Statistical properties of the gravitational force in a random homogeneous medium
- Resource Type
- Authors
- Payerne, Constantin
- Source
- [Research Report] Université Grenoble-alpes; Laboratoire de Physique et de Modélisation des Milieux Condensés. 2020
- Subject
- [PHYS]Physics [physics]
[STAT]Statistics [stat]
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
[PHYS.COND]Physics [physics]/Condensed Matter [cond-mat]
- Language
- English
We discuss the statistical distribution of the gravitational (Newtonian) force exerted on a test particle in a infinite random and homogeneous gas of non-correlated particles (stars, galaxies, ...) where the first configuration of particles in space is a Poisson distribution. The exact solution is known as the Holtsmark distribution at the limit of infinite system corresponding to the number of particle N within the volume and the volume go to infinity. The statistical behavior of the gravitational force for scale comparable to the inter-distance particle can be analyzed through the combination of the n-th nearest neighbor particle contribution to the total gravitational force, which can be derived from the joint probability density of location for a set of N particles. We investigate two independent approaches to derive the joint probability density of location for a set of N neighbors using integral forms and order statistics to give a general expression of such probability distribution with generalized dimension of space d.