Analytical study of the powered Swing-By maneuver for elliptical systems and analysis of its efficiency

  • Alessandra F. S. FerreiraEmail author
  • Antônio F. B. A. Prado
  • Othon C. Winter
  • Denilson P. S. Santos
Original Article


Analytical equations describing the velocity and energy variation of a spacecraft in a Powered Swing-By maneuver in an elliptic system are presented. The spacecraft motion is limited to the orbital plane of the primaries. In addition to gravity, the spacecraft suffers the effect of an impulsive maneuver applied when it passes by the periapsis of its orbit around the secondary body of the system. This impulsive maneuver is defined by its magnitude \(\delta V\) and the angle that defines the direction of the impulse with respect to the velocity of the spacecraft (\(\alpha\)). The maneuver occurs in a system of main bodies that are in elliptical orbits, where the velocity of the secondary body varies according to its position in the orbit following the rules of an elliptical orbit. The equations are dependent on this velocity. The study is done using the “patched-conics approximation”, which is a method of simplifying the calculations of the trajectory of a spacecraft traveling around more than one celestial body. Solutions for the velocity and energy variations as a function of the parameters that define the maneuver are presented. An analysis of the efficiency of the powered Swing-By maneuver is also made, comparing it with the pure gravity Swing-by maneuver with the addition of an impulse applied outside the sphere of influence of the secondary body. After a general study, the techniques developed here are applied to the systems Sun-Mercury and Sun-Mars, which are real and important systems with large eccentricity. This problem is highly nonlinear and the dynamics very complex, but very reach in applications.


Astrodynamics Powered Swing-By maneuvers Spacecraft trajectories Elliptical systems Impulsive maneuver 



The authors wish to express their appreciation for the support provided by grants # 406841/2016-0, 301338/2016-7 and 312813/2013-9 from the National Council for Scientific and Technological Development (CNPq); grants #2016/14665-2, 2016/24561-0, 2016/23542-1, and 2017/04643-4 from São Paulo Research Foundation (FAPESP) and the financial support from the National Council for the Improvement of Higher Education (CAPES).

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Instituto Nacional de Pesquisas Espaciais—INPESão José dos CamposBrazil
  2. 2.Grupo de Dinâmica Orbital e PlanetologiaSão Paulo State University—UNESPGuaratinguetáBrazil
  3. 3.São Paulo State University—UNESPSão João da Boa VistaBrazil

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