Reconstruction of the Satellite Orbit via Orientation Angles

A. M. Farag, Gunter Weiss

Abstract: This paper presents an efficient geometric method to find the mathematical model for the normal orbit of a moving satellite observed from a given station on the earth. The method relies on getting a sufficient number of observations oriented from the earth station to the satellite which moves on its predictable orbit on the celestial space. The concurrence of the revolution of the earth and the motion of the satellite is utilized to orient the calculated normal orbit in its fixed plane. Rather than deriving the geometric model for the case of a known orbital plane, we reformulate the method of solution to study the case of an unknown orbital plane. Since the earth station rotates with the earth and the satellite moves, the lines of observation are generatrices of a ruled surface with the elliptic orbit as one directrix. In this paper we assume that the satellite obeys the Keplerian laws and that the true anomaly of the orbit is the only time-dependent Kepler element.

Keywords: Applied Geometry, Celestial Mechanics, Satellite Orbits

Classification (MSC2000): 51N05; 70F15

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