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.

v1R1=v2R2

v12R = v24R

v1=2v2…(i)

Using energy conservation equation:

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

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

−GMm/4R=3/2mv12

v1 = √GM/6R

v2 = √2GM/3R

Radius of curvature =v2/an

= √8R/3