The long-term behavior of near-circular orbits in a zonal gravity field

A simple solution has been developed for the long term behavior of a near-circular orbit in a zonal gravity field. The solution is obtained by linearizing the singly averaged variational equations of motion and eliminating a degree of freedom with an integral of motion. The resulting solution is expressed in semiequinoctial elements (h and k), and has either an exponential or periodic form. The type of solution is dependent upon a stability factor determined by the inclination and the values of the gravity field coefficients. Frozen orbits correspond to the equilibrium solutions of the set of simplified variational equations. An approximate expression for the location of these orbits has been developed and can be useful for certain mission design applications.