In the far future, astronauts travel to the planet Saturn and land on Mimas, one of its 62 moons. Mimas is small compared with the Earth's moon, with mass M_m = 3.75 X 10¹⁹ kg and radius R_m = 1.98 x 10⁵ m, giving it a free-fall acceleration of g = 0.0636 m/s². One astronaut, being a baseball fan and hav­ing a strong arm, decides to see how high she can throw a ball in this reduced gravity. She throws the hall straight m from the surface of Minas at a speed of 40 m/s (about 90 mph. the speed of a good major league fastball).

a. Predict the maximum height of the ball assuming g is constant and using energy conservation. Mimas has no atmosphere, so there is no air resistance.

b. Now calculate the maximum height using universal gravi­tation.

c. How far off is your estimate of part (a)? Express your answer m a percent difference and indicate if the estimate is too high or too low.