End plate + half tether (gravity gradient alignment with 30 degree libration about nadir)= 0.269 m2 • Case 4: End plate + half tether (velocity vector alignment with 30 degree libration about ram direction) = 0.153 m2 – Mass estimate: 0.048 kg • Includes end plate + half tether A-110513-1 4

Long-Term Orbit Propagation • Precision integration code TRACE was used to propagate the upper stage – MSISE-86 atmosphere model – 70 x 70 modified WGS84 Earth gravity model – Sun and Moon gravity – Solar radiation p pressure ((assumed reflectivity y coefficient = 1.3)) • Primary source of uncertainty is solar activity, which affects atmospheric density and hence drag – Used MSFC monthly predictions (based on NOAA data) from October 2013 to 2030; for years after 2030, repeated last 11-years (2019-2030) of Marshall predicted data – Used 5, 50, and 95 percentile levels of solar flux (F10.7 ) and geomagnetic index ((Ap) • Did not model electrodynamic force – Conservative assumption for lifetime – Tether T th length l th iis ttoo short h t ttoo produce d significant i ifi t electrodynamic l t d i fforce A-110513-1 5

Collision Probability Assessment • Used an orbit trace crossing (OTC) method – All crossings of the orbit traces of the primary object (AC5) and the secondary (background) objects as they evolve are determined • Used TRACE evolution results – The collision probability at each crossing is computed assuming the in-track position iti off th the b background k d object bj t iis uniformly if l di distributed t ib t d over 360 d deg – Collision probabilities are accumulated across all OTCs over the probability assessment time interval A-110513-1 6

Computation of Collision Radius • Collision probability at an orbit trace crossing depends on the collision radius • For AC5 cases with no tether (Cases1, (Cases1 5, 5 and 9) – The primary (AC5) mean contact radius was computed by randomly picking unit vectors in three dimensions, using a simple rectangle model to represent the surfaces, and computing the root mean square – For each primary/background object pair, the combined mean collision radius is the sum of the fixed AC5 mean contact radius and the contact radius of the background object • For AC5 cases with a tether ((Cases 2-4,, 6-8,, 10-12)) – The combined mean collision radius is computed using a formulation that uses the AC5 tether configuration length and width (including cube sat and end plate) and the background object contact radius (assumes 3D random orientation of straight AC5 tether configuration) • Contact radii of the secondary objects are from the ADEPT model (see following slides) A-110513-1 7

Background Objects • Used the Aerospace Debris Environment Projection Tool (ADEPT) model of the current and future background population (Ref. 4) – Model includes orbit trajectories j and sizes for each object j – Extends from LEO to GEO – Selected the “Non-Compliance” population (see Ref. 4) – Retained objects larger than 10 cm for this study • Model projects out 200 years and includes the following populations: – 0th generation objects: Recent unclassified catalog population, a statistically- derived population of unknown objects (difference between cataloged and tracked populations) and a representation of future launched objects populations), – 1st generation debris from future explosions and from collisions between 0th generation objects (100 Monte Carlo scenarios) – 2nd g generation debris from collisions between 0th and 1st ggeneration objects j was not included in the upper stage collision probability analysis (contribution is small) A-110513-1 8

Collision Probability MSFC 5th percentile solar cycle, Cases 1 and 2 • The plot shows cumulative collision probability vs. time for AC5 for the MSFC 5th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 for all cases Case 2 (tether in gravity gradient Case 1 (no tether) alignment, no libration) NASA Standard 8719.14A threshold NASA Standard 8719.14A threshold min = 8.69 x 10-4 avg = 8.98 x 10-4 min = 7.32 x 10-5 max = 9.33 x 10-4 avg = 7.45 x 10-5 max = 7.64 x 10-5 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 9

Collision Probability MSFC 5th percentile solar cycle, Cases 3 and 4 • The plot shows cumulative collision probability vs. time for AC5 for the MSFC 5th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 for all cases Case 3 (tether in gravity gradient Case 4 (tether in velocity alignment with libration) alignment with libration) NASA Standard 8719.14A threshold NASA Standard 8719.14A threshold min = 7.88 x 10-5 avg = 8.01 x 10-5 min = 1.34 x 10-4 max = 8.23 x 10-5 avg = 1.36 x 10-4 max = 1.40 x 10-4 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 10

Collision Probability MSFC 50th percentile solar cycle, Cases 1 and 2 • The plot shows cumulative collision probability vs. time for AC5 for the MSFC 50th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 for all cases Case 2 (tether in gravity gradient Case 1 (no tether) alignment, no libration) NASA Standard 8719.14A threshold NASA Standard 8719.14A threshold min = 3.27 x 10-4 avg = 3.35 x 10-4 min = 4.95 x 10-5 max = 3.53 x 10-4 avg = 5.03 x 10-5 max = 5.16 x 10-5 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 11

