Mathematics – Probability
Scientific paper
May 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009adspr..43.1372b&link_type=abstract
Advances in Space Research, Volume 43, Issue 9, p. 1372-1390.
Mathematics
Probability
1
Scientific paper
We model the orbital debris environment by a set of differential equations with parameter values that capture many of the complexities of existing three-dimensional simulation models. We compute the probability that a spacecraft gets destroyed in a collision during its operational lifetime, and then define the sustainable risk level as the maximum of this probability over all future time. Focusing on the 900- to 1000-km altitude region, which is the most congested portion of low Earth orbit, we find that - despite the initial rise in the level of fragments - the sustainable risk remains below 10-3 if there is high (>98%) compliance to the existing 25-year postmission deorbiting guideline. We quantify the damage (via the number of future destroyed operational spacecraft) generated by past and future space activities. We estimate that the 2007 FengYun 1C antisatellite weapon test represents ≈1% of the legacy damage due to space objects having a characteristic size of ⩾10 cm, and causes the same damage as failing to deorbit 2.6 spacecraft after their operational life. Although the political and economic issues are daunting, these damage estimates can be used to help determine one-time legacy fees and fees on future activities (including deorbit noncompliance), which can deter future debris generation, compensate operational spacecraft that are destroyed in future collisions, and partially fund research and development into space debris mitigation technologies. Our results need to be confirmed with a high-fidelity three-dimensional model before they can provide the basis for any major decisions made by the space community.
Bradley Andrew M.
Wein Lawrence M.
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