Satellite Orbit Geometry Under Nonconservative Forces
The motions of satellite can be interpreted as the geodesic flows according to the object of connexion. The different objects of connexion define the different spaces. In the conservative force fields the motions of satellite can be treated as the geodesic flows on a Riemann manifold with respect to the Maupertuis metric which defines a metric and symmetric object of connexion, while in the nonconservative force fields the motions can be also explained as geodesic flows in Weyl space with respect to a semimetric and symmetric object of connexion. As a example the motion of charged satellite, e.g. LAGEOS, in the gravitational and geomagnetic field is investigated. The geomagnetic field produces a Lorentz force field which causes the classical Zeeman effect in the computation of the satellite’s orbital motion. Consequently, the frequence of orbital motion is split into three components: the first one is equal to the mean orbital motion and the other two is equal to the frequence of the mean orbital motion plus/minus a Larmor frequence which relates to the charge of satellite, the mass of satellite and the magnitude of geomagnetic field.