A numerical solution of the inverse problem in classical celestial mechanics, with application to Mercury's motion (Q1431683)

The author investigates the simultaneous optimization of all parameters of \(N\)-body problem: constant of gravitation, masses and initial conditions. The algorithm for the minimization of quadratic residual combines the linearization of all functions involved with the one-dimensional minimization. The approach allows to predict, up to a small error, the ephemerides involving general relativity corrections, by using a purely Newtonian calculation. The improvement is due to the optimization of initial conditions. The maximum angular difference of heliocentric positions of Mercury is ca. \(22''\) per century before the optimization, and ca. \(2''\) after it. The latter is still far above the observational accuracy. On the other hand, Mercury's longitude of the perihelion is not affected by the optimization: it keeps the linear advance of \(4''\) per century.