Gravitational Fields and Density.

  • #1

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 = mw2r


And subbing in the values;


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


So I cancelled 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.
 

Answers and Replies

  • #2
Doc Al
Mentor
45,140
1,439
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.
 
  • #3
1,506
18
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
 
Last edited:

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