Satellite orbital precessions caused by the first odd zonal J _{3} multipole of a nonspherical body arbitrarily oriented in space
Abstract
An astronomical body of mass M and radius R which is nonspherically symmetric generates a free space potential U which can be expanded in multipoles. As such, the trajectory of a test particle orbiting it is not a Keplerian ellipse fixed in the inertial space. The zonal harmonic coefficients J _{2}, J _{3},… of the multipolar expansion of the potential cause cumulative orbital perturbations which can be either harmonic or secular over time scales larger than the unperturbed Keplerian orbital period T. Here, I calculate the averaged rates of change of the osculating Keplerian orbital elements due to the odd zonal harmonic J _{3} by assuming an arbitrary orientation of the body's spin axis . I use the Lagrange planetary equations, and I make a firstorder calculation in J _{3}. I do not make apriori assumptions concerning the eccentricity e and the inclination i of the satellite's orbit.
 Publication:

Astrophysics and Space Science
 Pub Date:
 August 2014
 DOI:
 10.1007/s105090141915x
 Bibcode:
 2014Ap&SS.352..493R
 Keywords:

 Experimental studies of gravity;
 Satellite orbits;
 Harmonics of the gravity potential field