Question

A shuttle Captain flies a shuttle craft with a mass of 3000 kg in a circular orbit around a planet with a mass, M, of 9.5x10²⁵ kg and a radius, r, of 4.2x10⁷ m.     Do a little research on a typical orbit of a spacecraft around the earth.    How high above the earths surface?   What is the acceleration of gravity at that height?

a) The mass and radius numbers are closest to which planet?    Think we will be flying around this planet soon?

b) Solve for the period of the orbit of the Captain and spacecraft?

c) Solve for the speed of the shuttle craft?     Would this be the same as the velocity of the shuttle craft?

The Captain briefly fires the ‘forward’ thrusters to reduce the shuttle’s speed by 2.0%. Just at that time:

d) Solve for the speed of the shuttle craft?     In which direction is the acceleration of the shuttle craft during this maneuver?

e) Solve for the kinetic energy of the shuttle craft?   Solve for the gravitational potential energy of the shuttle craft?      What is the total mechanical energy of the shuttle craft?

The shuttle craft takes on an elliptical orbit after the retro-rockets were fired.

f) What is the semi-major axis of the elliptical orbit?

g) What is the difference between the period of the original circular orbit and the new elliptical orbit?

i) Which orbit has the smaller period?    Does this mean the shuttle craft now has more, the same or less speed than originally?

Answer 1