Interplanetary patched-conic approximation with an intermediary swing-by maneuver with the moon
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Interplanetary patched-conic approximation with an intermediary swing-by maneuver with the moon Luiz Arthur Gagg Filho1 · Sandro da Silva Fernandes1
Received: 20 March 2017 / Revised: 3 October 2017 / Accepted: 19 October 2017 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017
Abstract The present work quantifies the fuel consumption of a space vehicle in bi-impulsive interplanetary trajectories with an intermediary swing-by maneuver with the Moon. In this way, an interplanetary patched-conic approximation with a lunar swing-by maneuver is formulated with an important characteristic: the swing-by maneuver is designed before the determination of the trajectory by specifying its geometry. The transfer problem is then solved by a multi-point boundary value problem (MPBVP) with two constraints. The intermediary constraint is related to the geometry of the swing-by maneuver with the Moon, and the terminal constraint is related to the altitude of the arrival at the low orbit around the target planet. The proposed algorithm is built in such way that the MPBVP is split into two-point boundary value problems (TPBVPs): the first one is solved to ensure the satisfying of the intermediary constraint, and the second TPBVP is solved next to satisfy the final constraint. Both TPBVPs are solved by means of Newton–Raphson algorithm. The proposed algorithm is then utilized to determine the Earth–Mars and Earth–Venus trajectories with several geometric configurations. The geometric configuration with the smallest fuel consumption is obtained for both missions and compared to an interplanetary patched-conic approximation without swing-by maneuver with Moon. The results show advantages in performing swingby maneuver with the Moon for interplanetary missions by saving fuel consumption without much increase of the time of flight. Keywords Earth–Mars trajectory · Earth–Venus trajectory · Lunar swing-by maneuver · Interplanetary patched-conic approximation
Communicated by Elbert Macau, Antônio Fernando Bertachini de Almeida Prado and Othon Cabo Winter.
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Luiz Arthur Gagg Filho [email protected] Departamento de Matemática, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP 12228-900, Brazil
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L. A. G. Filho, S. da Silva Fernandes
1 Introduction The gravity-assisted space maneuvers (swing-by maneuvers) are much utilized in space missions, since these allow the space vehicle to gain or lose energy without fuel consumption. The gain or loss of velocity is, therefore, a natural effect of the dynamics of the celestial mechanics when the space vehicle has a close encounter with a body with considerable mass. Such maneuvers are useful for interplanetary mission and cometary mission (Broucke 1988), commonly performed with the Earth and Venus (Jones 2016a, c). Many effects of this maneuver are already known due to the great number of works on this subject. However, the majority of the works focus on the analysis of the swing-by maneuver independently of the entire trajectory to be performed by
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