Launch speed to reach a given orbital altitude

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SUMMARY

The discussion focuses on calculating the launch speed required for a space shuttle to release a satellite into a circular orbit at 720 km above Earth. The key equations involved are Newton's law of universal gravitation, F=GmM/r², and the centripetal force equation, Fc=mv²/r. It is established that the shuttle must match the orbital velocity of the satellite at the moment of release to ensure it enters the desired orbit. The shuttle's speed relative to Earth must be precisely calculated to achieve this outcome.

PREREQUISITES
  • Understanding of Newton's law of universal gravitation
  • Familiarity with centripetal force concepts
  • Knowledge of orbital mechanics
  • Basic algebra for solving equations
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  • Research the calculation of orbital velocity using the formula v = √(GM/r)
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Aerospace engineers, physics students, and anyone interested in orbital mechanics and satellite deployment strategies will benefit from this discussion.

horsecandy911
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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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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.
 

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