Short period elimination for the tesseral harmonics

An analytic theory for the motion of an artificial satellite is developed. The theory takes into account at first order the J sub 2 zonal harmonic and at second order the short period perturbations due to the tesseral harmonics. It is valid for satellites whose periods are not in resonance with the rotation rate of the earth. Two canonical transformations of the Lie type are constructed to eliminate the short period terms. The first transformation produces a simplified Hamiltonian in which the longitude dependent terms are expanded in series in the eccentricity. The second transformation averages the resulting Hamiltonian to produce the long period Hamiltonian. The literal expressions for the two transformations have been produced in the particular cases of a number of tesserals.