Mass in a satellite changes orbit

[Karol]

Homework Statement

A i kg mass is in a satellite must move to a higher orbit. energy must be added.
Can this energy be added at one time, by shooting the mass?

Homework Equations

Potential energy: $E_p=\frac{GMm}{r}$
Gravitational force: $F=\frac{GMm}{r^2}$

The Attempt at a Solution

The velocity at the higher circular orbit is lower but the potential energy much higher so energy must be added. but if i shoot the mass it reaches the higher orbit with the correct, lower energy but the direction isn't correct, i must change the velocity direction to tangent to earth, right?

 

[gneill]

You are basically correct. A one time impulse will change the satellite's orbit into an ellipse that will continue to revisit the same height as the starting point. This doesn't really count as a "higher orbit".

You might find investigating Hohmann Transfer Orbits will give you insight into the problem and its solution.