The planetary spin and rotation period: A modern approach

TL;DR

This paper introduces a new theoretical model for planetary rotation and radius, deriving formulas that align with observed properties of planets and exoplanets, and differs from traditional gravitomagnetism predictions.

Contribution

The paper presents a novel approach to planetary spin and radius calculations, incorporating a different spin-orbit coupling mechanism and deriving new formulas for tidally locked planets.

Findings

Predicted planetary rotation periods match observed data.

Derived formulas relate planetary radius and rotation period to mass and orbital distance.

Model differs from traditional gravitomagnetism predictions.

Abstract

Using a new approach, we have obtained a formula for calculating the rotation period and radius of planets. In the ordinary gravitomagnetism the gravitational spin ($S$) orbit ($L$) coupling, $\vec{L}\cdot\vec{S}\propto L^2$, while our model predicts that $\vec{L}\cdot\vec{S}\propto \frac{m}{M}\,L^2$, where $M$ and $m$ are the central and orbiting masses, respectively. Hence, planets during their evolution exchange $L$ and $S$ until they reach a final stability at which $MS\propto mL$, or $S\propto \frac{m^2}{v}$, where $v$ is the orbital velocity of the planet. Rotational properties of our planetary system and exoplanets are in agreement with our predictions. The radius ($R$) and rotational period ($D$) of tidally locked planet at a distance $a$ from its star, are related by, $D^2\propto \sqrt{\frac{M}{m^3}}\,\,R^3$ and that $R\propto \sqrt{\frac{m}{M}}\,\, a$.$a$ from its star, are related by, $D^2\propto \sqrt{\frac{M}{m^3}} R^3$ and that $R\propto \sqrt{\frac{m}{M}} a$.