Dynamical Principles

Abstract

In this chapter we lay down the dynamical equations that govern the motion and determine the structure of a planetary body and its environment. The basic model is that of a continuum, whose local properties are described by the matter density ρ, the flow velocity v and the temperature T. If the fluid is electrically conductive, we must add the magnetic field B. These quantities obey a set of partial differential equations which will be discussed in the relevant approximations, with examples and illustrations taken from the physics of the solar system. Gravitation plays an essential role here: a long range force, it becomes more and more important with increasing size. It determines the shape, the size and the structure of the planets, the stars, the galaxies and the universe itself. It is balanced primarily by the thermal pressure and secondarily by centrifugal forces: this balance is responsible for the usually spherical shape of cosmic bodies. When a body is sufficiently small and cold, however, it solidifies; its structure is then determined by elastic forces. In cosmic bodies different transport processes play important roles; in particular, the transport of momentum determines viscosity and the transport of energy is the basis for heat conduction. In an electrically conductive medium we have a large variety of electric and magnetic processes, like the generation of large scale magnetic fields in rotating bodies, acceleration of particles, propagation of different kinds of electromagnetic waves. In an ionized gas, when collisions are unimportant, the appropriate description requires the velocity space and gives rise to a much greater variety of phenomena.