Escape velocity FROM a satellite in orbit?

In summary, the question is asking for the speed needed to launch a small object from a satellite in circular orbit around Earth in order to escape Earth's gravity. The equation v = sqrt[(2Gm)/R] can be used, where m is the mass of the object and R is the distance from the center of the Earth. The main issue is determining the correct value for R.
  • #1
vineroon
12
0
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.
 
Physics news on Phys.org
  • #2
vineroon said:
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.
 
  • #3
LowlyPion said:
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?
 
  • #4
vineroon said:
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)
 
  • #5
vineroon said:
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.
 

1. What is escape velocity from a satellite in orbit?

Escape velocity from a satellite in orbit is the minimum speed that a satellite must reach in order to break free from the gravitational pull of the planet it is orbiting. It is the speed at which the satellite can overcome the gravitational force and continue moving away from the planet.

2. How is escape velocity from a satellite in orbit calculated?

Escape velocity from a satellite in orbit is calculated using the equation v = √(2GM/R), where v is the escape velocity, G is the universal gravitational constant, M is the mass of the planet, and R is the distance between the satellite and the center of the planet.

3. What factors affect the escape velocity from a satellite in orbit?

The escape velocity from a satellite in orbit is affected by the mass of the planet and the distance between the satellite and the center of the planet. The greater the mass of the planet, the higher the escape velocity. Similarly, the farther the distance of the satellite from the planet, the lower the escape velocity.

4. Can escape velocity from a satellite in orbit be achieved?

Yes, escape velocity from a satellite in orbit can be achieved. In fact, all satellites in orbit around a planet have achieved this velocity in order to remain in their orbit without falling back to the planet's surface. However, once the escape velocity is achieved, the satellite will continue to move away from the planet and will no longer be in orbit.

5. Can escape velocity from a satellite in orbit be exceeded?

Yes, escape velocity from a satellite in orbit can be exceeded. If a satellite is given a greater velocity than the escape velocity, it will have enough energy to completely escape from the planet's gravitational pull and move into space. This is known as hyperbolic escape velocity.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
995
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
2
Replies
39
Views
3K
  • Introductory Physics Homework Help
Replies
6
Views
1K
Replies
1
Views
913
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
996
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
Back
Top