A second-order satellite orbit theory, with compact results in cylindrical coordinates

Abstract

First-order perturbations of a low-eccentricity satellite orbit due to the general harmonic coefficient J 1m of the Earth’s gravitational field are derived, and compactly expressed (see equations (92)-(94)) in cylindrical polar coordinates. For the dominant harmonic J 2 , the perturbations are taken to second order, and it is shown how formulae for the second-order variation of the orbital elements depend on the definition of the mean elements used for reference. With a particular choice of mean elements, the formulae for perturbations in cylindrical coordinates are again very compact (see equations (297), (315) and (321)). The general approach also yields first-order perturbations due to lunisolar gravity and eclipse-free solar radiation. The paper finishes with a set of untruncated expressions (valid for any eccentricity) for J 2/2 secular and long-periodic perturbations.