Analysis of Lageos' altitude decrease

The paper treats the inverse problem of celestial mechanics which consists of determining the force field or potential from given or observed orbit(s). From the observational information, according to which Lageos loses approximately 1 mm altitude per day, a linear partial differential equation is formulated. The solution of this equation gives the field responsible for the above-mentioned, as yet unexplained, small but well established secular decrease in the semi-major axis. Note that the altitude-loss is not due to air-drag because of the very high altitude of this satellite.