Stellar dynamics

Stellar dynamics is the branch of astrophysics which describes in a statistical way the collective motions of stars subject to their mutual gravity. The essential difference from celestial mechanics is that each star contributes more or less equally to the total gravitational field, whereas in celestial mechanics the pull of a massive body dominates any satellite orbits. Stellar dynamics is usually concerned with the more global, statistical properties of several orbits rather than with the specific data on the positions and velocities of individual orbits. The motion of stars in a galaxy or in a globular cluster are principally determined by the average distribution of the other, distant stars, and little influenced by the nearest stars.

Recently, simulations of the N-body problem have provided an addition to the older analytical methods, enabling researchers to study systems that are otherwise intractable.

The long range of gravity and the slow "relaxation" of stellar systems prevent the use of the (conventional) methods of statistical physics, as stellar dynamical orbits tend to be much more irregular and chaotic than celestial mechanical orbits.

The "relaxation" of stars is the process deflecting the individual trajectories of stars from the one they would have if the distribution of matter was perfectly smooth. The "2-body relaxation" is induced by the individual star-star interactions, while the "violent relaxation" is induced by a large collective variation of the stellar system shape.

There is a mathematical undercurrent to stellar dynamics; the key physical theories, classical analytical mechanics, Newtonian gravity and (statistical) thermodynamics on the one hand are closely related to the mathematical branches of dynamical systems and ergodic theory (itself having major connections to DS theory) respectively. The possibility of gravitational interactions and collisions also lead to a treatment of mathematical scattering theory. As such a number of stellar dynamicists are also mathematicians by training.

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