Perturbations by the oblateness of the Earth and by the planets in the motion of the Moon

Perturbations in the motion of the Moon are computed for the effect by the oblateness of the Earth and for the indirect effect of planets. Based on Delaunay's analytical solution of the main problem, the computations are performed by a method of Fourier series operation. The effect of the oblateness of the Earth is obtained to the second order, partly adopting an analytical evaluation. Both in longitude and latitude are found a few terms whose coefficient differs from the current lunar ephemeris based on Brown's theory by about 0.01. While, concerning the indirect effect of planets, several periodic terms in the current ephemeris seem to have errors reaching 0.05.As for the secular variations of and due to the figure of the Earth and the indirect effect of planets, the newly-computed values agree within 1/cy with Brown's results reduced to the same values of the parameters. Further, the accelerations in the mean longitude, and caused by the secular changes in the eccentricity of the Earth's orbite and in the obliquity of the ecliptic are obtained. The comparison with Brown shows an agreement within 0.3/cy² for the former cause and 0.02/cy² for the latter. An error is found in the argument of the principal term for the perturbations due to the ecliptic motion in the current ephemeris.Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980.