Earth albedo and the orbit of Lageos

The long-period perturbations in the orbit of Lageos satellite due to the earth's albedo have been found using a new analytical formalism. The earth is assumed to be a sphere whose surface diffusely reflects sunlight according to Lambert's law. Specular reflection is not considered. The formalism is based on spherical harmonics; it produces equations which hold regardless of whether the terminator is seen by the satellite or not. Specializing in the case of a realistic zonal albedo shows that Lageos' orbital semimajor axis changes periodically by only about a centimeter and the eccentricity by two parts in 10⁵. The longitude of the node increases secularly by about 6×10^–4 arc sec yr^–1. The effect considered here can explain neither the secular decay of 1.1 mm day^–1 in the semimajor axis nor the observed along-track variations in acceleration of order 2×10^–12 ms^–2.