Horizontal velocity required to launch into orbit?

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Homework Help Overview

The discussion centers around determining the horizontal velocity required for a satellite to achieve a circular orbit when launched from the top of Mt. Everest, which has an elevation of 8848 m. The subject area involves concepts of gravitational and centripetal forces in the context of orbital mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks guidance on how to begin solving the problem. Some participants suggest starting with the relationship between centripetal and gravitational forces. Others express confusion regarding the various formulas available for these forces.

Discussion Status

The discussion is ongoing, with participants exploring different formulas related to centripetal and gravitational forces. There is an exchange of ideas about which formulas to use and how they relate to the problem at hand, but no consensus has been reached yet.

Contextual Notes

Participants are navigating the complexity of multiple formulas and their applications, indicating a need for clarity on the definitions and relationships between the forces involved in orbital mechanics.

fattydq
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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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