The planetary spin and rotation period: A modern approach

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 \(R\propto \sqrt{\frac{m}{M}} a\).