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Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 267–281 | Cite as

Some characteristics of orbits for a spacecraft around Mercury

  • J. P. S. CarvalhoEmail author
  • J. Cardoso dos Santos
  • A. F. B. A. Prado
  • R. Vilhena de Moraes
Article

Abstract

Solar sails are a type of propulsion that uses solar radiation pressure to generate acceleration. The fundamental goal for any solar sail design is to provide a large and flat reflective film which requires a minimum of structural support mass. This research takes into account the non-sphericity of the central body, the perturbation of the third body and the solar radiation pressure to analyze the behavior of the orbit of a spacecraft when it has a solar sail around Mercury. We present an approach where we plot maps to analyze frozen orbits with longer lifetimes around Mercury. A set of initial conditions, which may contribute with the scientific missions planned to visit the planet Mercury in the next few years, are presented. Frozen orbits were found, i.e., orbits with smaller variation of the orbital elements. An approach is also presented to analyze the effect of the non-sphericity of Mercury on the motion of the spacecraft. In addition, the \(J_{2}\) and \(J_{3}\) zonal terms are also considered, as well as the \(C_{22 }\) sectorial term.

Keywords

Solar sail Frozen orbits Third-body perturbation Solar radiation pressure Mercury 

Mathematics Subject Classification

70F15 70F99 

Notes

Acknowledgements

Sponsored by CNPq—Brazil. The authors are grateful to CNPq (National Council for Scientific and Technological Development) and FAPESP (So Paulo Research Foundation)—Brazil for contracts 306953/2014-5, 420674/2016-0 (CNPq) and 2013/26652-4 (FAPESP).

References

  1. Brouwer D, Clemence GM (1961) Methods of celestial mechanics. Academic, New York, p 595Google Scholar
  2. Carvalho JPS, Vilhena de Moraes R, Prado AFBA (2010) Some orbital characteristics of lunar artificial satellites. Celest Mech Dyn Astron 108:371–388MathSciNetCrossRefGoogle Scholar
  3. Carvalho JPS, Elipe A, Vilhena de Moraes R, Prado AFBA (2012) Low-altitude, near-polar and near-circular orbits around Europa. Adv Sp Res 49:994–1006CrossRefGoogle Scholar
  4. Carvalho JPS, Vilhena de Moraes R, Prado AFBA (2013) Dynamics of artificial satellites around Europa. Math Probl Eng 2013:2155–2171 (Article ID 182079)Google Scholar
  5. Elipe A, Lara M (2003) Frozen orbits about Moon. J Guid Control Dyn 26:238–243CrossRefGoogle Scholar
  6. Faria MCP (2009) Dinâmica orbital e controle de orientação de um veículo espacial com uma vela solar composta. Tese de doutorado em Engenharia e Tecnologia Espacial/Mecânica Espacial e Controle, INPEGoogle Scholar
  7. Fu B, Sperber E, Eke F (2016) Solar sail technology—a state of the art review. Progress Aerosp Sci 86:1–19Google Scholar
  8. Giacaglia GEO, Murphy J, Felsentreger T (1970) A semi-analytic theory for the motion of a lunar satellite. Celest Mech 3:3–66CrossRefGoogle Scholar
  9. Gomes VM, Domingos RC (2016) Studying the lifetime of orbits around Moons in elliptic motion. Comp Appl Math 35(3):653–661MathSciNetCrossRefGoogle Scholar
  10. Kinoshita H (1980) Comment on ’Poisson equations of rotational motion for a rigid triaxial body with application to a tumbling artificial satellite’ by Liu and Fitzpatrick. Celest Mech 21:253–257CrossRefGoogle Scholar
  11. Mazarico E, Genova A, Goossens S et al (2014) The gravity field, orientation, and ephemeris of Mercury from MESSENGER observations after three years in orbit. J Geophys Res Planets 119:2417–2436. doi: 10.1002/2014JE004675 CrossRefGoogle Scholar
  12. McInnes CR (1999) Solar sailing: technology, dynamics and mission applications, Springer-praxis series in space science and technology. Springer, BerlinCrossRefGoogle Scholar
  13. Meyer WK, Buglia JJ, Dsai PN (1994) Lifetimes of lunar satellite orbits. NASA STI/Recon Technical Report N-TP-3394 94, 27771Google Scholar
  14. Oliveira TC, Prado AFBA (2015) Evaluating orbits with potential to use solar sail for station-keeping maneuvers. Adv Astronaut Sci 153:1699–1718Google Scholar
  15. Rahoma WA, Abd El-Salam FA (2014) The effects of Moon’s Uneven mass distribution on the critical inclinations of a lunar orbiter. J Astron Sp Sci 31(4):285–294CrossRefGoogle Scholar
  16. Sehnal L (1959) The influence of the equatorial ellipticity of the Earth gravitational field on the motion of a close satellite. Bull Astronaut Inst Czechoslovak Acad Sci 11:90–93zbMATHGoogle Scholar
  17. Stark A, Oberst J, Hussmann H (2015) Mercury’s resonant rotation from secular orbital elements. Celest Mech Dyn Astron 123:263–277MathSciNetCrossRefGoogle Scholar
  18. Tresaco E, Elipe A, Carvalho JPS (2016) Frozen orbits for a solar sail around mercury. J Guid Control Dyn 39(7):1659–1666CrossRefGoogle Scholar
  19. Tresaco E, Carvalho JPS, Prado AFBA, Elipe A, Vilhena de Moraes R (2017) Effects of the solar radiation pressure and the \(C_{22}\) coefficient in frozen orbits around Mercury (to appear)Google Scholar

Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.UFRB-Centro de Ciência e Tecnologia em Energia e Sustentabilidade, Universidade Federal do Recôcavo da BahiaFeira de SantanaBrazil
  2. 2.UNESP-São Paulo State UniversityGuaratinguetáBrazil
  3. 3.Division of Space Mechanics and ControlINPESão José dos CamposBrazil
  4. 4.UNIFESP-Instituto de Ciência e Tecnologia, Universidade Federal de São PauloSão José dos CamposBrazil

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