The minimum and maximum distances of a satellite from the centre of the Earth are 2R and 4R respectively, where R is the radius of Earth and M is the Earth. The radius of curvature at the point of minimum distance is

 Using angular momentum conservation, which implies that any of the individual angular momenta can vary as long as the aggregate remains constant. When the external force on a system is zero, this equation is comparable to linear momentum being preserved. Angular momentum is just linear momentum that has been influenced by a tendency to turn in order for an item to remain at the same distance from a central point. Because linear momentum is preserved, angular momentum is conserved as well. In a circular motion, the distance travelled is just the angle in radians multiplied by the radius.


v12R = v24R


Using energy conservation equation:

−GMm/2R + 1/2mv12=−GMm/4R + 12mv22… (ii)

Substituting v2 in equation (ii) from equation (i)


v1 = √GM/6R

v2 = √2GM/3R

Radius of curvature =v2/an


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