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## Homework Statement

If a planet has a diameter of 6*10

^{3}km and, one of it's satellites is in a circular orbit of radius 9.0*10

^{3}km with a time period of 8.0 hours.

What is the density of the planet?

## Homework Equations

ρ=m/v - density v=4/3 *∏*r

^{2}

GMm/r

^{2}= mw

^{2}r

## The Attempt at a Solution

Firstly convert the Km into M,

Diameter of planet = 6*10

^{6}→ 3*10

^{3}

Radius of Satellite = 9.3*10

^{6}

Time period = 28800s

Where G = 6.7*10

^{-11}

Therefore I used

GMm/r

^{2}= mw

^{2}r

And subbing in the values;

(6.7*10

^{-11})Mm/(9.3*10

^{6}+3*10

^{6})=m.28800

^{2}(9.3*10

^{6}+3*10

^{6})

So I cancelled out the little m and rearranged the equation for M,

Giving M an answer as 1.87*10

^{33}

I then subbed it into the equation for Density,

1.87*10

^{33}/4/3*∏(3*10

^{6}) which gives me an answer of 4.96*10

^{19},

However the given answer is 4.6*10

^{3}, Any guidance would be appreciated ;D.