Finding Density of a Planet Using Period of Orbit

AI Thread Summary
To find the density of a planet using the orbital period of a satellite, the relevant equations include T² = (4π²r³)/(GM) and the volume of a sphere, V = (4/3)πr³. The user converted the orbital period from hours to seconds but encountered confusion when trying to isolate variables in the equations. They expressed difficulty in manipulating the equations to derive density, suggesting a need for clearer steps in the calculation process. The discussion emphasizes the importance of correctly applying the formulas to find the planet's density based on the satellite's orbital characteristics. Understanding these relationships is crucial for solving the problem effectively.
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Homework Statement



A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is T = 1.78 hours.
What is density (mass/volume) of the planet? Assume that the planet has a uniform density.

Homework Equations



T^{2}=4*PI^2*r^3/G*M
Density = Mass/Volume
Volume of Sphere = 4/3*PI*r^2

The Attempt at a Solution


I converted T into seconds, which I get 6408 seconds,

I have tried to solve for a single variable, but when I put it back into the equation, everything cancels out...

What should I do, I'm just super confused... :(
 
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So we have


T^2=\frac{4\pi^2 r^3}{GM}

and we know V=\frac{4}{3}\pi r^3


So if we divide the equation with T2 by 3, can we somehow factor out (4/3)πr3?
 

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