Newtonian scattering and cross section

n equal point particles are sent, along the X axis, with impact parameters -bmax < b < bmax, against a spherical target fixed at the origin of coordinates.

The potential is Newtonian, V(r) = -k/r, and depending on the sign of k, it can be attractive, repulsive or null.
The unit mass is chosen equal to the mass of each particle.
Below you can also choose from which abscissa (x) and with which velocity (v,0,0) are sent the particles, as well as the target radius R.
To get information on the other elements, put over them the mouse pointer to see the corresponding tooltip.

Activities

Discuss the scattering/capture cross section at least in the following cases:

k = 0 (bullets shot against a spherical target).
k = 15 (meteorites approaching Earth).
k = -15 (α particles against a fixed nucleus).
k = -15, v = 8 (the previous case with higher energy).
k = -15, v = 15, bmax = 3, n = 99, R = 0.1.

This is an English translation of the Basque original for a course on mechanics, oscillations and waves.
It requires Java 1.5 or newer and was created by Juan M. Aguirregabiria with Easy Java Simulations (Ejs) by Francisco Esquembre. I thank Wolfgang Christian and Francisco Esquembre for their help.