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# Softening

[saw-fuhn, sof-uhn]
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

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

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

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