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Atmospheric close approaches with the Earth considering drag and lift forces

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Abstract

A maneuver called “Aero-Gravity Assisted” is known in the literature to increase the energy gains given by a close approach between a spacecraft and a planet using the atmosphere of the planet. In a sequence of studies related to this problem, the present paper studies close approaches between a spacecraft and the Earth, in situations where the passage is close enough to the surface of the Earth such that the spacecraft crosses its atmosphere. The dynamical model considers the atmosphere of the Earth, in terms of drag and lift, the gravitational fields of the Earth and the Sun, assumed to be points of mass, and the spacecraft. The Earth and the Sun are assumed to be in circular coplanar orbits around their common center of mass. The equations of motion are the ones given by the circular planar restricted three-body problem with the addition of the forces generated by the atmospheric drag and lift. The primary objective is to map the variations of energy of the orbits of the spacecraft due to this close approach. The results show how the atmosphere affects the trajectory of the spacecraft, generating situations where the variation of energy changes sign with respect to the gravity part of the maneuver or where they have a zero net result, based in the equilibrium between atmospheric and gravity forces. This result opens the possibility of changing only the eccentricity of the orbit, keeping fixed its semi-major axis.

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Acknowledgments

The authors wish to express their appreciation for the support provided by Grants #473387/2012-3, 473164/2013-2 and 304700/2009-6 from the National Council for Scientific and Technological Development (CNPq); Grants # 2011/08171-3, 2011/13101-4, 2014/06688-7 and 2012/21023-6 from São Paulo Research Foundation (FAPESP) and the financial support from the National Council for the Improvement of Higher Education (CAPES).

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Authors and Affiliations

  1. Grupo de Dinâmica Orbital e Planetologia, Universidade Estadual Paulista-FEG/UNESP, Guaratinguetá, Brazil

    Vivian Martins Gomes

  2. Instituto Nacional de Pesquisas Espaciais-INPE, São José dos Campos, Brazil

    Jhonathan O. Murcia Piñeros & Antonio Fernando Bertachini de Almeida Prado

  3. Faculty of Physics, Astronomical Observatory Institute, Adam Mickiewicz University, Poznan, Poland

    Justyna Golebiewska

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  1. Vivian Martins Gomes
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  2. Jhonathan O. Murcia Piñeros
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  3. Antonio Fernando Bertachini de Almeida Prado
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  4. Justyna Golebiewska
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Correspondence to Vivian Martins Gomes.

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Communicated by Elbert E. N. Macau, Antônio Fernando Bertachini de Almeida Prado and Cristiano Fiorilo de Melo.

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Gomes, V.M., Piñeros, J.O.M., Prado, A.F.B.d.A. et al. Atmospheric close approaches with the Earth considering drag and lift forces. Comp. Appl. Math. 35, 817–833 (2016). https://doi.org/10.1007/s40314-015-0256-x

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  • DOI: https://doi.org/10.1007/s40314-015-0256-x

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