Non-Linearity in the Angles-Only Initial Orbit Determination Problem

  • Denise Kaya
  • Daniel Snow
Part of the NATO ASI Series book series (NSSB, volume 272)


An investigation has been initiated to examine the concept of determining an initial orbit using angles-only observations over a short arc from a single space based sensor. The methods of Laplace and Gauss for angles-only initial orbit determination were the methods of choice for this study. To apply these methods, one has to solve a system of non-linear equations which have multiple solutions. Typical solution schemes recommend using an iterative solution technique with a first guess to start. However, since only one solution will be found using such a technique, the success of this approach will depend entirely upon how good (or bad) the first guess is. We have found that this technique is not satisfactory for performing initial orbit determination over short arcs of data. In this paper we will discuss past methods used in solving these non-linear equations and then we will present our approach which involves finding all the necessary solutions and determining which solution is correct.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Danby, J.M.A., Fundamentals of Celestial Mechanics, Wilbnann- Bell, Inc., Richmond, Virginia, 1988, pp. 213–251.Google Scholar
  2. [2]
    Escobal, P.R., Methods of Orbit Determination, Robert E. Krieger Publishing Co., Malabar, FL, 1985, pp. 239–292.Google Scholar
  3. [3]
    Moulton, F.R., An Introduction to Celestial Mechanics, Dover Publications, Inc., New York, 1970, pp. 191–260.Google Scholar
  4. [4]
    Watson, James C., Theoretical Astronomy, J.B. Lippincott and Co., London, 1881, pp. 235–243.Google Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Denise Kaya
    • 1
  • Daniel Snow
    • 1
  1. 1.Air Force Space CommandColorado SpringsUSA

Personalised recommendations