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susus · Dec 16, 2010, 03:09 PM

Density of Planet
A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 1.65 hours. What is density of the planet? Assume that the planet has a uniform density.
(in kg/m^3)

ebaines · Dec 17, 2010, 06:58 AM

Susus:

Here's a hint to get you started: use good old F=ma, where F is the force of gravity between the planet and the satellite, and a is the acceleration of a mass in circular motion:

$<br /> F= \frac {GmM} {R^2} = m \omega^2 R<br />$

Recall that density = mass/volume, and the volume of a sphere is

$<br /> V = \frac 4 3 \pi R^3<br />$

Can you take it from here?

susus · Dec 17, 2010, 08:10 AM

Thanks I appreciate what you are doing.. I just too much fool for understanding what I have to do now :)

ebaines · Dec 17, 2010, 08:17 AM

Susus - please do not mark posts as unhelpful, unless it is actually in error.

The little m's cancel out- so it does not matter what the satellite's mass is.

You don't really care out big M, you only care about big M divided by R^3, because you are trying to determine the density of the planet, not its mass. If you manipulate the equations I gave you previously you can find a formula for M/R^3.

susus · Dec 17, 2010, 11:41 AM

4*pi^2*r/P^2 = G*m/r^2
4*pi^2*r^3/(G*P^2) = m

Now use the definition of density as mass divided by volume.
density = d = m/v = m/[(4/3)*pi*r^3]
d = 3*pi/(G*P^2)
d= 4000 ;) thanks..