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![Page 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.](https://reader034.fdocuments.in/reader034/viewer/2022051401/56649f055503460f94c196f8/html5/thumbnails/1.jpg)
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
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• 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
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External driversSolar activity Launch traffic
ExplosionsCompliance with
mitigation measures
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• 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
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• 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:
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• Collision rate for this case:
Idealised case𝑃 𝑖 , 𝑗=
12𝜋 2𝑑 ( 2𝜇
𝑎5 )12 𝜎
𝜎=4 𝐴
Combined collision cross-sectional
area:
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• 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
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• Comparison of collision rates:
Theory v Implementation in SDETK
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• 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
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• 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
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11
LEO 10 cm Population (May 2009)
ESA MASTER 2009 population seen in
DAMAGE
29,370 objects ≥ 10 cm
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• Overall collision rate estimates:
DAMAGE Results
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• 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
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• 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
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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