Application of perturbation theory to problem in orbital theory

Difficulties associated with critical values frequently arise in calculations of perturbations of earth satellite orbits (the critical values are e=o, 1=0 and 4-5 sin squared 1=0. The anomalous behavior at the critical points is not intrinsic to the physics but is an artifact of the computational methods. These difficulties are surmounted through the use of perturbation series expansions. For both critical and noncritical problems the secular terms can be eliminated and a periodic solution obtained.