Motion of a satellite around an oblate earth
Abstract
The motion of a satellite about an oblate earth with the gravitational potential independent of longitude is considered, neglecting atmospheric drag. Using cylindrical coordinates p, Z, , with the z axis along the polar axis, one may eliminate from the resulting equations by utilixing the constancy of M,, the moment of momentum about the z axis. The reduced equations possess an integral analogous to the energy integral, from which it is shown that the satellite orbit is forever confined to the interior of a certain toroidal region R. The equation of the boundary C of the section of R by a halfplane of constant is obtained, and C is plotted for three orbits for which Po = 0 Po = Zo = 0 and for which the initially osculating ellipses have eccentricities E=0.2, 0.4, 0.7.
 Publication:

The Astronomical Journal
 Pub Date:
 May 1962
 DOI:
 10.1086/108695
 Bibcode:
 1962AJ.....67..212P