Magnetic field generation in the cores of terrestrial bodies

Efforts to find some scaling law for the dipole moments of planets seem illusory for, although dynamo theory is still in a rudimentary state, once the critical magnetic Reynolds Number is exceeded it appears that the field strength is determined by the energy source, it it is permissible to treat the core as a heat engine. For this reason the lunar magnetic field is of special significance as the paleomagnetic evidence strongly suggests that the surface field was about 1 G 3.9 by diminishing exponentially to about .02 G 3.2 by ago and completely disappearing some time later.