Softening

Softening is a numerical trick used in N-body techniques to prevent numerical divergences when a particle comes too close to another (and the force goes to infinity). This is obtained by modifying the gravitational potential of each particle as

$\Phi =-{\frac {1}{\sqrt {r^{2}+\epsilon ^{2}}}},$

where $\epsilon$ is the softening parameter. The value of the softening parameter should be set small enough to keep simulations realistic.