Skip to main content
Skip to article control options
No AccessEngineering Note

Series for Collision Probability in Short-Encounter Model

Published Online:
Free first page


  • [1] Liou J.-C., Rossi A., Krag H., Xavier James Raj M., Anilkumar A. K., Hanada T. and Lewis H., “Stability of the Future LEO Environment,” Inter Agency Space Debris Coordination Committee. Working Group 2, Rept.  IADC-12-08, 2013. Google Scholar

  • [2] Sanmartín J. R., Martínez-Sánchez M. and Ahedo E., “Bare Wire Anodes for Electrodynamic Tethers,” Journal of Propulsion and Power, Vol. 9, No. 3, 1993, pp. 353–360. doi: JPPOEL 0748-4658 LinkGoogle Scholar

  • [3] Newman K., Frigm R. and McKinley D., “It’s Not a Big Sky After All: Justification for a Close Approach Prediction and Risk Assessment Process,” AAS/AIAA Astrodynamics Specialist Conference, AAS Paper  09-369, Pittsburgh, PA, 2009. Google Scholar

  • [4] LaPorte F. and Sasot E., “Operational Management of Collision Risks for LEO Satellites at CNES,” Space Operations Communicator, Vol. 5, No. 4, 2008, pp. 1–13. doi: Google Scholar

  • [5] Righetti P., Sancho F., Lazaro D. and Damiano A., “Handling of Conjunction Warnings in EUMETSAT Flight Dynamics,” Journal of Aerospace Engineering, Sciences and Applications, Vol. 3, No. 2, 2011, p. 53. doi: CrossrefGoogle Scholar

  • [6] Stoll E., Merz K., Krag H., D’ Souza B. and Bastida Virgili B., “Collision Probability Assessment for the Rapideye Satellite Constellation,” 6th European Conference on Space Debris, Spacebooks, 2013. Google Scholar

  • [7] Krag H., Flohrer T. and Lemmens S., “Consideration of Space Debris Mitigation Requirements in the Operation of LEO Missions,” SpaceOps Conference, SpaceOps, 2012, Paper 1257086. Google Scholar

  • [8] Foster J. L. and Estes H. S., “A Parametric Analysis of Orbital Debris Collision Probability and Maneuver Rate for Space Vehicles,” NASA JSC-25898, 1992. Google Scholar

  • [9] Akella M. R. and Alfriend K. T., “Probability of Collision Between Space Objects,” Journal of Guidance, Control and Dynamics, Vol. 23, No. 5, 2000, pp. 769–772. doi: LinkGoogle Scholar

  • [10] Khutorovsky Z. N., Boikov V. F. and Kamensky S. Y., “Direct Method for the Analysis of Collision Probability of Artificial Space Objects in LEO: Techniques, Results and Applications,” Proceedings of the first European Conference on Space Debris, Vol. 81, European Space Agency, Paris, April 1993, pp. 491–508. Google Scholar

  • [11] Patera R. P., “General Method for Calculating Satellite Collision Probability,” Journal of Guidance, Control, and Dynamics, Vol. 24, No. 4, 2001, pp. 716–722. doi: JGCODS 0731-5090 LinkGoogle Scholar

  • [12] Patera R. P., “Calculating Collision Probability for Arbitrary Space Vehicle Shapes via Numerical Quadrature,” Journal of Guidance, Control, and Dynamics, Vol. 28, No. 6, 2005, pp. 1326–1328. doi: JGCODS 0731-5090 LinkGoogle Scholar

  • [13] Chan F. K., Spacecraft Collision Probability, Aerospace Press, El Segundo, CA, 2008, pp. 63–97. LinkGoogle Scholar

  • [14] Alfano S., “A Numerical Implementation of Spherical Object Collision Probability,” The Journal of the Astronautical Sciences, Vol. 53, No. 1, 2005, pp. 103–109. CrossrefGoogle Scholar

  • [15] Serra R., Arzelier D., Joldes M., Lasserre J.-B., Rondepierre A. and Salvy B., “Fast and Accurate Computation of Orbital Collision Probability for Short-Term Encounters,” Journal of Guidance, Control, and Dynamics (to be published). doi: Google Scholar

  • [16] Schneider R., Convex Bodies: The Brunn-Minkowski Theory, 2nd ed., Cambridge Univ. Press, Cambridge, England, U.K., 2014, pp. 139–207. Google Scholar

  • [17] Coppola V. T., “Including Velocity Uncertainty in the Probability of Collision Between Space Objects,” AAS/AIAA Spaceflight Mechanics Meeting, AAS Paper  12-247, Charleston, SC, 2012. Google Scholar

  • [18] Bombardelli C. and Hernando-Ayuso J., “Optimal Impulsive Collision Avoidance in Low Earth Orbit,” Journal of Guidance, Control, and Dynamics, Vol. 38, No. 2, 2015, pp. 217–225. doi: JGCODS 0731-5090 LinkGoogle Scholar

  • [19] Spivak M., Calculus, 4th ed., Benjamin, New York, 2008, pp. 491–516. Google Scholar

  • [20] Gradshteyn I. S. and Ryzhik I. M., Table of Integrals, Series and Products, 8th ed., edited by Zwilinger D., Academic Press, Waltham, MA, 2015. Google Scholar

  • [21] García-Pelayo R., “Moments of the Distribution of Distance,” Journal of Mathematical Physics, Vol. 52, No. 3, 2011, Paper 033505. doi: CrossrefGoogle Scholar

  • [22] García-Pelayo R., “Erratum: Moments of the Distribution of Distance,” Journal of Mathematical Physics, Vol. 52, No. 9, 2011, Paper 099901; also Journal of Mathematical Physics, Vol. 54, 2013. doi: CrossrefGoogle Scholar

  • [23] Hochstadt H., The Functions of Mathematical Physics, Dover, New York, 1986, p. 42. Google Scholar

  • [24] Kingman J. F. C., “Random Walks with Spherical Symmetry,” Acta Mathematica, Vol. 109, No. 1, 1963, pp. 11–53. doi: ACMAA8 0001-5962 CrossrefGoogle Scholar

  • [25] García-Pelayo R., “The Random Flight and the Persistent Random Walk,” Statistical Mechanics and Random Walks: Principles, Processes and Applications, Nova Science, New York, 2012, Google Scholar

  • [26] Sánchez-Ortiz N., Grande-Olalla I., Pulido J. A. and Merz K., “Collision Risk Assessment and Avoidance Maneuvers-The New CORAM Tool for ESA,” 64th International Astronautical Congress, International Astronautical Congress Paper  13.A6.7.7, Beijing, 2013, pp. 2390–2404. Google Scholar

  • [27] Klinkrad H., Alarcón J. and Sánchez N., “Operational Collision Avoidance with Regard to Catalog Objects,” Space Debris: Models and Risk Analysis, Springer–Verlag, Berlin, 2006, pp. 215–240. CrossrefGoogle Scholar

  • [28] Alfano S. and Greer M. L., “Determining If Two Solid Ellipsoids Intersect,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 1, 2003, pp. 106–110. doi: JGCODS 0731-5090 LinkGoogle Scholar

  • [29] Bérend N., “A New Approach for Conjunction Analysis and Collision Risk Ranking,” 63th International Astronautical Congress, International Astronautical Congress IAC-12-A6.2.1, Naples, Italy, 2012. Google Scholar

  • [30] Alfano S., “Review of Conjunction Probability Methods for Short-Term Encounters,” AAS Specialist Conference, AAS Paper  07-148, Sedona, AZ, 2007. Google Scholar