Tides in a body librating about a spin–orbit resonance: generalisation of the Darwin–Kaula theory View Full Text


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Article Info

DATE

2017-06-28

AUTHORS

Julien Frouard, Michael Efroimsky

ABSTRACT

The Darwin-Kaula theory of bodily tides is intended for celestial bodies rotating without libration. We demonstrate that this theory, in its customary form, is inapplicable to a librating body. Specifically, in the presence of libration in longitude, the actual spectrum of Fourier tidal modes differs from the conventional spectrum rendered by the Darwin–Kaula theory for a nonlibrating celestial object. This necessitates derivation of formulae for the tidal torque and the tidal heating rate, that are applicable under libration. We derive the tidal spectrum for longitudinal forced libration with one and two main frequencies, generalisation to more main frequencies being straightforward. (By main frequencies we understand those emerging due to the triaxiality of the librating body.) Separately, we consider a case of free libration at one frequency (once again, generalisation to more frequencies being straightforward). We also calculate the tidal torque. This torque provides correction to the triaxiality-caused physical libration. Our theory is not self-consistent: we assume that the tidal torque is much smaller than the permanent-triaxiality-caused torque, so the additional libration due to tides is much weaker than the main libration due to the permanent triaxiality. Finally, we calculate the tidal dissipation rate in a body experiencing forced libration at the main mode, or free libration at one frequency, or superimposed forced and free librations. More... »

PAGES

177-214

References to SciGraph publications

  • 2010-10-26. The Moon’s physical librations and determination of their free modes in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2008-07-01. On the inclination functions and a rapid stable procedure for their evaluation together with derivatives in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2010-09-14. Tidal evolution of close binary asteroid systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2008-05-07. Tidal friction in close-in satellites and exoplanets: The Darwin theory re-visited in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2012-11-22. Bodily tides near the 1:1 spin-orbit resonance: correction to Goldreich’s dynamical model in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2015-06-27. Tidal synchronization of close-in satellites and exoplanets: II. Spin dynamics and extension to Mercury and exoplanet host stars in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2012-03-02. Bodily tides near spin–orbit resonances in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1981-08. Theory of the libration of the moon in EARTH, MOON, AND PLANETS
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