Two planets of equal density, what do they share?

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1MileCrash
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Homework Statement



Consider two uniform spherical planets of equal density but unequal radius. Which of the following quantities is the same for both planets?

Homework Equations





The Attempt at a Solution




I can't really attempt to solve it because it's not really a "problem."

The escape velocity from the planet's surface.
The acceleration due to gravity at the planet's surface.
The orbital period of a satellite in a circular orbit just above the planet's surface.
The orbital period of a satellite in a circular orbit at a given distance from the planet's center.
None of the above.

I can't find any equations having to do with any of things things that don't rely on either density or radius.
 

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1MileCrash said:

Homework Statement



Consider two uniform spherical planets of equal density but unequal radius. Which of the following quantities is the same for both planets?

Homework Equations





The Attempt at a Solution




I can't really attempt to solve it because it's not really a "problem."

The escape velocity from the planet's surface.
The acceleration due to gravity at the planet's surface.
The orbital period of a satellite in a circular orbit just above the planet's surface.
The orbital period of a satellite in a circular orbit at a given distance from the planet's center.
None of the above.

I can't find any equations having to do with any of things things that don't rely on either density or radius.

Try starting with the equation for gravitational attraction, and the equations of uniform circular motion...
 
Gravitational attraction is out, divide by r squared. So is uniform circular motion.
 
1MileCrash said:
Gravitational attraction is out, divide by r squared. So is uniform circular motion.

Sorry, I'm not able to parse your response.

Using the equations that I suggested solves most of the questions that you listed...
 
I don't understand, all of that relies on radius. I am told radius is not equal.
 
1MileCrash said:
I don't understand, all of that relies on radius. I am told radius is not equal.

Exactly. Write out the equations, and see if you can answer some of the questions.

For example, write out the equations for "acceleration due to gravity at the planet's surface" for two different planets that have the same density but different radii...
 
Maybe you should start by figuring out the mass of each planet. Once you do that, you should be able to see how to figure the rest out.