Abstract
In this communication we present an analytical model for the restricted three-body problem, in the case where the perturber is in a parabolic orbit with respect to the central mass. The equations of motion are derived explicitly using the so-called Global Expansion of the disturbing function, and are valid for any eccentricity of the massless body, as well as in the case where both secondary masses have crossing orbits. Integrating the equations of motion over the complete passage of the perturber through the system, we are then able to construct a first-order algebraic mapping for the change in semimajor axis, eccentricity and inclination of the perturbed body.
Comparisons with numerical solutions of the exact equations show that the map yields precise results, as long as the minimum distance between both bodies is not too small. Finally, we discuss several possible applications of this model, including the evolution of asteroidal satellites due to background bodies, and simulations of passing stars on extra-solar planets.
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Beaugé, C. The Parabolic Three-Body Problem. Celestial Mechanics and Dynamical Astronomy 88, 51–68 (2004). https://doi.org/10.1023/B:CELE.0000009382.85594.d4
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DOI: https://doi.org/10.1023/B:CELE.0000009382.85594.d4