A natural first approximation to low-thrust trajectories between satellite orbits of the earth and moon

Abstract

This paper describes a new techniqfue for generating approximate low-thrust trajectories between satellite orbits of the earth and moon, using a series of two-body trajectories in combination with a systematic synthesizing process. The composite trajectories obtained by this method consist of constant tangential thrust powered spirals, one ascending and one descending for each one-way trip, joined by a connected pair of coasting arcs. The transition between the earth-influenced and moon-influenced portions of the physical model occurs at the junction of the two coasting arcs. The two-body powered trajectory segments are integrated numerically by a computer program, which also calculates regularly certain properties of the osculating Keplerian orbit corresponding to the instantaneous state of the vehicle. Families of these osculating orbits are later compared, obtaining matching conditions at the apoapsides of a particular pair of geocentric and selenocentric orbits. Since only apsidal points are matched, all coasting arc junctions fall along the earth-moon line (cislunar and translunar matches are possible). The paper presents the results of applying the synthesizing technique to the earth-moon transfer problem for a set of parametric variations in the powered spirals. The results are compared to previously published data, and an over-all evaluation is presented. Nomenclature c = propellant exhaust speed e = eccentricity F = thrust = thrust acceleration (F/m) h = angular momentum K = gravitational parameter m = mass of vehicle M = mean anomaly n = mean motion p = parameter (semilatus rectum) r = radial distance TA = radial distance of apoapsis RM = earth-moon distance t = time TRC = receding coast time (cutoff to apoapsis) 0 = angular displacement (powered trajectory) VA = speed at apoapsis VM = orbital speed of moon Av = velocity increment (J* f dt)