Abstract
This paper calls into question the validity of the well-known formulae for the perturbations in the Keplerian elements, over one revolution of an orbit, for the motion of a drag-perturbed artificial satellite. These formulae are derived from Gauss's form of the planetary equations, by averaging over a single revolution of the orbit, and using the eccentric anomaly as the independent variable.
It is shown that for light balloon-type satellites in near-circular orbits neither the eccentric anomaly nor the true longitude is a suitable choice of independent variable for the averaging procedure. Under these circumstances, it would seem that simple formulae for the variations in the elements cannot be derived from Gauss's equations.
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References
King-Hele, D.: 1964,Theory of Satellite Orbits in an Atmosphere, Butterworths, London.
McCuskey, S. W.: 1963,Introduction to Celestial Mechanics, Adison-Wesley.
Sterne, T. E.: 1960,An Introduction to Celestial Mechanics, Interscience.
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Jupp, A.H. Some investigations into the atmospheric drag problem. Celestial Mechanics 14, 335–339 (1976). https://doi.org/10.1007/BF01228519
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DOI: https://doi.org/10.1007/BF01228519