Influence of tides in viscoelastic bodies of planet and satellite on the satellite’s orbital motion

The problem of influence of tidal friction in both planetary and satellite bodies upon satellite’s orbital motion is considered. Using the differential equations in satellite’s rectangular planetocentric coordinates, the differential equations describing the changes in semimajor axis and eccentricity are derived. The equations in rectangular coordinates were taken from earlier works on the problem. The calculations carried out for a number of test examples prove that the averaged solutions of equations in coordinates and precise solutions of averaged equations in the Keplerian elements are identical. For the problem of tides raised on planet’s body, it was found that, if satellite’s mean motion n is equal to |1118 |⁠, where Ω is the planet’s angular rotation rate, the orbital eccentricity does not change. This conclusion is in agreement with the results of other authors. It was also found that there is essential discrepancy between the equations in the elements obtained in this paper and analogous equations published by earlier researchers.