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V. J. Slabinski (Earth Orientation Dept., USNO)
Efroimsky(2003) and Newman and Efroimsky(2003) have proposed a generalization of Lagrange's perturbation equations by omitting the requirement that the orbital elements be osculating, that is, that the satellite velocity computed from the unperturbed elements be the same as the velocity computed from the perturbed elements. The arbitrary difference between the two velocities is specified by a ``gauge velocity'' analogous to the gauge in electromagnetic potentials. This gauge velocity is zero for osculating elements.
As a simple, illustrative example of how this gauge freedom can simplify the resulting element expressions, we compute the J2 gravity perturbations to the plane of a circular satellite orbit. We find the gauge velocity that keeps the orbit inclination constant, with no short-period terms. This gauge velocity then results in a node position that moves uniformly with time, also with no short-period terms.
King-Hele(1958) obtained similar results by a method that implicitly used non-osculating elements. We relate our solution to the first-order osculating element expressions given by Kozai(1959).
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Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.