Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 202–219

# Planar powered Swing-By maneuvers to brake a spacecraft

• Alessandra F. S. Ferreira
• Antônio F. B. A. Prado
• Othon C. Winter
Article

## Abstract

The Swing-By maneuver is a technique used in many space mission to modify the trajectory of a spacecraft. The most usual goal is to increase the energy of the spacecraft, but it is also possible to reduce this energy. An important application is to break a spacecraft coming to the Earth using a Swing-By with the moon, which is the example used in the present paper. Other possibilities also exist, such as reducing the velocity of a spacecraft going to the planets Mercury or Venus. The goal is to help a possible capture by the planet, or at least to provide a passage with smaller velocities to allow better observations during the passage. Therefore, the goal of the present paper is to study the energy loss that a spacecraft may have during a powered Swing-By maneuver, which is a maneuver that combines a close approach by a celestial body with the application of an impulsive maneuver. The behavior of the energy variation is analyzed as a function of the parameters related to the pure gravity maneuver: periapsis radius, angle of approach and approach velocity; and the parameters related to the impulsive maneuver: the location of application of the impulse and its direction and magnitude. The maneuver is performed in a system composed by two bodies, such as the Earth–moon system, around the secondary body, and the energy is measured with respect to the primary body of the system. This problem is solved by developing a mathematical algorithm that guides larger efforts in terms of computer simulations. The results show maps of conditions made from the numerical simulations for different points of application and direction of the impulse, where the maneuver is advantageous and how much more energy can be removed from the spacecraft.

## Keywords

Powered Swing-By Close approach Impulsive maneuvers Spacecraft trajectory Energy decrease

## Mathematics Subject Classification

70Fxx 70F07 70F15

## Notes

### Acknowledgements

The authors wish to express their appreciation for the support provided by the National Council for the Improvement of Higher Education (CAPES), the National Institute for Space Research (INPE), the Grants # 406841/2016-0 and 301338/2016-7 from the National Council for Scientific and Technological Development (CNPq), and the Grants # 2011/08171-3, 2016/14665-2, from Sao Paulo Research Foundation (FAPESP).

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## Authors and Affiliations

• Alessandra F. S. Ferreira
• 1
Email author
• Antônio F. B. A. Prado
• 1
• Othon C. Winter
• 2
1. 1.Instituto Nacional de Pesquisas EspaciaisSão PauloBrazil