Calculate Density of Spherical Planet - 2.58hr Orbit

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To calculate the density of a spherical planet with a satellite in a 2.58-hour orbit, the relevant equations include T^2=(4pi^2/GM)*r^3 and density=mass/volume. The user initially struggles to isolate the radius and mass needed for density calculation, expressing a need for more information. A suggestion is made to combine the equations, leading to a clearer understanding of how to express density in terms of the orbital period and radius. Ultimately, the user feels they have resolved the issue and can proceed with the calculations.
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Homework Statement



A satellite is in orbit very close to the surface of a spherical planet. The orbital period is 2.58 hours. What is the density of the planet? Assume the planet has a uniform density.

Homework Equations



T^2=(4pi^2/GM)*r^3

Density=m*v

The Attempt at a Solution



I've posted in several other forums, but no one can seem to help me with this problem. I can't find a way to solve for radius or mass, and i need both of those to ultimately find the density of the planet.
 
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lempkema said:

Homework Statement



A satellite is in orbit very close to the surface of a spherical planet. The orbital period is 2.58 hours. What is the density of the planet? Assume the planet has a uniform density.

Homework Equations



T^2=(4pi^2/GM)*r^3

Density=m*v

This formula is incorrect; density is mass/volume.

So what is the formula for the volume? Since you have two equation, have you tried putting them together (solving for one and plugging into the other)? What does that give?
 
that would give me:


T^2=(4pi^s/(G*(Density*v))*r^3

but that would give me three unknowns instead of just two. i just feel like i need more information to solve this problem.
 
lempkema said:
that would give me:


T^2=(4pi^s/(G*(Density*v))*r^3

but that would give me three unknowns instead of just two. i just feel like i need more information to solve this problem.

What is the formula for the volume? Plug that into the equation. Do you see how that helps?
 
or it would give me:

T^2=(4pi^2/(G*density*(4/3pi)*r^3))*r^3, which is T^2=(4pi^2/(G*density))

thank you so much, i think I've got it from here :)
 
haha i mean (4pi^2/(G*(4/3)*pi*density))
 
That sounds right to me.
 
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