Analytic solution to the relative orbital motion around an oblate planet

The paper offers a vectorial approach to the J2-perturbed relative orbital motion. The model uses mean orbital elements in order to derive closed form expressions for the relative position and relative velocity with respect to the LVLH frame attached on a main satellite. The advantage of the present approach is that only the motion of one satellite must be known, together with the initial conditions with respect to LVLH of the other satellites. As in the previous works of the authors, a tensorial instrument is used in order to transfer the motion from inertial to non-inertial reference frames and back. In this way, a concise instrument for the study of the satellites formations under the influence of the oblateness factor J2 is offered. Copyright © 2009 by Daniel Condurache and Vladimir Martinusi