Center of Mass - Physics?

Posted on 2016-03-03 18:52:00 in Physics by RONIC

Two identical probes are sent along the same path toward a neutron star. A neutron star is very dense, packing as much as 2 solar masses into a sphere with a radius on the order of 10 km. At the moment shown, the two probes are 61.9 km and 178 km away from the center of the neutron star, respectively. 
Find the distance between the center of mass of the two probe system and its center of gravity. 

Hint: 
For many systems, the center of gravity is essentially the same as the center of mass. However, in systems like the one above, the variation of the gravitational force with position must be considered. The coordinates of the center of gravity can be expressed just like the coordinates of the center of mass, except with the mass of each body replaced by the force of gravity acting on that body. Assume that the probes are small enough to be treated like point masses and their masses are negligible compared to the neutron star mass.

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