Analysis of \(J_2\)-perturbed motion using mean non-osculating orbital elements
The perturbed motion of a satellite in the gravitational field of the oblate planet is well formulated problem of celestial mechanics since Lagrange (his name is given to the proper differential equations), has the long history and a huge amount of publications. It is well known that if one takes into consideration only the second harmonic of the gravitational potential of the oblate planet \(J_2\) the so called positional orbit elements, i.e. the semi-major axis, the eccentricity and the inclination of the osculating orbit, are constant in the averaged problem. Here, a so-called gauge-generalization of the Lagrange equations (the terminology was adopted from the electrodynamics by \textit{M. Efroimsky} and \textit{P. Goldreich} [J. Math. Phys. 44, No. 12, 5958--5977 (2003; Zbl 1063.70008)] is used to show that if one adopts the secular variations of the eccentricity and inclination then some angular orbit elements (say, the node and the argument of periapsis) can be constant. In any case a combination of three orbit elements (position and angular as well) can be chosen as constants.
scientific article; zbMATH DE number 2139810