Numerical Study of the Gravitational Capture in the Bi-Circular Four-Body Problem

Machuy A. L. , Bertachini De Almeida Prado A. F. , Stuchi T. D. J.

11th WSEAS International Conference on Automatic Control, Modelling and Simulation, İstanbul, Turkey, 30 May - 01 June 2009, pp.456-458 identifier

  • Publication Type: Conference Paper / Full Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.456-458
  • Istanbul Technical University Affiliated: No


A gravitational capture Occurs when a spacecraft (or any particle with negligible mass) change from a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy Without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third and the fourth bodies involved in the dynamics. In this way, those forces are used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon. The concept of gravitational capture is used, together with the basic ideas of the gravity-assisted maneuver and the bi-elliptic transfer orbit, to generate a trajectory that requires a fuel consumption smaller than the one required by the Hohmann transfer. The goal of the present paper is to Study the energy required for the ballistic gravitational capture in a dynamical model that has the presence Of four bodies. In particular, the Earth-Moon-Sun-Spacecraft system is considered.