A comparison of the “patched-conics approach” and the restricted problem for swing-bys Original Research Article

In the present paper we study swing-by maneuvers that use the planet Jupiter as the body for the close approach. The main goal is to simulate a large variety of initial conditions for those orbits and study the effects caused by the close approach with Jupiter in the orbit of the spacecraft. The planar restricted circular three-body problem and the “patched-conics” approach are used as the mathematical models. For the planar restricted circular three-body problem, the equations are regularized (using Lemaıˆtre’s regularization), so it is possible to avoid the numerical problems that come from the close approach with Jupiter. Then, the results obtained with these well-known dynamics are compared. We see that there is a good agreement of the two models studied in the majority of the situations, but there are large discrepancies in the results of the semi-major axis when the energy before or after the passage is small. There are differences in semi-major axis larger than 10% of the Sun–Jupiter distance in about 5% of the trajectories simulated. Differences in the order of several hundreds of the Sun–Jupiter distances were also encountered.