The planetary spin and rotation period: A modern approach

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 $R\propto \sqrt{\frac{m}{M}} a$.