Escape velocity FROM a satellite in orbit?

[vineroon]

The question:

At what speed would a small object have to be launched from the satellite in order to escape earth’s gravity, assuming that the satellite is not moving?

The satellite is in circular orbit around the Earth and the radius of the orbit is 4.22 x 10^7.

The main problem I am having with this question is figuring out the escape velocity from the equation v = sqrt[(2Gm)/R], m being the body that the object is being launched from and R being its radius.

Any help would be greatly appreciated.

 

[LowlyPion]

The question:

At what speed would a small object have to be launched from the satellite in order to escape earth’s gravity, assuming that the satellite is not moving?

The satellite is in circular orbit around the Earth and the radius of the orbit is 4.22 x 10^7.

The main problem I am having with this question is figuring out the escape velocity from the equation v = sqrt[(2Gm)/R], m being the body that the object is being launched from and R being its radius.

Any help would be greatly appreciated.

I think what they are asking is, starting from some point in space, how fast must a rocket be moving to escape Earth all together.

Your equation is based on the Potential that needs to be overcome to get totally free. But if you are already at the initial starting point 4.22*10⁷, then that's potential from gravity that the object has already overcome isn't it?

So ... all it has to do is overcome the difference.

 

[vineroon]

I think what they are asking is, starting from some point in space, how fast must a rocket be moving to escape Earth all together.

Your equation is based on the Potential that needs to be overcome to get totally free. But if you are already at the initial starting point 4.22*10⁷, then that's potential from gravity that the object has already overcome isn't it?

So ... all it has to do is overcome the difference.

I understand that somewhat, but how am I supposed to find the velocity from that? Can I just find the work needed for the object to escape Earth using the change in mechanical energy and then use the work-energy theorem? If so, what mass would I use?

 

[LowlyPion]

I understand that somewhat, but how am I supposed to find the velocity from that? Can I just find the work needed for the object to escape Earth using the change in mechanical energy and then use the work-energy theorem? If so, what mass would I use?

Look at it like this:

1/2*m*v² = GMm/R - GMm/4.22*10⁷

v² = (2*GM/R - 2*GM/4.22*10⁷)

 

[Janus]

The question:

At what speed would a small object have to be launched from the satellite in order to escape earth’s gravity, assuming that the satellite is not moving?

The satellite is in circular orbit around the Earth and the radius of the orbit is 4.22 x 10^7.

The main problem I am having with this question is figuring out the escape velocity from the equation v = sqrt[(2Gm)/R], m being the body that the object is being launched from and R being its radius.

Any help would be greatly appreciated.

R equals the radius of the object being launched from only under the special case where you are launching from the object's surface. More generally, it equals your distance from the center of the object.