The contributions of Carl Friedrich Gauss to geomagnetism

AbstractThe three areas of geomagnetism in which Gauss made great contributions were those related to the absolute measurement of the field, the analysis in terms of spherical harmonics, and the organization and equipping of magnetic observatories. His approaches and accomplishments in these areas are examined in some detail. Because of the insufficiency of observations over the globe at the time he worked, many of the investigations which he proposed on the basis of the spherical harmonic analysis had to await later workers. These include the quantitative separation of internal and external sources, the effect of the earth's ellipsoidal shape, the possible non-vanishing of the constant term in the expression for the potential and the possible existence of a non-potential portion of the field. The results of these later investigations are outlined

Geophysical constraints on mirror matter within the Earth

We have performed a detailed investigation of geophysical constraints on the possible admixture of mirror matter inside the Earth. On the basis of the Preliminary Reference Earth Model (PREM) -- the `Standard Model' of the Earth's interior -- we have developed a method which allows one to compute changes in various quantities characterising the Earth (mass, moment of inertia, normal mode frequencies etc.)due to the presence of mirror matter. As a result we have been able to obtain for the first time the direct upper bounds on the possible concentration of the mirror matter in the Earth. In terms of the ratio of the mirror mass to the Earth mass a conservative upper bound is $3.8\times 10^{-3}$. We then analysed possible mechanisms (such as lunar and solar tidal forces, meteorite impacts and earthquakes) of exciting mirror matter oscillations around the Earth centre. Such oscillations could manifest themselves through global variations of the gravitational acceleration at the Earth's surface. We conclude that such variations are too small to be observed. Our results are valid for other types of hypothetical matter coupled to ordinary matter by gravitation only (e.g. the shadow matter of superstring theories).Comment: 25 pages, in RevTeX, to appear in Phys.Rev.