Dear sir,

The equations of motion governing the orbits of celestial bodies, such a planet around a star (the gravitational two-body problem in classical mechanics), do not include the spin angular momentum because the bodies are assumed to be point masses. Hence, only the orbital angular momentum plays a role in the equations of motion.

In reality, celestial bodies are not point masses, but are extended bodies having complex internal structures. Also, (Newtonian) gravity is a non-uniform force field. Therefore, the equations of motion of real celestial bodies must be modified by the inclusion of terms corresponding to tidal gravitational forces, which can act in the convective and radiative regions of low-mass stars, and within planets.

These tidal terms certainly depend on the spin angular momenta of the planet and the star. When the complex internal structures of stars and planets are considered along with tides, then we can no longer have simple equations of motion which can be analytically solved. We usually obtain a system of coupled differential equations which must be numerically solved.

For more details, please refer to the following assortment of references showing the derivation of the tidal terms for close-in planets around low-mass stars, how they are included in the planetary equations of motion, and the results of the numerical simulations:

Article Tidal Dissipation in Rotating Solar‐Type Stars

Article Tides in rotating barotropic fluid bodies: The contribution ...

Article Variation of tidal dissipation in the convective envelope of...

Article Effect of the rotation and tidal dissipation history of star...

Article Star-planet interactions V. Dynamical and equilibrium tides ...

Article Star-planet interactions. VI. Tides, stellar activity, and p...

Hello!

Celestial mechanics continue to be mathematical abstraction. So...