Collision Probability MSFC 50th percentile solar cycle, Cases 3 and 4 • The plot shows cumulative collision probability vs. time for AC5 for the MSFC 50th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 for all cases Case 3 (tether in gravity gradient Case 4 (tether in velocity alignment with libration) alignment with libration) NASA Standard 8719.14A threshold NASA Standard 8719.14A threshold min = 5.02 x 10-5 avg = 5.10 x 10-5 min = 7.99 x 10-5 max = 5.23 x 10-5 avg = 8.12 x 10-5 max = 8.35 x 10-5 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 12

Collision Probability MSFC 95th percentile solar cycle, Cases 1 and 2 • The plot shows cumulative collision probability vs. time for AC5 for the MSFC 95th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 for all cases Case 2 (tether in gravity gradient Case 1 (no tether) alignment, no libration) NASA Standard 8719.14A threshold NASA Standard 8719.14A threshold min = 1.63 x 10-4 avg = 1.68 x 10-4 min = 3.90 x 10-5 max = 1.77 x 10-4 avg = 3.96 x 10-5 max = 4.10 x 10-5 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 13

Collision Probability MSFC 95th percentile solar cycle, Cases 3 and 4 • The plot shows cumulative collision probability vs. time for AC5 for the MSFC 95th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 for all cases Case 3 (tether in gravity gradient Case 4 (tether in velocity alignment with libration) alignment with libration) NASA Standard 8719.14A threshold NASA Standard 8719.14A threshold min = 3.93 x 10-5 avg = 3.99 x 10-5 min = 4.78 x 10-5 max = 4.11 x 10-5 avg = 4.86 x 10-5 max = 5.01 x 10-5 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 14

Collision Probability for Severed Tether Half Attached to AC5 MSFC 5th percentile solar cycle, Case 2 • The plot shows cumulative collision probability vs. time for the severed tether half attached to AC5 for the MSFC 5th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 Case 2 (tether in gravity gradient alignment, no libration) NASA Standard 8719.14A threshold min = 6.45 x 10-5 avg = 6.56 x 10-5 max = 6.88 x 10-5 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 15

Collision Probability for Severed Tether Half Attached to AC5 MSFC 5th percentile solar cycle, Cases 3 and 4 • The plot shows cumulative collision probability vs. time for the severed tether half attached to AC5 for the MSFC 5th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 for all cases Case 3 (tether in gravity gradient Case 4 (tether in velocity alignment with libration) alignment with libration) NASA Standard 8719.14A threshold NASA Standard 8719.14A threshold min = 7.10 x 10-5 avg = 7.20 x 10-5 min = 1.32 x 10-4 max = 7.53 x 10-5 avg = 1.34 x 10-4 max = 1.38 x 10-4 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 16

Collision Probability for Severed Tether Half Attached to AC5 MSFC 50th percentile solar cycle, Case 2 • The plot shows cumulative collision probability vs. time for the severed tether half attached to AC5 for the MSFC 50th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 Case 2 (tether in gravity gradient alignment, no libration) NASA Standard 8719.14A threshold min = 3.03 x 10-5 avg = 3.08 x 10-5 max = 3.18 x 10-5 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 17

Collision Probability for Severed Tether Half Attached to AC5 MSFC 50th percentile solar cycle, Cases 3 and 4 • The plot shows cumulative collision probability vs. time for the severed tether half attached to AC5 for the MSFC 50th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 for all cases Case 3 (tether in gravity gradient Case 4 (tether in velocity alignment with libration) alignment with libration) NASA Standard 8719.14A threshold NASA Standard 8719.14A threshold min = 3.28 x 10-5 min = 7.95 x 10-5 avg = 3.34 x 10-5 avg = 8.09 x 10-5 max = 3.53 x 10-5 max = 8.39 x 10-5 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 18

Collision Probability for Severed Tether Half Attached to AC5 MSFC 95th percentile solar cycle, Case 2 • The plot shows cumulative collision probability vs. time for the severed tether half attached to AC5 for the MSFC 95th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 Case 2 (tether in gravity gradient alignment, no libration) NASA Standard 8719.14A threshold min = 1.13 x 10-5 avg = 1 15 x 10-55 1.15 max = 1.22 x 10-5 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 19

Collision Probability for Severed Tether Half Attached to AC5 MSFC 95th percentile solar cycle, Cases 3 and 4 • The plot shows cumulative collision probability vs. time for the severed tether half attached to AC5 for the MSFC 95th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 for all cases Case 3 (tether in gravity gradient Case 4 (tether in velocity alignment with libration) alignment with libration) NASA Standard 8719.14A threshold NASA Standard 8719.14A threshold min = 1.19 x 10-5 avg = 1 21 x 10-5 1.21 max = 1.26 x 10-5 min = 2.68 x 10-5 avg = 2.73 x 10-5 max = 2.88 x 10-5 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 20

