The Earth is bound to the Sun due to the gravitational pull, Mm F(r)=-G- G>0. Here M and m are the masses of the Sun and Earth, respectively. Assume the Earth's angular momentum is L. (a) Write the effective potential, V(r). Set the zero point of V(r) at infinity. (6 marks) (b) Since the eccentricity of the Earth's orbit is very small, we can assume the Earth's orbit is circular. If the Sun's mass suddenly reduces to half of its original value, show that Earth will shoot out following a parabolic trajectory. (10 marks)