# Planet density

1. Dec 18, 2003

### tandoorichicken

A strange new planet that has no atmosphere has a satellite that orbits very close to the planet's surface with a period of 1.50 hours. What is the approximate density of the planet? (Assume that the radius of orbit equals the radius of the planet.)

2. Dec 18, 2003

### SEG9585

Maybe I'm wrong...but it sounds like something is missing here:
It only gives you the time it takes to complete a revolution?
I would think u either need to know the planet's radius, mass, or ship velocity to calculate the density...

Because, say a person drives a car around the Earth's equator, and someone else flies a plane around the same distance. Without knowing velocity of the objects, the period of each revolution would be different, even though its the same planet, hence same density...

3. Dec 18, 2003

### jamesrc

How about just equating the gravitational force to the centripetal force?
$\frac{mGM}{R^2} = m\omega^2R$

and since $\rho = \frac{M}{R^3}$ and v = R&omega; and $T = \frac{2\pi}{\omega}$ you can solve for density as a function of period. So I think:

$\rho = \frac{1}{G}\left(\frac{2\pi}{T}\right)^2$