Launch speed to reach a given orbital altitude

In summary, the problem asks for the necessary speed of the space shuttle when it releases a satellite into a circular orbit 720 km above the Earth. The relevant equations are the universal law of gravitation and the centripetal force equation. The solution requires the shuttle to have the same speed as the satellite at the time of release in order for it to end up in the desired orbit.
  • #1
horsecandy911
17
0

Homework Statement



[EDIT: My first statement of the problem was wrong.]

1. The space shuttle releases a satellite into a circular orbit 720 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs?

Homework Equations



F=GmM/r^2

Fc = mv^2/r

The Attempt at a Solution



Cannot figure out how to do this. I can solve for the orbital velocity (the speed at which the satellite will move around the Earth), but what does this have to do with the speed at which the space shuttle is moving relative to the Earth?
 
Last edited:
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  • #2
When the satellite is released, it will be moving at the same speed as the shuttle is. Therefore, the shuttle had better have the right speed in order for the satellite to end up in the desired orbit. In other words, the shuttle basically also has to be in that orbit at the time of release. That's all.
 

Related to Launch speed to reach a given orbital altitude

1. What is launch speed?

Launch speed refers to the initial velocity at which a spacecraft or satellite is launched into space. It is typically measured in meters per second (m/s) or kilometers per hour (km/h).

2. How is launch speed determined?

The launch speed required to reach a given orbital altitude is determined by a combination of factors, including the mass of the spacecraft, the gravitational pull of the Earth, and the desired altitude. This calculation is typically performed using mathematical equations and simulations.

3. Can launch speed vary for different orbital altitudes?

Yes, the launch speed required to reach a given orbital altitude can vary depending on the desired altitude. For example, a higher altitude will require a higher launch speed in order to overcome the Earth's gravitational pull and maintain a stable orbit.

4. What is the relationship between launch speed and orbital altitude?

The relationship between launch speed and orbital altitude is inverse. This means that as the desired orbital altitude increases, the required launch speed also increases. However, the relationship is not linear and can vary based on other factors such as the shape and size of the spacecraft.

5. How does a change in launch speed affect the orbit?

A change in launch speed can significantly affect the orbit of a spacecraft. If the launch speed is too low, the spacecraft will not be able to reach the desired altitude and may fall back to Earth. On the other hand, if the launch speed is too high, the spacecraft may enter a higher orbit or even escape the Earth's gravitational pull.

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