The probability of asteroid-earth collisions by way of the positional uncertainty ellipsoid

Christopher J. Polito, David B. Spencer

Research output: Chapter in Book/Report/Conference proceedingConference contribution


An alternative to the conventional method for determining impact probability by an asteroid is presented that utilizes the positional uncertainty ellipsoid. This method is used commonly for Earth-orbiting satellite collision probability. In the scaling up process, the gravitational influence of one of the bodies in the collision is taken into account, namely that of the Earth. The restricted three-body problem is sufficient to provide a backdrop for the probability analysis, while making sure to note that the results are only hypothetical given a simplified dynamic model. Uncertainty is represented mathematically by the covariance matrix and is propagated into the future. Encounter regions are defined as regions along the nominal trajectory of the asteroid where the propagated uncertainty encloses the Earth. Probability is calculated by a triple integral of the probability density function (pdf) over the volume swept out by the Earth through the encounter region. The trend in probability calculated vs. initial uncertainty is investigated, and it is found that higher probabilities result from initial uncertainties that are tighter in the radial, in-track and out-of-plane directions.

Original languageEnglish (US)
Title of host publicationASTRODYNAMICS 2011 - Advances in the Astronautical Sciences
Subtitle of host publicationProceedings of the AAS/AIAA Astrodynamics Specialist Conference
Number of pages13
StatePublished - Dec 1 2012
Event2011 AAS/AIAA Astrodynamics Specialist Conference, ASTRODYNAMICS 2011 - Girdwood, AK, United States
Duration: Jul 31 2011Aug 4 2011

Publication series

NameAdvances in the Astronautical Sciences
ISSN (Print)0065-3438


Other2011 AAS/AIAA Astrodynamics Specialist Conference, ASTRODYNAMICS 2011
Country/TerritoryUnited States
CityGirdwood, AK

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science


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