Nature 281, 552 - 553 (18 October 1979); doi:10.1038/281552a0

Scaling law test and two predictions of planetary magnetic moments

C. T. Russell

Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90024

The scaling law for the strength of planetary magnetic dynamos, originally derived from a magnetohydrodynamic (MHD) theory¹, has recently been independently re-derived using simple dimensional analysis². While dimensional analysis is certainly no replacement for a solution based on a physical mechanism, this analysis does lend more credence to the scaling law by the implicit suggestion that the form of the scaling law is not an artefact of the MHD solution. We show here that the scaling law holds quite well in ordering the three well determined planetary magnetic moments. The present meagre data suggest that the terrestrial magnetic moment is about twice the value expected when compared with the other planets. Assuming that Earth is anomalous, rather than Mercury and Jupiter, and that the scaling law is valid, we predict that Saturn will be found to have a moment of 1.210²⁹ G cm³ and Io a moment of 6.510²² G cm³.

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