Scaling Law for the Magnetic Field of the Planets Based on a Thermodynamic Model

Abstract

A thermodynamic model for the generation of magnetic fields in the planets is proposed, considering crossed effects between gravitational and electric forces. The magnetic field of the Earth is estimated and found to be in agreement with the actual field. The ratio between the field of several planets and that of the Earth is calculated in the model and compared with the same ratio for the measured fields. These comparisons are found to be qualitatively consistent. Once the value of the magnetic field is calculated, the model is used to obtain the tilt of the magnetic dipole with respect to the rotation axis. This model can explain why Uranus and Neptune magnetic fields have higher quadrupole moment than the other magnetic fields of the Solar System and why Saturn, that has a highly axysymmetric field, has lower quadrupolar component. The model also explains the double peak of the magnetic field observed by Voyager 2 while recording the field of Neptune. The Earth paleomagnetic data are analysed and found to be consistent with the model, that predicts higher quadrupole components for the more tilted dipoles. A field is predicted for all the planets and satellites of the Solar System with enough mass. Objections are made to the theories that predict that this effect could not generate a field agreeing with the measured one.