Deriving an expression for the radius of a satellite's orbit around Earth(?)

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Homework Help Overview

The discussion revolves around deriving an expression for the radius of a satellite's orbit around Earth, specifically in relation to the period of revolution, the universal gravitation constant, and Earth's mass.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about the meaning of deriving an equation and seeks assistance. Some participants suggest balancing gravitational and centrifugal forces as a starting point. Others emphasize the importance of using the centripetal force formula that incorporates the period of revolution.

Discussion Status

Participants are exploring different approaches to the problem, with some providing guidance on the relationship between forces involved in orbital motion. There is a focus on ensuring the correct formulas are applied, but no consensus has been reached regarding a specific method or solution.

Contextual Notes

The original poster's confusion about the derivation process indicates a potential gap in understanding fundamental concepts related to circular motion and gravitational forces.

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Homework Statement


Derive an expression for the radius of a satellite's orbit around Earth in terms of the period of revolution, the universal gravitation constant, and Earth's mass.


Homework Equations


The final equation should be: r = [tex]\sqrt[3]{\frac{T^{2}Gm_{E}}{4\prod^{2}}}[/tex]


The Attempt at a Solution


I have no idea how to do this. To be honest, I'm not even really sure what it means to derive an equation. Someone please help me with this?
 
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A satelite (or anything else) in orbit has a gravitational force inward toward Earth balanced by a centrifugal force outward.
You need the formulae for gravitational attraction (depends on the radius, mass of Earth and satellite) and the centrifugal force (depends on radius and mass of satellite)
Set the two equations equal to each other and rearrange them to get radius
 
Last edited:
All circular satellite calculations begin with "centripetal force = force of gravity".
Fill in the formulas for the two forces and solve for the quantity you want.
Be sure to use the centripetal force formula with period in it since that is specified in the question.
 
Delphi51 said:
All circular satellite calculations begin with "centripetal force = force of gravity".
Fill in the formulas for the two forces and solve for the quantity you want.
Be sure to use the centripetal force formula with period in it since that is specified in the question.

Once it was explained like this, it was dead easy!

Thanks a bunch =).
 

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