Gravitational *N*-Body Problem
pp 18-21 |
Cite as

# A Certain Discontinuous Markov Process in Stellar Dynamics

Conference paper

## Abstract

The basic assumption in Chandrasekhar’s approach of statistical stellar dynamics (Chandrasekhar, 1942) is the postulate that a test star within a stellar system being stationary in the sense of collisionless continuum theory suffers random displacements in velocity space generated by the fluctuating part of the gravitational field in a manner that can be described in terms of a random walk. This is equivalent to the assertion that the increments of velocity are regarded as stochastically independent in disjoint time intervals. From this Chandrasekhar derived a diffusion process in velocity space. The equation of motion of the probability density

*W*(*r, u, t*) in the whole 6-dimensional phase space is then written in the form of a Fokker-Planck-type equation:$$\frac{{\partial W}}{{\partial t}}+u\cdot{\nabla_r}W+{\nabla_r}\Phi\cdot{\nabla_u}W={\nabla_u}\left({q{\nabla_u}W+\eta{W_u}}\right)$$

(1)

*r, u*= position, velocity vector;*Φ*= gravitational potential of the ‘smoothed out’ distribution of matter;*q*= diffusion coefficient; and*η*= coefficient of dynamical friction.## Preview

Unable to display preview. Download preview PDF.

## References

- Chandrasekhar, S.: 1942,
*Principles of Stellar Dynamics*,New York.Google Scholar - Feller, W.: 1966,
*An Introduction to Probability Theory and Its Applications*, Vol. II, New York.zbMATHGoogle Scholar - Wielen, R.: 1967,
*Veröff. Astron. Rechen-Inst. Heidelberg*,No. 19.Google Scholar

## Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1972