The determination of preliminary orbit from two series of observations by the continuation method with optimal parametrization
UDC
521.3Abstract
The method of determination of preliminary orbit by the angle topocentric coordinates and their velocities of observed body in two instants of time is considered. The main equation of the method is based on the integral of areas and integral of the energy of the two-body problem. For its solving the continuation method with optimal parametrization is proposed. This method does not require the polynomial form of solved equation. The problem is reduced to solving the Cauchy problem for two ordinary differential equations (ODE) with initial conditions what does not depends on data of original equation. The arc calculated along the solution curve is the optimal continuation parameter for this solution. The such parametrization is the best for the continuation method. In this way, all possible solutions are obtained. As example, the determination of the orbit of asteroid (1685) Toro is presented.
Keywords:
preliminary orbit, two-body integrals, continuation method with optimal parametrizationReferences
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