Suppose a satellite is in a circular orbit 4.225 Earth radii above the surface of the Earth (5.225 Earth radii from the center of the Earth). By how much does it have to increase its speed in order to be able to escape Earth? [Hint: You need to calculate the orbital speed and the escape speed.]
PLEASE I NEED THIS IN 10 MINUTES!!!

Question

Suppose a satellite is in a circular orbit 4.225 Earth radii above the surface of the Earth (5.225 Earth radii from the center of the Earth). By how much does it have to increase its speed in order to be able to escape Earth? [Hint: You need to calculate the orbital speed and the escape speed.]
 PLEASE I NEED THIS IN 10 MINUTES!!!

jamesj · Answer

Well, it's speed in the orbit is the speed for which the centripetal force is precisely given by the gravitational force, hence
$$ \frac{v^2}{r} = \frac{GM}{r^2} $$
Solve for v.

Then the escape velocity is the speed which will give the satellite a kinetic energy equal to the negative of the gravitational potential energy.

anonymous · Answer

ok but what do I plug in for M?

jamesj · Answer

The mass of the earth