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    Dr. Antonio Fernando Almeida Prado, Instituto Nacional de Pesquisas Espaciais (INPE), Brazil



    This research is an application of mathematical models in space trajectories to visit bodies in the solar system, in particular the Moon. It is studied the gravitational capture, that is a characteristic of some dynamical systems in celestial mechanics, like the restricted four-body problem that is considered in this paper. The basic idea is that a hyperbolic orbit with a small positive energy around a celestial body can be transformed into an elliptic orbit, with a small negative energy, without the use of any propulsive system. One of the most important applications of this property is the construction of trajectories to the Moon. In this paper, the physical reasons of this phenomenon is studied. Numerical simulations show the effects of the forces involved. Analytical equations for the forces involved in this problem are derived to know their rules. Some approximations are made and they are justified by the simulations. In the restricted four-body problem, the gravitational capture occurs when the massless particle come close enough to one of the primaries and stay near it for some time. This phenomenon is temporary in this dynamical model. This means that, after some time of the approximation, the massless particle escapes from near the primary. The current literature study this problem based in the energy defined similarly to the two-body problem. The value of this energy is related to the velocity variation needed to change a spacecraft from the elliptical to the circular motion. Lower values of energy give lower values for the impulses, and the fuel consumption to perform this maneuver is reduced. So, the search for the minimum values of energy is very important. In the numerical approach, the values of the energy are verified all the time during the trajectory. If there is a change of signal from negative (closed trajectory) to positive (open trajectory) this is considered an escape trajectory, so a capture, in the inverse sense of time. In this work, analytical equations are derived to understand the behavior of the trajectories and the relative importance of the primaries in this phenomenon.
    Abstract document


    Manuscript document

    IAC-09.A3.2INT.16.pdf (🔒 authorized access only).

    To get the manuscript, please contact IAF Secretariat.