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COBEM 2017
24th ABCM International Congress of Mechanical Engineering
OPTIMAL TWO-IMPULSE TRAJECTORIES FOR EARTH-MOON FLIGHT IN THE ELLIPTIC RESTRICTED THREE-BODY PROBLEM
Submission Author:
Sandro da Silva Fernandes , SP
Co-Authors:
Marcus Macêdo, Luiz Arthur Gagg Filho, Sandro da Silva Fernandes
Presenter: Marcus Macêdo
doi://10.26678/ABCM.COBEM2017.COB17-0378
Abstract
In this paper, the problem of transferring a space vehicle from a circular low Earth orbit (LEO) to a circular low Moon orbit (LMO) with minimum fuel consumption is considered. It is assumed that the propulsion system delivers infinite thrusts during negligible times such that the velocity changes are instantaneous, that is, the propulsion system is capable of delivering impulses. This kind of propulsion system is taken as a limit of constant ejection velocity propulsion system for highly thrust level. The class of two impulse trajectories is considered: a first accelerating velocity impulse, tangential to the space vehicle velocity relative to Earth, is applied at a circular low Earth orbit and a second braking velocity impulse, tangential to the space vehicle velocity relative to Moon, is applied at a circular low Moon orbit. The minimization of fuel consumption is equivalent to the minimization of the total characteristic velocity which is defined by the arithmetic sum of velocity changes. The optimization problem has been formulated using an extension of the classic patched-conic approximation which includes the eccentricity of the Moon orbit, and two versions of the planar elliptic restricted three-body problem (PER3BP). In the extended patched-conic approximation model, the parameters to be optimized are three: initial phase angle of space vehicle, initial position of the Moon in its orbit, and the first velocity impulse or, equivalently, the velocity of the vehicle at the insertion point in the geocentric phase. In this formulation, the time of flight and the second velocity impulse are determined from the two-body dynamics. In the PER3BP models, the parameters to be optimized are five: initial phase angle of space vehicle, time of flight, the first and the second velocity impulses, and the initial position of the Moon in its orbit. In all cases, the optimization problem has been solved using a gradient algorithm in conjunction with Newton-Raphson method, considering several final altitudes of a clockwise or counterclockwise circular low Moon orbit for a specified altitude of a counterclockwise circular low Earth orbit. In all models, a second optimization problem can be formulated if the initial position of the Moon is prescribed. In this way, a study about the fuel consumption parameterized by the initial position of the Moon is performed and some interesting results can be obtained.
Keywords
Earth-Moon trajectories, elliptic restricted three-body problem, optimal two-impulse trajectories, patched-conic approximation
