Ask Me Help Desk - Density and orbit

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density and orbit

A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is T = 2.59 hours.
What is density (mass/volume) of the planet? Assume that the planet has a uniform density.

Hm... did you try this?

$F = mr\omega^2 = \frac{GMm}{r^2}$

$r^3\omega^2 = GM$

Density = Mass / Volume

Volume = 4pir^3/3

.: Density = (3*Mass)/(4pi r^3)

$\frac{\omega^2}{G} = \frac{M}{r^3}$

$\frac{3\omega^2}{4 \pi G} = \frac{3M}{4\pi r^3}$

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