Using velocity vector in determining Keplerian orbit of geodectic satellite

The problem of determining the Keplerian orbit of a satellite on the basis of the known values of its velocity vector at three moments in time is examined and two methods for its solution are presented. Solution of this problem can be used in preliminary determination of the orbit of a planetary satellite on the basis of measurements of radial velocity and directions from three stations whose coordinates are unknown. The satellite velocity vector is found by solution of a system of three linear equations. After formulating the problem a geometrical solution is obtained. A solution with the use of derivatives requiring solution of a system of four nonlinear equations with four unknowns is also presented. A series of expressions is derived which give a solution of the problem of determining satellite orbit from the velocity vector stipulated at three moments in time.