Gravitational Fields and Density.

[FlyingSpartan]

Homework Statement

If a planet has a diameter of 6*10³km and, one of it's satellites is in a circular orbit of radius 9.0*10³km with a time period of 8.0 hours.
What is the density of the planet?

Homework Equations

ρ=m/v - density v=4/3 *∏*r²
GMm/r² = mw²r

The Attempt at a Solution

Firstly convert the Km into M,
Diameter of planet = 6*10⁶ → 3*10³
Radius of Satellite = 9.3*10⁶
Time period = 28800s

Where G = 6.7*10^-11

Therefore I used

GMm/r² = mw²rAnd subbing in the values;(6.7*10^-11)Mm/(9.3*10⁶+3*10⁶)=m.28800²(9.3*10⁶+3*10⁶)So I canceled out the little m and rearranged the equation for M,Giving M an answer as 1.87*10³³

I then subbed it into the equation for Density,1.87*10³³/4/3*∏(3*10⁶) which gives me an answer of 4.96*10¹⁹,

However the given answer is 4.6*10³, Any guidance would be appreciated ;D.

 

[Doc Al]

Therefore I used

GMm/r² = mw²r

OK.

And subbing in the values;


(6.7*10^-11)Mm/(9.3*10⁶+3*10⁶)=m.28800²(9.3*10⁶+3*10⁶)

(1) Why did you add the radii?
(2) ω is the angular frequency, not the period.
(3) On the left side, that radius must be squared.

 

[technician]

volume is (4/3)πr^3 you have written (4/3)πr^2 and you have not cubed the value in your calculation
Also ω = 2π/T and you have used T as pointed out by Doc Al