νA 2-DOF triaxial model for the roto-orbital coupling in a binary system. The slow rotation regime
Abstract
The Full Gravitational 2-Body Problem is far from being integrable and continues to be a challenge. From the analytical point of view, several approximations are studied ranging from fundamental astronomy to space mission applications. A classical approach, that we assume from now on is to consider the roto-orbital dynamics of a triaxial body around a primary homogeneous sphere. In this regard, the gravitational potential is commonly assumed to be the MacCullagh's truncation, although several recent papers go further than this approximation. We investigate analytical approximations, integrable or not, that could drastically simplify the search for special families of periodic or quasi-periodic orbit, where the influence of the roto-orbital coupling is considered. In this regard, we have presented recently some results [2], [3]. Our formulation is in Hamiltonian form and the variables in which the model is expressed are crucial in order to get compact expressions and intuitive geometric insight. Our choice is variables referred to the total angular momentum [1], which carry out the elimination of the nodes. The model is chosen from the MacCullagh's approximation without averaging. More precisely we choose the terms of the potential with depends only on the orbital variable r and the angular variable ν. Thus the Hamiltonian takes the form H = H(r,ν, R, N) is a 2-DOF system made of the Kepler and free rigid body together with the mentioned simplified potential. We examine families of relative equilibria leading to constant and non-constant radius solutions. We focus on the regime of slow rotations of the triaxial body, an assumption that brings different scenarios from the classical free rigid body. These families of relative equilibria include some of the classical ones, including `conic' trajectories reported in the literature and some new types showing the critical role played by the triaxiality. The applicability of our model is assessed numerically.
[1] J.M. Ferrandiz and M.E. Sansaturio, Celest. Mech. Dyn. Astr. 46 (1989), 307-320; [2] F. Crespo, F.J. Molero, S. Ferrer and D. Scheeres, J. of the Astro. Sci 65, (2018), 1-28; [3] F. Crespo and S. Ferrer, Ad. in Space Research 61 (2018), 2725-2739.- Publication:
-
AAS/Division of Dynamical Astronomy Meeting
- Pub Date:
- June 2019
- Bibcode:
- 2019DDA....5040105F