A Coupled 2D Translational-Rotational-Tidal model on Solar system bodies using a Maxwell viscoelastic rheology

A Coupled 2D Translational-Rotational-Tidal model on Solar system bodies using a Maxwell viscoelastic rheology

Mol, Jelle (TU Delft Aerospace Engineering)

Dirkx, D. (mentor)
Vermeersen, L.L.A. (graduation committee)
Menicucci, A. (graduation committee)

Delft University of Technology

Aerospace Engineering

2021-01-25

Planetary observational accuracy increases and the dynamical modeling of tidal behaviour has to follow. In this thesis, a newly developed method (Correia et al. 2014; Boue et al. 2016) to deal with tidal interactions in a 2D two body problem is validated and for the first time applied to Solar system dynamics on a short time-scale. This method uses a Maxwell rheology for the tidally perturbed body, to calculate the instantaneous deformation of the body with a differential equation at the same time as its position, spin vector and orientation. The coupling between the translational, rotational, and tidal dynamics is incorporated in a consistent way, taking into account the frequency dependency of classical tidal parameters. The coupled model is more general and is in contrast to currently used models valid for every eccentricity, spin rate and orientation. The model is applied to the Mars-Phobos and Earth-Moon systems and the tides are determined separately on both the central as the satellite body in various propagations. Several parameters of tidal effects of these systems are obtained and compared with currently available literature approximations and currently used tidal models. The instantaneous deformation of the tidal body and the evolution of the system's orbit for the tides on the primary compare to the literature approximations and currently used direct tidal force model (Lainey et al. 2007). However, the coupled model displays behaviour of the tidal time lag and angle, which are accompanied with the deformation, that cannot be captured by the classical method. Small differences between final states of the coupled model and the direct tidal force model are obtained that could potentially be important in future space missions and ephemeris determination. The tides on the locked secondary show a larger difference between the coupled model and the current tidal direct force models (Lainey et al. 2007; Lari et al. 2018) in the case of an existing libration. Phobos has such a libration and huge differences in evolution of the states and orbit are found. The coupled model's evolution values can be partly justified by the theoretical work of Efroimsky et al. (2018) that states the additional dissipation in these bodies with large librations. Altogether, currently used methods or literature approximations can still be used for inaccurate propagations. However, for more accurate propagations, and for bodies with large physical librations, it rewards to switch to a coupled method. Especially when regarding the tides on the satellite body a coupled model is beneficial.

Tidal dynamics
Maxwell model
Tidal evolution
Libration

http://resolver.tudelft.nl/uuid:e6b32ec7-6a17-433f-b179-e55aeec2cc35

2023-01-30

Student theses

master thesis

© 2021 Jelle Mol