The orbit of a satellite of an oblate planet

. The pape gives a solution of the problem of motion of a particle in the potential field V - I/r + 2kP2 (sin O)/r3 + k'P4 (sin O)/r1, where k and k' are small parameters. The first approximation is furnished by a V8 that incorporates a major portion of the second spherical harmonic and leads to a closed solution with no secular variations of order k. The perturbations of this non-Keplenan intermediary orbit are derived here by the von-Zeipel modification of the method of Delaunay. The secular variations are carried up to orders k2 and k', and the periodic variations to orders k and k'/k. A computational summary is included; the effect of the third spherical harmonic is appended.