Tidal evolution for any rheological model using a vectorial approach expressed in Hansen coefficients
arXiv:2306.03449 · doi:10.1007/s10569-022-10079-3
Abstract
We revisit the two body problem, where one body can be deformed under the action of tides raised by the companion. Tidal deformation and consequent dissipation result in spin and orbital evolution of the system. In general, the equations of motion are derived from the tidal potential developed in Fourier series expressed in terms of Keplerian elliptical elements, so that the variation of dissipation with amplitude and frequency can be examined. However, this method introduces multiple index summations and some orbital elements depend on the chosen frame, which is prone to confusion and errors. Here, we develop the quadrupole tidal potential solely in a series of Hansen coefficients, which are widely used in celestial mechanics and depend just on the eccentricity. We derive the secular equations of motion in a vectorial formalism, which is frame independent and valid for any rheological model. We provide expressions for a single average over the mean anomaly and for an additional average over the argument of the pericentre. These equations are suitable to model the long-term evolution of a large variety of systems and configurations, from planet satellite to stellar binaries. We also compute the tidal energy released inside the body for an arbitrary configuration of the system.
arXiv comment33 pages, 1 figure, 2 tables
References in corpus (20)
- Tidal dissipation in rotating giant planets
- Tidal dissipation in rotating solar-type stars
- Tidally Heated Terrestrial Exoplanets: Viscoelastic Response Models
- The Physics of Bodily Tides in Terrestrial Planets, and the Appropriate Scales of Dynamical Evolution
- Bodily tides near spin-orbit resonances
- Tidal torques. A critical review of some techniques
- Tidal evolution of hierarchical and inclined systems
- Increased Tidal Dissipation Using Advanced Rheological Models: Implications for Io and Tidally Active Exoplanets
- Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology
- Tidal synchronization of close-in satellites and exoplanets. A rheophysical approach
- Explicit expansion of the three-body disturbing function for arbitrary eccentricities and inclinations
- Anelastic tidal dissipation in multi-layer planets
- Secular evolution of a satellite by tidal effect. Application to Triton
- Compact planetary systems perturbed by an inclined companion: I. Vectorial representation of the secular model
- Complete spin and orbital evolution of close-in bodies using a Maxwell viscoelastic rheology
- Secular and tidal evolution of circumbinary systems
- Tidal Evolution of Close Binary Asteroid Systems
- Andrade rheology in time-domain. Application to Enceladus' dissipation of energy due to forced libration
- Precession Relaxation of Viscoelastic Oblate Rotators
- On the Stability of Extrasolar Planetary Systems and other Closely Orbiting Pairs
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