Plummer model

The Plummer potential is an abstract mathematical potential. It was named after HC Plummer, which it introduced in 1911 for the calculation of globular clusters. It is useful in the numerical treatment of problems that include terms such as the limit.

Due to its close relationship with the Coulomb and gravitational potential - both are special cases of the Plummer potential - to find the most applications of this potential in electrodynamics and gravitation theory.

The potential function has the form

If, now, we obtain the classical ( Coulomb ) potential, which plays an important role in Newtonian gravitational theory and in electrodynamics:

Or

It the perfect place to to face the Plummer potential and the Coulomb potential: In contrast to the Coulomb potential, the Plummer potential at the site has no singularity, but has a finite value; the normal potential yields, however, for the undefined expression. For the Plummer potential in the zero point is continuous and differentiable, which is interesting for analytical calculations.

Application

An important application for the Plummer potential is found in astronomy, in the simulation of the dynamics of star clusters and galaxies. In simulations with many bodies ( so-called multi-body simulations) one is often not primarily interested in the collisions or near collisions between the body but. Adjoined by a large scale structures forming Since it is practically impossible to eliminate such collisions already at the initial conditions of a simulation, one is delighted with the Plummer potential, as it is a good approximation of the gravitational potential at large distances and does not grow for small distances across all borders. Come two bodies now too close, then they fly practically messed up, without excessive force occurs.

• Gravity
• Electrodynamics