Calculate Density of Spherical Planet - 2.58hr Orbit

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Homework Help Overview

The problem involves calculating the density of a spherical planet based on the orbital period of a satellite in close orbit. The orbital period is given as 2.58 hours, and it is assumed that the planet has a uniform density.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the orbital period and the radius and mass of the planet using the equation T^2=(4pi^2/GM)*r^3. There is an exploration of how to combine equations for density and volume, with some participants expressing uncertainty about the number of unknowns involved.

Discussion Status

Some participants have offered guidance on how to manipulate the equations, suggesting that plugging in the volume formula could help clarify the relationships. There is a sense of progress as one participant indicates they feel they are close to a solution, while others continue to explore the implications of the equations.

Contextual Notes

Participants note a perceived need for additional information to resolve the problem, particularly regarding the number of unknowns in the equations being discussed.

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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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