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


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.


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

Mathematics Subject Classification

70F15 70F99 



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).


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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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