Question

the scattering angle in inverse cube law force

Answer 1

You can obtain the trajectory starting from the conserved quantities, which are the total energy and the angular momentum. By parametrizing the motion using polar coordinates in the plane of the orbit (the orbit is in a plane owing to conservation of angular momentum) you get

E=12mr˙2+12mr2θ˙2+ar+br2

for the energy and

Lz=mr2θ˙

for the component of angular momentum