Mathematics – Probability
Scientific paper
May 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995jgr...100.9439c&link_type=abstract
Journal of Geophysical Research (ISSN 0148-0227), vol. 100, no. E5, p. 9439-9454
Mathematics
Probability
13
Angular Momentum, Magnetic Dipoles, Magnetic Fields, Magnetic Moments, Poloidal Flux, Solar System, Solar System Evolution, Statistical Analysis, Astronomical Models, Correlation, Earth (Planet), Io, Mars (Planet), Mathematical Models, Monte Carlo Method, Venus (Planet)
Scientific paper
The magnetic moments and angular momenta of Solar System bodies are compared to evaluate the statistical reality of the relation that has come to be called the 'magnetic Bode law.' Runcorn has suggested that this 'law', giving a slope of about 3/5 on a log-log plot, is only a geometrical effect of the angular momenta being proportional to the fifth power of radius and the magnetic moment the cube. The best fit line to the six planets with nonzero magnetic fields is log(m/me) = -0.2(+/- 0.2) + 0.82(+/- 0.05) log(L/Le), where the subscripts denote the values for Earth. The value 0.82 is shown to be consistent with the 3/5 slope once estimation bias is accounted for. Monte Carlo analysis was used to construct (2500) synthetic solar systems from the variables representing the range of the planet's radii, densities, coefficients of inertia, periods of rotation, and surface poloidal field intensity. If these variables are considered independent, it was found that the probability of obtaining a slope as different from 0.6 as suggested by Runcorn is 34%, but only a 0.2% chance of obtaining values that are so linear as the actual data on this plot. If instead the covariances of the actual planets are included in the analysis, the mean slope is 0.82 with small deviation, but the odds of obtaining such a tight fit as that observed in the actual Solar System becomes 63%. It is concluded that considering the lack of physical plausibility of the correlations between the physical parameters besides field, the strong correlation with rotation as an important factor in computing the angular momentum is spurious.
Beaumont Paul
Cain Joseph C.
Holter William
Nevanlinna Heikki
Wang Zhigang
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