Non integrability of theJ _{2} problem
Abstract
We consider the motion of a massless particle around an oblate planet, keeping only in the expression of the perturbing potential the second degree zonal harmonic. We prove the analytical non integrability of this problem, by using Ziglin's theorem and the Yoshida criterion for homogeneous potentials.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 March 1993
 DOI:
 10.1007/BF00692515
 Bibcode:
 1993CeMDA..55..281I
 Keywords:

 Orbital Mechanics;
 Perturbation Theory;
 Planetary Orbits;
 Degrees Of Freedom;
 Hamiltonian Functions;
 Harmonics;
 Numerical Integration;
 Astrophysics;
 Non integrability;
 second degree zonal harmonic