Cartography of the b-plane of a close encounter I: semimajor axes of post-encounter orbits

• Published in: Celestial mechanics and dynamical astronomy Vol. 130; no. 2; pp. 1 - 14
• Main Authors: Valsecchi, G. B., Alessi, E. M., Rossi, A.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2018; Springer Nature B.V
• Subjects: Aerospace Technology and Astronautics; Astrophysics and Astroparticles; Cartography; Classical Mechanics; Close Approaches and Collisions in Planetary Systems; Dynamical Systems and Ergodic Theory; Evolution; Geophysics/Geodesy; Initial conditions; Mathematical analysis; Numerical integration; Orbital elements; Orbits; Original Article; Physics; Physics and Astronomy; Planetary evolution; Solar system; Solar system evolution; Close encounter; Perturbation
• ISSN: 0923-2958; 1572-9478
• DOI: 10.1007/s10569-017-9810-8

Close planetary encounters play an important role in the evolution of the orbits of small Solar system bodies and are usually studied with the help of numerical integrations. Here we study close encounters in the framework of an analytic theory, focusing on the so-called b -plane, which is the plane centred on the planet and perpendicular to the planetocentric velocity at infinity of the small body. As shown in previous papers, it is possible to identify the initial conditions on the b -plane that lead to post-encounter orbits of given semimajor axis. In this paper we exploit analytical relationships between b -plane coordinates and pre-encounter orbital elements and compute the probability of transition to these post-encounter states, and numerically check the validity of the analytic approach.