New method of orbit determination from two position vectors based on solving Gauss’s equations

The classic problem of finding the orbit of a celestial body from its two position vectors for two instants of time is considered. A solution to the problem free from uncertainties is obtained which can be applied for all three kinds of Keplerian movement. The main part of the computational procedure is reduced to solving one equation with one unknown. Formulas are derived for the initial value of the equation root, which makes the application of the Newton-Raphson method successful. The efficiency and reliability of the suggested algorithm is illustrated by examples of the orbit determination for the asteroids Adeona and Icarus, as well as for Halley’s Comet and Bowell’s Comet.