V. Summary The purpose of this paper was to take a problem from classical celestial mechanics and turn it into one of orbit radial probability and statistics. Using analysis of functions of a random variable, several significant conclusions with respect to satellite orbits were discovered, one being the independence of the average surveillance area as a function of eccentricity (equation III.2), and another regarding search patterns and search values. This paper is concluded by presenting a compendium of radial orbital probability functions and statistics (random variate: time) in Appendix I, and a useful computer program in appendix II. Acknowledgements I would like to thank Dr Andrew H. Cutler for his support and encouragement, Dr Daniel E. Snow for reviewing and contributing to the original Air Force Space Command technical note on Statistical Quantities of Elliptical Keplerian Orbits, and Lt Colonel Douglas Kirkpatrick, USAF for his assistance and insight. REFERENCES [1] Parzen, Emanuelle (Ed.) (1960) Integratable in the Lebesque sense, Modern Probability Theory and Its Applications (New York, John Wiley). [2] Ibid., p. 78. [3] Ibid., pp. 148-150. [4] Fowles, Grant R. (1970) Analytical Mechanics, 2nd edn., p. 150 (New York, Holt Rinehart & Winston). [5] Stumpff, K., Himmelsmechanik, vol. 1, 1956 and vol. 2 1965 (Berlin, Deutscher Verlag der Wissenschaften). [6] Korn, Granino A. & Korn, Theresa M. (1961) Mathematical Handbook for Scientists and Engineers, p. 732 (New York, McGraw Hill). [7] Spiegel, Murray (1971) Theory and Problems of Advanced Mathematics for Engineers and Scientists, Schaums’ Outline, p. 203 (New York, McGraw-Hill). [8] Parzen, op. cit., p. 203. [9] This considering orbit geometry factors only. A more general treatment would include intrinsic sensor limitations and characteristics, in addition to other physical factors. BIBLIOGRAPHY Escobal, Pedro (1965) Methods of Orbit Determination (New York, John Wiley). Hoel, Paul G. (1971) Introduction to Mathematical Statistics (New York, John Wiley). Mueller, D., Bate, R. & White, J. (1971) Fundamentals of Astrodynamics (New York, Dover Publications).
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