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

## 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

## Answers and Replies

kuruman
Science Advisor
Homework Helper
Gold Member
Sometimes you may have to look things up.

## 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

kuruman
Science Advisor
Homework Helper
Gold Member
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

kuruman
Science Advisor
Homework Helper
Gold Member
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?
to make things clear.