Determination of the orbits of inner Jupiter satellites

Abstract

Some problems in determining the orbits of inner satellites associated with the complex behavior of the target function, which is strongly ravine and which possesses multiple minima in the case of the satellite orbit is determined based on fragmentary observations distributed over a rather long time interval, are studied. These peculiarities of the inverse problems are considered by the example of the dynamics of the inner Jupiter satellites: Amalthea, Thebe, Adrastea, and Metis. Numerical models of the satellite motions whose parameters were determined based on ground-based observations available at the moment to date have been constructed. A composite approach has been proposed for the effective search for minima of the target function. The approach allows one to obtain the respective evaluations of the orbital parameters only for several tens of iter- ations even in the case of very rough initial approximations. If two groups of observations are available (Adrastea), a formal minimization of the target function is shown to give a solution set, which is the best solu- tion from the point of view of representation of the orbital motion, which is impossible to choose. Other esti- mates are given characterizing the specific nature of the inverse problems.