Horizontal velocity required to launch into orbit?

AI Thread Summary
To launch a satellite into a circular orbit from the top of Mt. Everest, the horizontal velocity must be calculated using the relationship between centripetal force and gravitational force. The centripetal force can be expressed as F = mv²/R or F = 4π²mR/T², with the first formula being suitable for finding velocity. The gravitational force formula accounts for the mass of the Earth and the satellite, ensuring that the centripetal force equals the gravitational force for stable orbit. If the satellite's speed exceeds a certain threshold, the centripetal force will surpass gravitational pull, preventing it from maintaining orbit. Understanding these forces and their equations is crucial for determining the required launch velocity.
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At what horizontal velocity would a satellite have to be launched from the top of Mt. Everest (elevation 8848 m) to be placed in a circular orbit around Earth?


I'm not sure where I'd start here, any tips?
 
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All circular orbit problems begin with
Centripetal force = Gravitational force
Fill in the detailed formulas and solve for whatever you want.
 
What are these "detailed formulas" searching online it seems there's many formulas related to these forces?
 
For centripetal force, you have your choice of F = mv^2/R or
F = 4π²mR/T². If you know or want to find v, you use the first one. If you know or want to find the period T, use the second.

For the gravitational force, you must use the formula that gives the force exerted by one mass (the Earth) on another (the satellite).
Fc = Fg means that the centripetal force holding it in circular motion is provided by the gravitational pull of the Earth. Fc increases with speed, so if it is going too fast Fc will be too large for the Fg to hold it in circular motion.
 

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