Orbit Determination: Preliminary Orbits

Abstract

Having at our disposal at the Observatory some photographic plates of artificial satellites and, also, facilities to get plates of natural celestial bodies of the solar system, by the installation of a new optical telescope, we had need to write a computer program for a fast determination of preliminary orbits, both geocentric and heliocentric, by using a reduced set of observational data.

We started with the classical methods of Laplace, Gauss and Gibbs, and very soon we realized the different behaviour of these methods with regard to the different characteristics of the orbits considered.

We used the opportunity to look in more detail for the efficiency of the methods, and this was done in two directions:

• Modification of the original scheme, what was accomplished for the method of Laplace, however, with the charge of increasing the number of observations;

• Comparative study of the results derived from the three methods, by using real orbital data at different distances from the dynamical center.