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COBEM 2019
25th International Congress of Mechanical Engineering
OPTIMAL INTERPLANETARY TRAJECTORIES USING THE TWO-BODY, FOUR-BODY, AND, FIVE-BODY PROBLEMS
Submission Author:
Luiz Arthur Gagg Filho , SP
Co-Authors:
Luiz Arthur Gagg Filho, Sandro da Silva Fernandes
Presenter: Luiz Arthur Gagg Filho
doi://10.26678/ABCM.COBEM2019.COB2019-0106
Abstract
This work formulates an interplanetary transfer problem from a circular low Earth orbit (LEO) to a circular low orbit around a target planet (Mars or Venus) by using two impulses tangential to the terminal orbits. Models based on the two-body, four-body, and, five-body problems are considered. Among the models based on the two-body problem there are the interplanetary patched-conic approximation based on the Hohmann transfer; the interplanetary patched-conic approximation based on the Gauss problem; and, the patched-conic approximation based on a detailed geometry which can include a swing-by maneuver with the Moon. In the context of the restricted four-body problem (Sun-Earth-target planet-space vehicle), the present work formulates the transfer problem utilizing Cartesian coordinates in three sets of differential equations of motion to improve the integrator sensitivity. A two-point boundary value problem and two optimization problems, with one or two degrees of freedom, are enunciated. Thus, optimal trajectories are determined in order to minimize the fuel consumption. The lunar swing-by maneuver is then formulated in a five-body problem. The optimal trajectories are compared among the models with and without lunar swing-by maneuver. The results show that the saving of fuel consumption due to the lunar swing-by maneuver is substantial with no greater changes in the time of flight.
Keywords
interplanetary transfer, optimal trajectory, lunar swing-by, four-body problem, ve-body problem
