English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Tidal dissipation of kinetic energy, when it is strong enough, tends tosynchronize the rotation of planets and moons with the mean orbital motion, ordrive it into long-term stable spin-orbit resonances. As the orbital motionundergoes periodic acceleration due to a finite orbital eccentricity, the spinrate oscillates around the equilibrium mean value too, giving rise to theforced, or eccentricity-driven, librations. Both the shape and amplitude offorced librations of synchronous viscoelastic planets and moons are defined bya combination of two different types of perturbative torque, the tidal torqueand the triaxial torque. Consequently, forced librations can be tidallydominated (e.g., Io and possibly Titan) or deformation-dominated (e.g., theMoon) depending on a set of orbital, rheological, and other physicalparameters. With small eccentricities, for the former kind, the largest term inthe libration angle can be minus cosine of the mean anomaly, whereas for thelatter kind, it is minus sine of the mean anomaly. The shape and the amplitudeof tidal forced librations determine the rate of orbital evolution ofsynchronous planets and moons, i.e., the rate of dissipative damping ofsemimajor axis and eccentricity. The known super-Earth exoplanets can exhibitboth kinds of libration, or a mixture thereof, depending on, for example, theeffective Maxwell time of their rigid mantles. Our approach can be extended toestimate the amplitudes of other libration harmonics, as well as the forcedlibration in non-synchronous spin-orbit resonances.

Forced libration of tidally synchronized planets and moons