Calculate Satellite Period of Iron Planet

[vaxopy]

A hypothetical spherical planet consists entirely of iron. What is the period of a satellite that orbits this planet just above its surface?

Im stumped :/
density of iron is 7860 kg/m^3

 

[hypermorphism]

You have the tools you need: an equation relating centripetal force to tangential velocity or period, Newton's gravitational force law, and the volume of a sphere. Use these and tell us where you get stuck.

 

[cepheid]

Hi, I'm not the original poster, but I'm just curious: are they looking for the answer as a function of the radius of the planet, r? If not, how else would it be done? You've got density, so you've got the mass of the planet expressed in terms of that, and the volume of the planet, which depends on r, an unknown. Hmm, I guess that's all they're looking for...

 

[dextercioby]

There's a trick here...I am sure that in the final equation some term proportional to the density of the planet will appear and so the problem is completely solvable...

Daniel.

 

[BobG]

If you know the density and the volume, you can calculate the total amount of mass. Then you could plug this into Newton's law of gravitation to find acceleration due to gravity.

Actually, it's a little simpler. Multiply the mass of the planet by the universal gravitational constant (6.67 x 10^-11 m^3 kg^-1 sec^-2). Now you have a gravitational constant for your planet. Then use the following equation based on Kepler's third law:

$$\tau=\sqrt{\frac{4 \pi^2 a^3}{\mu}}$$
$$a$$ is your semi-major axis
$$\mu$$ is the gravitational constant for your planet

Just make sure your units are all consistent (all meters or all kilometers)

 

[dextercioby]

Well,Bob,since he/she's givent the mass density,wouldn't u find more intuitive if he/she left in that formula the ratio radius^{3}/mass...?

Daniel.

 

[learningphysics]

Hi, I'm not the original poster, but I'm just curious: are they looking for the answer as a function of the radius of the planet, r? If not, how else would it be done? You've got density, so you've got the mass of the planet expressed in terms of that, and the volume of the planet, which depends on r, an unknown. Hmm, I guess that's all they're looking for...

If you set the gravitational force=centripetal force (and plug in mass of the planet and velocity in terms of R), you'll see that the R's cancel each other out.

 

[BobG]

Well,Bob,since he/she's givent the mass density,wouldn't u find more intuitive if he/she left in that formula the ratio radius^{3}/mass...?

Daniel.

You mean the gravitational constant times the mass? Yes, as long as he only has to do one calculation with that number. For what he probably needs this for, a single problem, that probably is best.