A geostationary satellite is orbiting in circular orbit. Due to internal forces suppose rotating earth automatically shrinks to half the present radius. Assuming mass of the earth remains constant. With respect to a point on equator, now the satellite

The angular momentum of earth will remain conserved. Since moment of inertia will reduce to one fourth the new angular speed of the earth will become four times the old angular speed while the angular speed of the satellite will not change. The relative angular speed will become 3 and hence it will take three times less time to complete the cycle w.r.t earth. Since earth moves from west to east, the satellite will be seen to move in opposite direction i.e, westward with time period.

$\frac{2\pi }{3\omega }=\frac{1}{3}\left(\frac{2\pi }{\omega }\right)=\frac{1}{3}\left(24hrs\right)=8hrs$