1. The effect of modelling assumptions on predictions of the space debris environment R. Blake and H.G. Lewis Astronautics Research Group, Faculty of Engineering & the Environment, University of Southampton, UK IAC-14-A6.2.4

2. Evolutionary models are used to guide technical solutions to the space debris problem –These tools incorporate simplified models for estimating orbital motion and collision probability, for example –Simulations using these models make assumptions to reduce the many degrees of freedom that exist Some research has already been done to understand the influence of assumptions made about external drivers (e.g. solar activity) Little research has been done to understand the influence of the model simplifications/assumptions Introduction Focus of this presentation is the Cube approach

3. External drivers Solar activityLaunch traffic Explosions Compliance with mitigation measures

4. Evaluates collision probabilities between orbiting objects using a “sampling in time” approach: Number of collisions: Collision rate: Spatial density: The Cube Approach U d

5. Two identical objects i and j in circular, polar orbits of a = 7000 km and intersecting at 90  : Idealised case Relative velocity: Residential probability:

6. Collision rate for this case: Idealised case Combined collision cross-sectional area:

7. Space Debris Environment Tool Kit: –Orbit propagator & Cube approach implemented in Python Implementation in SDETK ParameterValue 2009 3009 t s+1 - t s (days)0.5, 0.05 and 0.005 d (km)1, 10 and 100

8. Comparison of collision rates: Theory v Implementation in SDETK

9. Collision rate is inversely proportional to the cube size: Increasing time-interval or decreasing cube size reduces the consistency of collision rate estimates –Cube sizes ≥ 10 km, and –Time-intervals  0.05 days, are preferred Increasing the number of Monte Carlo runs also enables good sampling of the space Findings Computational cost

10. DAMAGE: full LEO-to-GEO evolutionary model –Uses target-centred version of Cube: Cube Implementation in DAMAGE Identifies all cases where a debris object resides within a bounding sphere centred on the target Size of volume element is proportional to the size of the cube element

11. 11 LEO 10 cm Population (May 2009) ESA MASTER 2009 population seen in DAMAGE 29,370 objects ≥ 10 cm

12. Overall collision rate estimates: DAMAGE Results

13. For the idealised, two-object case the number of co- occurring pairs in the cube remains constant but the volume increases (A): collision rate decreases In DAMAGE simulation, the number of unique co- occurring pairs in each cube increases as volume increases (B) or (C): overall collision rate appears ~constant DAMAGE Results ABC

14. Collision rate between two orbiting objects is inversely proportional to the cube size: –Shown in theory –Observed in SDETK implementation Increasing number of Monte Carlo runs and cube size, or decreasing time-interval improves the consistency of collision rate estimates –Default parameters in DAMAGE (and other evolutionary models using Cube) likely to be sub-optimal –Collision rates appear ~constant for changing cube size –Difficult to address due to computational cost Further research is required to understand implications Conclusions

15. Thank you for your attention Contact: hglewis@soton.ac.uk Thanks to Holger Krag (ESA Space Debris Office) for permission to use the MASTER reference population, and Aleksander Lidtke (University of Southampton) for valuable discussions about the work