Question

Problem: Orbital Mechanics

A spaceship is waiting for launch at the Kennedy Space Center (Located at Latitude 28.52o North of the Equator) . The spaceship has a mass of m = 2000 kg.

a) What is the gravitational potential energy the spaceship has sitting and waiting for launch.

b) What is the kinetic energy the spaceship has sitting and waiting (calculate K relative to the center of the earth).

c) The spaceship is attached to rockets that are going to push the ship into orbit. The goal is to give the ship enough kinetic energy to get it into low earth circular orbit. What is the gravitational potential energy of the low earth orbit? (400 km above the earth).

d) How much work must the rockets do on the spacecraft to get it into the low earth circular orbit (don’t forget to consider the kinetic energy it has in part b)?

e) In the low earth orbit, the spaceship docks with the International space station and picks up some supplies. They then depart to go repair a satellite in a geosynchronous orbit. What distance away is the geosynchronous orbit? (A geosynchronous orbit is a circular orbit where the object orbiting stays above the same spot on the earth as the earth rotates).

f) In order to make it to the new orbit, the spaceship fires its thrusters to increase its speed. It is a short and powerful burst, giving it a new speed while still at the low earth orbit. This new speed destroys the circular motion and the puts the craft into an elliptical orbit. This starting point becomes the orbit’s perigee. What speed is required to make the apogee of the orbit at the geosynchronous orbit distance? (Conservation of energy should tell you about the changes of the kinetic energy and potential energy required. Because gravity will not put any torque on the craft relative to the center of the orbit, use conservation of angular momentum to find the required speeds at the apogee and perigee.)

g) When the apogee has been reached, how must the speed be changed in order to establish a circular orbit?

Answer 1