An analytical solution for the swing-by problem

• Published in: Celestial mechanics and dynamical astronomy Vol. 123; no. 2; pp. 151 - 166
• Main Authors: Valsecchi, G. B., Alessi, E. M., Rossi, A.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.10.2015; Springer Nature B.V
• Subjects: Aerospace Technology and Astronautics; Algorithms; Astrophysics; Astrophysics and Astroparticles; Circular orbits; Classical Mechanics; Dynamical Systems and Ergodic Theory; Eccentricity; Encounters; Geometry; Geophysics/Geodesy; Inclination; Mathematical analysis; Orbits; Original Article; Physics; Physics and Astronomy; Planetary probes; Space debris; Spacecraft; Extended Öpik theory; JUICE encounters; Close encounter orbit; Apophis; Collision
• ISSN: 0923-2958; 1572-9478
• DOI: 10.1007/s10569-015-9631-6

The extension of Öpik’s theory of close encounters developed in the last decades allows a fully analytical, quantitative treatment of the motion of a small body encountering a massive perturber on a circular orbit. In this paper we derive explicit expressions for the initial values of the angular elements of the small body orbit, of given semimajor axis, eccentricity and inclination, in order to obtain a post-encounter orbit with prescribed values of semimajor axis, eccentricity and inclination. We describe the geometrical aspects of the algorithm, and give two examples of application; the first of them concerns the geometry of the 2029 Earth encounter of Apophis, while the second illustrates a sequence of close encounters with Callisto of the JUICE probe, aimed at changing the inclination of the spacecraft orbit. In the planning of complex space missions involving multiple encounters with planets or satellites, the algorithm described in the paper could provide a reliable initial guess to start the computationally intensive optimization process.