Problems concerning the perturbation due to the tesseral harmonic terms in the nonspherical gravitational potential of the earth

Perturbation due to the nonspherical gravitational potential is most important for the motion of artificial satellites around the earth. We discuss the perturbation due to the tesseral terms which are often neglected. Although their effect on low satellites corresponds only to the second order of the J(2) term and furthermore is periodic with short periods, it contains earth rotation term that is more than 10 times larger and should be given aattention. We have obtained the perturbed solution for the tesseral terms of all orders and have isolated the earth rotation term; for the semi-major axis a we have also added the earth rotation term in the combined (J2 × Jlm) perturbation, to provide a basis for theoretical analysis and application in the analytical orbit determination and prediction.