# 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

kuruman
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
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