Spacecraft motion around artificial equilibrium points

Abstract

The main goal of this paper is to describe the motion of a spacecraft around an artificial equilibrium point in the circular restricted three-body problem. The spacecraft is under the gravitational influence of the Sun and the Earth, as primary and secondary bodies, subjected to the force due to the solar radiation pressure and some extra perturbations. Analytical solutions for the equations of motion of the spacecraft are found using several methods and for different extra perturbations. These solutions are strictly valid at the artificial equilibrium point, but they are used as approximations to describe the motion around this artificial equilibrium point. As an application of the method, the perturbation due to the gravitational influence of Jupiter and Venus is added to a spacecraft located at a chosen artificial equilibrium point, near the \(L_3\) Lagrangian point of the Sun–Earth system. The system is propagated starting from this point using analytical and numerical solutions. Comparisons between analytical–analytical and analytical–numerical solutions for several kinds of perturbations are made to guide the choice of the best analytical solution, with the best accuracy.

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Acknowledgements

The authors acknowledge financial support from CAPES—Coordination for the Improvement of Higher Education Personnel; from CNPQ—National Council for Scientific and Technological Development, Grants 305834/2013-4, 406841/2016-0 and 301338/2016-7; and from FAPESP—São Paulo Research Foundation, Grants 2016/14665-2, 2016/24561-0, 2014/22293-2 and 2014/22295-5.

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Correspondence to A. K. de Almeida Jr..

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de Almeida, A.K., Prado, A.F.B.A., Yokoyama, T. et al. Spacecraft motion around artificial equilibrium points. Nonlinear Dyn 91, 1473–1489 (2018). https://doi.org/10.1007/s11071-017-3959-2

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Keywords

  • Astrodynamics
  • Equilibrium points
  • Restricted three-body problem
  • Nonlinear systems