GMm The gravitational potential energy, in Joules, of a rocket above earth's surface can be calculated by Eg= where G is the universal gravitational constant (6.67 x 10 Nm/kg), M is the mass of the earth (5.98x 10 kg), mis the mass of the rocket in kg, and r is the distance from the earth's centre. The radius of the earth is 6.38 x 10 m. The mass of the rocket decreases while it is ascending as it is burning fuel. Consider a rocket for which the mass changes linearly (in real rockets it doesn't!) and the total mass of the rocket can be obtained by the equation m = 15000 - 60 (t) where it is the time since take-off, in seconds. a. Determine the gravitational energy of this rocket if it reached height of 200 km above the earth's surface in 120 s. b. Determine the average rate of change of gravitational energy of the rocket from 120 to 125 seconds, assuming it ascends another 10 km during that time.