Long period variations of the motion of a satellite due to non-resonant tesseral harmonics of a gravity potential

The main effects of tesseral harmonics of a gravity potential expansion on the motion of a satellite, are short period variations as well as long period variations due to resonances. However, other smaller long period and secular variations can arise from interactions between tesseral terms of the same order. The analytical integration of these effects is developed, using numerical evaluation of Kaula eccentricity and inclination functions. Examples for some Earth's geodetic satellites show that secular effects can reach a few decameters per year. The secular variations can even reach several hundred of meters per year for the Mars natural satellite Phobos.