Energy-Optimal Solution to the Lambert Problem

Abstract

T HE Lambert problem offers a substantial way of determining theminimumenergy transfer between twoknownpoints along a Keplerian orbit. Most of the analysis for this problem relies on a geometrical approach, since the problem’s definition is attuned to the geometry [1,2]. The main idea of the Lambert minimum-energy problem starts by defining the length between two position vectors. Consequently, it states geometrically that the semimajor axis of the minimum-energy orbit is related to the chord length and length of the position vectors [1]. Currently, there is no other analytical approach besides the geometric analysis for solving the problem. In this note, however, an alternative analytical method for solving the Lambert minimum-energy problem is proposed. Theminimum velocity at the initial position is obtained by applying a constrained optimization tool. As the initial position vector in the problem is fixed, it is apparent that determining theminimum initial velocity is the same as obtaining theminimum-energy orbit. Using the alternative technique could give us new insight into solving various orbital problems.