Can this gravity problem be solved without using the Earth's mass

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Homework Help Overview

The problem involves a satellite in a geosynchronous orbit around the Earth, with a focus on determining the radius of its orbit without the mass of the Earth being provided. The context is rooted in gravitational physics and orbital mechanics.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the possibility of solving the problem without the Earth's mass, with some suggesting rearranging known equations to express the mass in terms of other variables. Others question the necessity of looking up the Earth's radius for calculations.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem and suggesting that an answer could be expressed in terms of the Earth's radius if the mass is not provided. There is no explicit consensus on the best approach yet.

Contextual Notes

There is mention of typical reference tables providing the Earth's radius rather than its mass, which may influence how participants approach the problem. The lack of explicit values for certain variables is acknowledged as a constraint in the discussion.

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Homework Statement


A satellite orbits the Earth in a geosynchronous orbit around the equator, meaning that its period is 24 hours and it stays above the same location on Earth at all times. (G = 6.67 x 10⁻¹¹ Nm²/kg².) What is the radius of its orbit?

Homework Equations


GM/r2 = v2/r = w2r

The Attempt at a Solution


I can solve this if the mass of Earth is given but since it isn't I'd like to know if there is a way to solve this without using Earth's mass
 
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Sometimes you may have to look things up.
 
hndalama said:

Homework Statement


A satellite orbits the Earth in a geosynchronous orbit around the equator, meaning that its period is 24 hours and it stays above the same location on Earth at all times. (G = 6.67 x 10⁻¹¹ Nm²/kg².) What is the radius of its orbit?

Homework Equations


GM/r2 = v2/r = w2r

The Attempt at a Solution


I can solve this if the mass of Earth is given but since it isn't I'd like to know if there is a way to solve this without using Earth's mass

You know that g = GM/re2, rearrange this to give you the expression for M then go from there
 
lychette said:
You know that g = GM/re2, rearrange this to give you the expression for M then go from there
Sure, but then re needs to be looked up.
 
This is true enough and in general I think that re is given in data tables rather than M.(certainly in A level reference tables)
Also the combination GM usually crops up on both side of gravitational equations and therefore cancel out
In this example for the Earth gE = GME/rE2 and for the satellite gs = GME/rs2
This gives gErE2 = gsrs2
knowing that gs = v2/rs and further substitution enables rs to be calculated.
If re is not given then an answer can still be obtained in terms of re
 
lychette said:
If re is not given then an answer can still be obtained in terms of re
This is, of course, correct. Perhaps the problem should have asked
What is the radius of its orbit as a fraction of the Earth's radius[/color]?
to make things clear.
 

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