Help with Determining Planet Density from Orbital Period

[ninjagowoowoo]

I have no idea where to start on this:

A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 1.69 hours.
What is density of the planet? Assume that the planet has a uniform density.

Perhaps someone could point me in the right direction? Thanks.

 

[Astronuc]

Hint: Kepler's Third Law of Planetary Motion

and the fact that the satellite is near the planet's surface.

http://scienceworld.wolfram.com/physics/KeplersThirdLaw.html

http://scienceworld.wolfram.com/physics/MeanMotion.html

 

[ZapperZ]

I have no idea where to start on this:

A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 1.69 hours.
What is density of the planet? Assume that the planet has a uniform density.

Perhaps someone could point me in the right direction? Thanks.

Let the mass of the planet be M, the mass of the satellite be m, the radius of the planet be R, and all the other symbols have their usual meanings.

1. You should know that the centripetal force causing the satellite to be in the circular orbit is due to the gravitational force, so equate the two, i.e.

$$\frac{GmM}{R^2} = \frac{mv^2}{R}$$

2. But you also know that

$$v = r\omega$$
$$\omega =2\pi/T$$
$$\rho = \frac{M}{4/3 \pi R^3}$$

3. A bunch of things cancel out and you should be able to do the simple algebra to find the density.

Zz.