Resonant Satellite Geodesy by High Speed Analysis of Mean Kepler Elements
A general resonant orbit and gravity constant determining program has been developed accepting short arc mean Kepler elements as data. The evolution of these elements is calculated by numerical integration of their long period and secular variations.
With only slowly-changing mean element coordinates being integrated, a step size of the order of an orbit revolution or more is achieved. Satellite ephemerides over 5000 revolutions are calculated in about a minute on an IBM/360 computer. Partial derivatives of the evolved mean elements with respect to initial values and gravity constants are readily evaluated from numerically generated variant trajectories.
To test the method, simulated and actual orbit data from long resonant twelve-hour trajectories have been processed for gravity information by a least-squares technique. The gravity recovery is in excellent agreement with the model for the simulated data, and with previous analytic results from the actual data on Cosmos 41.
Extensive data from many resonant 12 and 24 h satellites is currently being processed by the mean element program. Preliminary determinations from this data are given. The final result should be definitive information on more than a quarter of the longitude harmonics through 8,8.
KeywordsSemimajor Axis Gravity Recovery Disturbing Potential Resonant Orbit Gravity Constant
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