A rocket carrying a new 945-kg satellite into orbit misfires and places the satellite in an orbit with an altitude of 175 km, well below its operational altitude in low-Earth orbit. (a) What would be the height of the satellite’s orbit if its total energy were 450 MJ greater? km (b) What would be the difference in the system’s kinetic energy? (Include the sign of the value in your answer.) Mj (c) What would be the difference in the system’s potential energy? (Include the sign of the value in your answer.) Mj In the far future, astronauts travel to the planet Saturn and land on Mirnas, one of its 62 muons. Mirnas is small compared with the Earth’s moon, with mass M_m = 3.75 times 10^19 kg and radius R_m = 1.98 times 10^5 m, giving it a free-fall acceleration of g = 0.0636 m/s^2. 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 ball straight up from the surface of Mirnas at a speed of 36 m/s (about 81 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. Mirns has no atmosphere, so there is no air resistance. m (b) Now calculate the maximum height using universal gravitation. m (c) How far off is your estimate of part (a)? Express your answer as a percent difference and indicate if the estimate is too high or too low. % A planet (m = 5.342 times 10^75 kg) is in orbit around a star (M = 1.756 times 10^11 kg) in another part of our galaxy. (a) What is the total orbital mechanical energy of the planet star system if its orbit is circular with a radius of 5.95 times 10^12 m? J (b) What is the total orbital mechanical energy of the planet-star system if its orbit is instead elliptical and if its maximum distance is 7.01 times 10^12 m from the star? J
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