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