The problem of construction of an elliptical orbit of transition between two orbits with small eccentricities with random and given phases of identical direction motions in the equatorial plane of an axisymmetrical planet is solved. The transition may contain some number of free orbits around the planet and is realized by means of changes of velocity on the initial and final orbits. The problem is solved by the method of approximate solution of variational problems. With accuracy to a small parameter, the transition osculatory ellipse is selected, which minimizes the consumption of fuel for maneuvering. It is assumed that maneuvering is restricted. Equations are derived which allow to determine the optimal orbit of transition. Author
Edited machine trans. of Trudy. Astronomicheskoi Observatorii, v26 n44 p97-113 1969 (sic), by Joseph E. Pearson.