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The effect of modelling assumptions on predictions of the space debris environmentR. Blake and H.G. Lewis
Astronautics Research Group, Faculty of Engineering & the Environment, University of Southampton, UK
IAC-14-A6.2.4
• 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
External driversSolar activity Launch traffic
ExplosionsCompliance with
mitigation measures
• Evaluates collision probabilities between orbiting objects using a “sampling in time” approach:
Number of collisions:
Collision rate:
Spatial density:
The Cube Approach
𝑁𝑡𝑜𝑡= ∫𝑠=0
𝑠=𝐿
[𝑡 𝑠+1− 𝑡𝑠 ] 𝑃 𝑖 , 𝑗 ( 𝑠) 𝑑𝑠
𝑃 𝑖 , 𝑗=𝑠𝑖𝑠 𝑗𝑉 𝑖𝑚𝑝 𝜎𝑈
𝑈=𝑑3
Ud𝑠𝑖=𝑃𝑟𝑒𝑠
𝑈=
𝑃𝑟𝑒𝑠
𝑑3
• Two identical objects i and j in circular, polar orbits of a = 7000 km and intersecting at 90:
Idealised case
𝑉 𝑖𝑚𝑝=( 2𝜇𝑎 )
12
𝑃𝑟𝑒𝑠≈𝑑2𝜋 𝑎
Relative velocity:
Residential probability:
• Collision rate for this case:
Idealised case𝑃 𝑖 , 𝑗=
12𝜋 2𝑑 ( 2𝜇
𝑎5 )12 𝜎
𝜎=4 𝐴
Combined collision cross-sectional
area:
• Space Debris Environment Tool Kit:– Orbit propagator & Cube approach implemented in
Python
Implementation in SDETK
Parameter Value
(year) 2009
(year) 3009
ts+1 - ts (days) 0.5, 0.05 and 0.005
d (km) 1, 10 and 100
• Comparison of collision rates:
Theory v Implementation in SDETK
• 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
𝑃 𝑖 , 𝑗=1
2𝜋 2𝑑 ( 2𝜇𝑎5 )
12 𝜎
Computational cost
• 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
LEO 10 cm Population (May 2009)
ESA MASTER 2009 population seen in
DAMAGE
29,370 objects ≥ 10 cm
• Overall collision rate estimates:
DAMAGE Results
• 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
A B C
• 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
Thank you for your attention
Contact: [email protected]
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