CONCEPT: Elliptical Orbits Consider a spacecraft in an elliptical ...

NAME:PS 160 Extra Credit Due 22 February 2012Please print and staple. Please write your solutions on the question sheet. No points will beawarded if I cannot understand what you have written, so please write clearly. Show allcalculations. There are eight questions for a total of 20 points.CONCEPT: Elliptical OrbitsConsider a spacecraft in an elliptical orbit around Mars. At the low point, orperigee, of it’s orbit, it is 300 miles above the Mars’s surface. At the high point, orapogee, it is 3000 miles above the Mars’s surface. (Mars radius R = 3.4 x 10 6 m,and mass M = 6.4 x 10 23 kg (1mile = 1.609 km, G = 6.67 x 10 -11 N m 2 /kg 2 .)a) What is the period of the spacecraft’s orbit? (3 points)b) Using the conservation of energy and angular momentum, find the speed atperigee.(3 points)c) Using the conservation of angular momentum, find the speed at apogee.(2 points)

NAME:d) What is the escape velocity for any object located at a distance from Marsequal to the perigee distance of the spacecraft? (3 points)e) What is the escape velocity for any object located at a distance from Marsequal to the apogee distance of the spacecraft? (3 points)f) It is necessary to have the spacecraft escape from the Mars completely. If thespacecrafts rockets are fired at perigee, by how much would the speed haveto be increased above orbital velocity to achieve this?(2 points)g) It is necessary to have the spacecraft escape from the Mars completely. If thespacecrafts rockets are fired at apogee, by how much would the speed haveto be increased above orbital velocity to achieve this?(2 points)h) Which escape route would cost less fuel – fleeing at apogee or perigee?Explain your answer.(2 points)