Imagine a solid sphere with practically zero mass (say made of cork). Embedded randomly within it are two point like masses of mass M1 and M2 (imagine two mahogany pellets). Now it is easy to find the combined centre of mass. But what methods are there of determining the positions of the two point masses? The only knowledge that we have is that there are 2 mass points inside the sphere (invisible to the external observer.) We are allowed to do anything to the sphere, move it, shake it whatever. Is it possible to determine the positions (and mass ratios) of the two mass points?