Orbit determination in satellite geodesy Original Research Article

For centuries orbit determination in Celestial Mechanics was a synonym for the determination of six so-called Keplerian elements of the orbit of a minor planet or a comet based on a short series of (three or more) astrometric places observed from one or more observatories on the Earthʹs surface. With the advent of the space age the problem changed considerably in several respects: (1) orbits have to be determined for a new class of celestial objects, namely for artificial Earth satellites; (2) new observation types, in particular topocentric distances and radial velocities, are available for the establishment of highly accurate satellite orbits; (3) even for comparatively short arcs (up to a few revolutions) the orbit model that has to be used is much more complicated than for comparable problems in the planetary system: in addition to the gravitational perturbations due to Moon and planets higher-order terms in the Earthʹs gravity field have to be taken into account as well as non-gravitational effects like atmospheric drag and/or radiation pressure; (4) the parameter space is often of higher than the sixth dimension, because not only the six osculating elements referring to the initial epoch of an arc, but dynamical parameters defining the (a priori imperfectly known) force field have to be determined, as well. It may even be necessary to account for stochastic velocity changes. Orbit determination is not a well-known task in satellit geodesy. This is mainly due to the fact that orbit determination is often imbedded in a much more general parameter estimation problem, where other parameter types (referred to station positions, Earth rotation, atmosphere, etc.) have to be determined, as well. Three examples of “pure” orbit determination problems will be discussed subsequently: