1. © The Aerospace Corporation 2015 CubeSat Collision Probability Analysis Andrew J. Abraham Roger C. Thompson Mission Analysis & Operations Department Systems Engineering Division June 10, 2015

2. Background Which poses a greater risk to resident space objects: –Case 1: 1 satellite with a cross-sectional area of 1m 2 or… –Case 2: 100 satellites, each with a cross-sectional area of 0.01m 2 ? Holding the remaining parameters fixed (except true anomaly) what is the difference in –Collision risk –Conjunction frequency This information is useful when addressing the influence cubesat constellations may have to the safety, operations, and efficiency of other satellite constellations –Conjunction/collision assessments have operational impact even if maneuvers are not required –Increasing number of collision avoidance maneuvers may increase cost This study will illustrate these concerns by creating a hypothetical cubesat constellation and assessing its impact to a large Resident Space Object (RSO) constellation with 66 members (Ex: Iridium) 2

3. Case 1: One Satellite vs. Constellation 3 Red: 1 Satellite –780km altitude –51.65 o inclination –Circular –0 o RAAN –Cross-Sectional-Area: 1.00m 2 Cyan: RSO Constellation –780km altitude –86.4 o inclination –Circular –6 planes (0 o,30 o,60 o,90 o,120 o,150 o ) –Cross-Sectional-Area: 33.02m 2

4. Case 2: 100 CubeSats vs. Constellation Red: 100 CubeSats –780km altitude –51.65 o inclination –Circular –0 o RAAN –Cross-Sectional-Area: 0.01m 2 –Spaced in True Anomaly Cyan: RSO Constellation –780km altitude –86.4 o inclination –Circular –6 planes (0 o,30 o,60 o,90 o,120 o,150 o ) –Cross-Sectional-Area: 33.02m 2 4

5. Conjunction & Probability 5 v2v2 RSO v1v1 Small Sat Probability dominated by 3 factors: –Miss distance –Small Sat’s large uncertainty RSO’s uncertainty is negligible by comparison –RSO’s large Cross Sectional Area CSA is summed between target and projectile Small Sat’s CSA is negligible by comparison Makes no difference if Small Sat represents Case 1 or Case 2 (i.e. 34.02m 2 and 33.03m 2 are nearly identical) Conjunctions are defined as any approach that is closer than 50 km 1-σ Uncertainty ellipsoid of RSO 1-σ Uncertainty ellipsoid of Small Sat

6. Conjunction Illustration 6

7. Impact Probability Between Constellation and CubeSats/Single-Sat

8. Conjunctions Between Constellation and CubeSats/Single-Sat

9. Results 9 Conjunctions (50km) MinMax Mean Case 1: Single Sat (1m 2 )01577.0 Case 2: 100 CubeSats (0.01m 2 )218470346.9 Case 2/Case 1Undef3x50x Impact Risk (Impacts/30-days) MinMax Mean Case 1: Single Sat (1m 2 )06.0E-52.2E-6 Case 2: 100 CubeSats (0.01m 2 )2.0E-51.1E-46.5E-5 Case 2/Case 1Undef2x30x

10. Conclusions Proliferation of CubeSats can pose a significant conjunction/collision risk –Small size of CubeSats does not significantly reduce risk Sum of hard-body radii is the dominate factor (assuming covariance is similar) The collision risk between a large satellite and a CubeSat is not significantly less than the risk between a large satellite and a 1 m 2 object –Larger number of conjunctions increase risk A CubeSat constellation can significantly increase the number and frequency of conjunctions compared to a monolithic satellite architecture –Increases the number of collision avoidance assessments that must be taken Collision assessment must be done even if no maneuver is required –Require more resources from other satellite operators (avoidance maneuvers, computational resources, manpower) The issue of long-term disposal of CubeSats should not be ignored 10

11. © The Aerospace Corporation 2015 Backup Slides

12. DART DART stands for the Debris Analysis Response Tool Provides satellite collision risk assessment resulting from a debris producing event in space. History: Developed in 2007 as a result of the Chinese ASAT test that destroyed the FY-1C spacecraft Semi-analytic propagator –MSISE-00 atmosphere model –Sun and moon gravity –Solar radiation pressure

13. © The Aerospace Corporation 2015 Approved for Public Release 1C08B9885DAEB5A188257E4400545DD1