Collision Probability for Severed Tether Half Attached to End Plate MSFC 5th percentile solar cycle, Case 2 • The plot shows cumulative collision probability vs. time for the severed tether half attached to the end plate for the MSFC 5th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 Case 2 (tether in gravity gradient alignment, no libration) NASA Standard 8719.14A threshold min = 1.04 x 10-6 avg = 1 06 x 10-66 1.06 max = 1.10 x 10-6 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 21

Collision Probability for Severed Tether Half Attached to End Plate MSFC 5th percentile solar cycle, Cases 3 and 4 • The plot shows cumulative collision probability vs. time for the severed tether half attached to the end plate for the MSFC 5th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 for all cases Case 3 (tether in gravity gradient Case 4 (tether in velocity alignment with libration) alignment with libration) NASA Standard 8719.14A threshold NASA Standard 8719.14A threshold min = 1.03 x 10-6 avg = 1 05 x 10-6 1.05 min = 1.83 x 10-6 max = 1.12 x 10-6 avg = 1.87 x 10-6 max = 1.98 x 10-6 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 22

Collision Probability for Severed Tether Half Attached to End Plate MSFC 50th percentile solar cycle, Case 2 • The plot shows cumulative collision probability vs. time for the severed tether half attached to the end plate for the MSFC 50th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 Case 2 (tether in gravity gradient alignment, no libration) NASA Standard 8719.14A threshold min = 7.25 x 10-7 avg = 7 38 x 10-77 7.38 max = 7.71 x 10-7 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 23

Collision Probability for Severed Tether Half Attached to End Plate MSFC 50th percentile solar cycle, Cases 3 and 4 • The plot shows cumulative collision probability vs. time for the severed tether half attached to the end plate for the MSFC 50th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 for all cases Case 3 (tether in gravity gradient Case 4 (tether in velocity alignment with libration) alignment with libration) NASA Standard 8719.14A threshold NASA Standard 8719.14A threshold min = 7.61 x 10-7 avg = 7 75 x 10-7 7.75 min = 1.23 x 10-6 max = 8.23 x 10-7 avg = 1.25 x 10-6 max = 1.32 x 10-6 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 24

Collision Probability for Severed Tether Half Attached to End Plate MSFC 95th percentile solar cycle, Case 2 • The plot shows cumulative collision probability vs. time for the severed tether half attached to the end plate for the MSFC 95th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 Case 2 (tether in gravity gradient alignment, no libration) NASA Standard 8719.14A threshold min = 3.47 x 10-7 avg = 3 53 x 10-77 3.53 max = 3.72 x 10-7 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 25

Collision Probability for Severed Tether Half Attached to End Plate MSFC 95th percentile solar cycle, Cases 3 and 4 • The plot shows cumulative collision probability vs. time for the severed tether half attached to the end plate for the MSFC 95th percentile solar cycle profile (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 for all cases Case 3 (tether in gravity gradient Case 4 (tether in velocity alignment with libration) alignment with libration) NASA Standard 8719.14A threshold NASA Standard 8719.14A threshold min = 3.61 x 10-7 avg = 3 68 x 10-7 3.68 min = 6.54 x 10-7 max = 4.28 x 10-7 avg = 6.67 x 10-7 max = 6.92 x 10-7 Cumulative collision probability curves become h i horizontally ll fl flat after f re-entry A-110513-1 26

Collision Probability ”Peas” • The plots show cumulative collision probability vs. time for a single “pea” for all three MSFC solar cycle profiles (one curve for each of 100 Monte Carlo debris populations) • Collision probability < 0.001 for all cases MSFC 5th percentile MSFC 50th percentile MSFC 95th percentile AFI 91-217 threshold AFI 91-217 threshold min = 1.57 x 10-5 avg = 1.60 x 10-5 max = 1.69 x 10-5 min = 1 08 x 10-4 1.08 avg = 1.11 x 10-4 min = 3.59 x 10-5 max = 1.15 x 10-4 avg = 3.67 x 10-5 max = 3.97 x 10-5 Cumulative collision probability curves become horizontally flat after re-entry A-110513-1 27

Conclusions • The collision probability between AC5 and large background objects for all tether configurations considered is less than the 0.001 threshold in NASA Standard 8719.14A 8719 14A • The collision probability between the severed tether halves and large background objects for all tether configurations considered is less than the 0.001 threshold in NASA Standard 8719.14A • The collision probability between the “peas” and large background objects is less than the 0.001 threshold in NASA Standard 8719.14A A-110513-1 28


Document Created: 2013-11-05 17:58:10
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