The discovery of chemical elements in celestial bodies and the first estimates of the chemical composition of the solar atmosphere were early results of Astrophysics - the subdiscipline of Astronomy that was originally concerned with the general laws of radiation and with spectroscopy. Following the initial quantitative abundance studies by Henry Norris Russell and by Cecilia Payne-Gaposchkin, a tremendous amount of theoretical, observa tional, laboratory and computational work led to a steadily improving body of knowledge of photospheric abundances - a body of knowledge that served to guide the theory of stellar evolution. Solar abundances determined from photospheric spectra, together with the very similar abundances determined from carbonaceous chondrites (where extensive information on isotopic composition is available as well), are nowadays the reference for all cosmic composition measures. Early astrophysical studies of the solar photospheric composition made use of atmosphere models and atomic data. Consistent abundances derived from different atmospheric layers and from lines of different strength helped to confirm and estab lish both models and atomic data, and eventually led to the now accepted, so-called "absolute" abundance values - which, for practical reasons, however, are usually given relative to the number of hydrogen nuclei.

Starting in 1995 numerical modeling of the Earth's dynamo has ourished with remarkable success. Direct numerical simulation of convection-driven MHD- ow in a rotating spherical shell show magnetic elds that resemble the geomagnetic eld in many respects: they are dominated by the axial dipole of approximately the right strength, they show spatial power spectra similar to that of Earth, and the magnetic eld morphology and the temporal var- tion of the eld resembles that of the geomagnetic eld (Christensen and Wicht 2007). Some models show stochastic dipole reversals whose details agree with what has been inferred from paleomagnetic data (Glatzmaier and Roberts 1995; Kutzner and Christensen 2002; Wicht 2005). While these models represent direct numerical simulations of the fundamental MHD equations without parameterized induction effects, they do not match actual pla- tary conditions in a number of respects. Speci cally, they rotate too slowly, are much less turbulent, and use a viscosity and thermal diffusivity that is far too large in comparison to magnetic diffusivity. Because of these discrepancies, the success of geodynamo models may seem surprising. In order to better understand the extent to which the models are applicable to planetary dynamos, scaling laws that relate basic properties of the dynamo to the fundamental control parameters play an important role. In recent years rst attempts have been made to derive such scaling laws from a set of numerical simulations that span the accessible parameter space (Christensen and Tilgner 2004; Christensen and Aubert 2006).

The discovery of chemical elements in celestial bodies and the first estimates of the chemical composition of the solar atmosphere were early results of Astrophysics - the subdiscipline of Astronomy that was originally concerned with the general laws of radiation and with spectroscopy. Following the initial quantitative abundance studies by Henry Norris Russell and by Cecilia Payne-Gaposchkin, a tremendous amount of theoretical, observa tional, laboratory and computational work led to a steadily improving body of knowledge of photospheric abundances - a body of knowledge that served to guide the theory of stellar evolution. Solar abundances determined from photospheric spectra, together with the very similar abundances determined from carbonaceous chondrites (where extensive information on isotopic composition is available as well), are nowadays the reference for all cosmic composition measures. Early astrophysical studies of the solar photospheric composition made use of atmosphere models and atomic data. Consistent abundances derived from different atmospheric layers and from lines of different strength helped to confirm and estab lish both models and atomic data, and eventually led to the now accepted, so-called "absolute" abundance values - which, for practical reasons, however, are usually given relative to the number of hydrogen nuclei.

Starting in 1995 numerical modeling of the Earth's dynamo has ourished with remarkable success. Direct numerical simulation of convection-driven MHD- ow in a rotating spherical shell show magnetic elds that resemble the geomagnetic eld in many respects: they are dominated by the axial dipole of approximately the right strength, they show spatial power spectra similar to that of Earth, and the magnetic eld morphology and the temporal var- tion of the eld resembles that of the geomagnetic eld (Christensen and Wicht 2007). Some models show stochastic dipole reversals whose details agree with what has been inferred from paleomagnetic data (Glatzmaier and Roberts 1995; Kutzner and Christensen 2002; Wicht 2005). While these models represent direct numerical simulations of the fundamental MHD equations without parameterized induction effects, they do not match actual pla- tary conditions in a number of respects. Speci cally, they rotate too slowly, are much less turbulent, and use a viscosity and thermal diffusivity that is far too large in comparison to magnetic diffusivity. Because of these discrepancies, the success of geodynamo models may seem surprising. In order to better understand the extent to which the models are applicable to planetary dynamos, scaling laws that relate basic properties of the dynamo to the fundamental control parameters play an important role. In recent years rst attempts have been made to derive such scaling laws from a set of numerical simulations that span the accessible parameter space (Christensen and Tilgner 2004; Christensen and Aubert 2006).