Application of Tisserand’s Criterion to the Analysis of Gravity Assist
- Paper number
IAC-06-A3.P.02
- Author
Mr. Qiao Dong, Harbin Institute of Technology, China
- Coauthor
Mr. Pingyuan Cui, Harbin Institute of Technology, China
- Coauthor
Mr. Cui Hutao, Harbin Institute of Technology, China
- Coauthor
Mrs. Yan Xia, China
- Year
2006
- Abstract
Gravity assist involves the use of the gravitational attraction of an intermediate planet to increase the orbit energy of a spacecraft, enabling it to attain the target planet. Gravity assist trajectories are an important class of trajectories that have been used by Voyager, Galileo, Cassini, and other missions to tour the solar system. The missions that involve planetary gravity assists are commonplace. Analytical express relating outgoing to incoming geocentric orbital elements after a planetary gravity assist (planetary flyby or swing-by) can be helpful as a guide in the interplanetary mission design and complementary to numerical analysis. In this paper, we derive analytical expressions for the final geocentric semi-major axis and eccentricity after a planetary gravity assist. During a planetary flyby, the periapse vector lies in the plane of the planet-centric hyperbolic trajectory and this condition reduces the number of its independent components form three to two. The two components we use are the magnitude of the periapse vector and one angle defined as the angle between the periapse vector and the orbital velocity vector of the planetary. To calculate the scattering angle, we need to know another parameter, the asymptotic speed of the spacecraft in the planetary frame, V-inf. With three standard approximations, we derive analytical expressions for the final semi-major axis and eccentricity after the planetary gravity assist, respectively. The analytical expressions are a function of the three scattering parameters as well as functions of the initial semi-major and eccentricity. We then compare the analytical results with integrated numerical which include the point mass gravitational field of the Sun and planets. The numerical results are obtained using ephemeris data that include the position and velocity of the Sun, planets. The analytical result is not confined to the Sun-Planets system and can be applied to any other system where one object moves roughly in circular motion about a much more massive object.
- Abstract document