Abstract
A study of optimal two-impulse trajectories with moderate flight time for Earth-Moon missions is presented. The optimization criterion is the total characteristic velocity. Three dynamical models are used to describe the motion of the space vehicle: the well-known patched-conic approximation and two versions of the planar circular restricted three-body problem (PCR3BP). In the patched-conic approximation model, the parameters to be optimized are two: initial phase angle of space vehicle and the first velocity impulse. In the PCR3BP models, the parameters to be optimized are four: initial phase angle of space vehicle, flight time, and the first and the second velocity impulses. In all cases, the optimization problem has one degree of freedom and can be solved by means of an algorithm based on gradient method in conjunction with Newton-Raphson method.
Highlights
In the last two decades, new types of trajectories have been proposed to transfer a spacecraft from an Earth orbit to a Moon orbit which reduce the cost of the traditional Hohmann transfer based on the two-body dynamics 1
Consider an inertial reference frame Gxy contained in the Moon orbital plane: its origin is the center of mass of the Earth-Moon system; the x-axis points towards the Moon position at the initial time and the y-axis is perpendicular to the x-axis
Consider a rotating reference frame Gξη contained in the Moon orbital plane: its origin is the center of mass of the Earth-Moon; the ξ-axis points towards the Moon position at any time t and the η-axis is perpendicular to the ξ-axis
Summary
In the last two decades, new types of trajectories have been proposed to transfer a spacecraft from an Earth orbit to a Moon orbit which reduce the cost of the traditional Hohmann transfer based on the two-body dynamics 1. In the patched-conic approximation model, the parameters to be optimized are two: initial phase angle of space vehicle and the first velocity impulse. In this approach, the two-point boundary value problem involves only one final constraint. In the PCR3BP models, the parameters to be optimized are four: initial phase angle of space vehicle, flight time, and the first and the second velocity impulses. In these formulations, the two-point boundary value problem involves three final constraints. The results for maneuvers with multiple revolutions show that fuel can be saved if a lunar swing-by occurs
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