Both models obtain their density by integrating a <galactic distribution function> over <velocity>. The planar model integrates one vertical <velocity>, whereas the spherical model integrates all three components. In each case the resulting density must also generate its own <gravitational potential> through the <Poisson equation for Newtonian gravity>. The two printed numerical subparts are treated separately below.

Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 72 / 1 / Solution

 Solution (source code)