Analytical theory of the spin-orbit state of a binary asteroid deflected by a kinetic impactor

• Published in: Celestial mechanics and dynamical astronomy Vol. 136; no. 4; p. 32
• Main Authors: Gaitanas, Michalis, Efthymiopoulos, Christos, Gkolias, Ioannis, Voyatzis, George, Tsiganis, Kleomenis
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.08.2024; Springer Nature B.V
• Subjects: Aerospace Technology and Astronautics; Asteroids; Astrophysics and Astroparticles; Axisymmetric bodies; Classical Mechanics; Deflection; Dynamical Systems and Ergodic Theory; Geophysics/Geodesy; Impact analysis; Mathematical analysis; Momentum transfer; Orbits; Original Article; Physics; Physics and Astronomy; Rigid structures; Shape effects; Kinetic impactor; Canonical perturbation theory; Dynamical evolution; Binary asteroid
• ISSN: 0923-2958; 1572-9478
• DOI: 10.1007/s10569-024-10204-4

We study the perturbed-from-synchronous librational state of a double asteroid, modeled by the Full Two Rigid Body Problem (F2RBP), with primary emphasis on deriving analytical formulas which describe the system’s evolution after deflection by a kinetic impactor. To this end, both linear and nonlinear (canonical) theories are developed. We make the simplifying approximations (to be relaxed in a forthcoming paper) of planar binary orbit and axisymmetric shape of the primary body. To study the effect of a DART-like hit on the secondary body, the momentum transfer enhancement parameter β is introduced and retained as a symbolic variable throughout all formulas derived, either by linear or nonlinear theory. Our approach can be of use in the context of the analysis of the post-impact data from kinetic impactor missions, by providing a precise modeling of the impactor’s effect on the seconadry’s librational state as a function of β .