The idea of a point mass in Physics

Some physical phenomena are complex to describe so it is very useful to make some simplifications. One of the them is the idea of a point mass, an object with finite mass whose dimensions we deem negligible, so it is specified completely with a geometric point in space. The simplification of a body as a point mass is appropriate occasionally. For example, the Earth can be specified successfully as a point mass when we study its trajectory around the sun, but obviously, the simplification fails when we study the propagation of shock waves within the earth.