Abstract
This analysis demonstrates that the energy integral or any known exact integral of motion can be used to determine certain higher-order terms in the time history of satellite motion after the geometry of the orbit has been obtained. The method, or slight modifications thereof, can be applied to any theory which gives the position of the satellite as a function of some angular variable rather than time. Th such cases, the equation for the time has to be integrated separately, and results in loss of accuracy due to the presence of secular and long-period terms. It is demonstrated how this difficulty may be overcome for the case of a satellite problem discussed in an earlier paper by the authors.
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