In: Physics
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 masses2 solar masses into a sphere with a radius on the order of 10 km. At the moment shown, the two probes are d=55.3 kmd=55.3 km and D=178 kmD=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.
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For center of mass
=> X cm = ( M*55.3 + M*178 ) /2M
= 116.65 km
For center of gravity
Gravitational Force , F1 = GMm/55.32
Gravitational Force , F2 = GMm/1782
=> Center of gravity = ( GMm/55.32 * 55.3 + GMm/1782 * 178) / ( GMm/55.32 + GMm/1782 )
= 66.1004 km
=> distance b/w center of mass and center of gravity = 116.65 km - 66.1004 km
= 50.55 km
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