Using Okhotsimsky–Egorov’s method for solving the Euler–Lambert’s problem

Abstract

The solution of the Euler–Lambert’s problem, which consists in constructing an orbit passing through two given points of the central Newtonian gravitational field for a given central transfer angle and a given transfer time, is considered. A method for solving this problem has been investigated, which consists, as suggested by V.A. Egorov, in selecting the angle of inclination of the initial velocity vector of a material point to the transversal, so that the flight time between given points in space is equal to the given one. In this case, setting the specified angle of inclination of the initial velocity to the transversal allows, using the Okhotsimsky formula, to analytically determine the value of this velocity and then determine the entire orbit. It is concluded that this method, which was proposed to be given the name Okhotsimsky–Egorov, can be used as the basis for solving the Euler–Lambert’s problem.