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The Scientific World Journal
Volume 2013 (2013), Article ID 489645, 6 pages
Research Article

Dynamics of Space Particles and Spacecrafts Passing by the Atmosphere of the Earth

1Grupo de Dinâmica Orbital e Planetologia, Universidade Estadual Paulista, FEG/UNESP, 12516-410 Guaratinguetá, SP, Brazil
2Instituto Nacional de Pesquisas Espaciais (INPE), 12227-010 São José dos Campos, SP, Brazil
3Astronomical Observatory Institute, Faculty of Physics, Adam Mickiewicz University, 60-286 Poznan, Poland

Received 11 September 2013; Accepted 7 November 2013

Academic Editors: G. Pascazio and C. Zhang

Copyright © 2013 Vivian Martins Gomes et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The present research studies the motion of a particle or a spacecraft that comes from an orbit around the Sun, which can be elliptic or hyperbolic, and that makes a passage close enough to the Earth such that it crosses its atmosphere. The idea is to measure the Sun-particle two-body energy before and after this passage in order to verify its variation as a function of the periapsis distance, angle of approach, and velocity at the periapsis of the particle. The full system is formed by the Sun, the Earth, and the particle or the spacecraft. The Sun and the Earth are in circular orbits around their center of mass and the motion is planar for all the bodies involved. The equations of motion consider the restricted circular planar three-body problem with the addition of the atmospheric drag. The initial conditions of the particle or spacecraft (position and velocity) are given at the periapsis of its trajectory around the Earth.