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 Mm = 3.75 X 1019 kg and radius Rm = 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.