It was believed until very recently that a near-equatorial satellite would always keep up with the planet’s equator (with oscillations in inclination, but without a secular drift). As explained in Efroimsky and Goldreich (2004), this misconception originated from a wrong interpretation of a (mathematically correct) result obtained in terms of non-osculating orbital elements. A similar analysis ...

We revisit the Lagrange and Delaunay systems of equations for the six osculating orbital elements, and point out a previously neglected aspect of these equations. A careful re-examination of the derivation of these systems shows that in both cases the orbit resides on a certain 9-dimensional submanifold of the 12-dimensional space spanned by the osculating elements and their time derivatives. W...

It was believed until very recently that a near-equatorial satellite would always keep up with the planet’s equator (with oscillations in inclination, but without a secular drift). As explained in Efroimsky and Goldreich (2004), this misconception originated from a wrong interpretation of a (mathematically correct) result obtained in terms of non-osculating orbital elements. A similar analysis ...

There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it. This paper presents a mapping between the elements of highly non-Keplerian orbits and classical orbital elements. Three sets of elements are discussed and mappings are derived in closed, analytical form for both the direct and inverse problem. ...