  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
opinion originated from a wrong interpretation of a (mathematically correct)
result obtained in terms of non-osculating orbital elements. A similar analysis
carried out in the language of osculating elements will endow the planetary
equations with some extra terms caused by the planet's obliquity change. Some
of these terms will be nontrivial, in that they will not be amendments to the
disturbing function. Due to the extra terms, the variations of a planet's
obliquity may cause a secular drift of its satellite orbit inclination. In this
article we set out the analytical formalism for our study of this drift. We
demonstrate that, in the case of uniform precession, the drift will be
extremely slow, because the first-order terms responsible for the drift will be
short-period and, thus, will have vanishing orbital averages (as anticipated 40
years ago by Peter Goldreich), while the secular terms will be of the second
order only. However, it turns out that variations of the planetary precession
make the first-order terms secular. For example, the planetary nutations will
resonate with the satellite's orbital frequency and, thereby, may instigate a
secular drift. A detailed study of this process will be offered in the
subsequent publication, while here we work out the required mathematical
formalism and point out the key aspects of the dynamics.
