Calculate Satellite Period of Iron Planet

In summary, we are trying to find the period of a satellite orbiting a hypothetical spherical planet made entirely of iron. With the tools of an equation relating centripetal force to tangential velocity or period, Newton's gravitational force law, and the volume of a sphere, we can calculate the total mass of the planet and then use that to find the gravitational constant for the planet. From there, we can use Kepler's third law to find the period of the satellite's orbit. The key is to make sure all units are consistent and that the R's in the equations cancel out.
  • #1
vaxopy
26
0
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
 
Physics news on Phys.org
  • #2
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.
 
  • #3
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...
 
  • #4
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...:wink:

Daniel.
 
  • #5
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:

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

Just make sure your units are all consistent (all meters or all kilometers)
 
  • #6
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.
 
  • #7
cepheid said:
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.
 
  • #8
dextercioby said:
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.
 

What is a satellite period?

A satellite period is the amount of time it takes for a satellite to complete one orbit around its parent planet or object.

What is an iron planet?

An iron planet is a type of planet that is predominantly made up of iron and silicate materials. These planets typically have a high density and a solid, rocky surface.

How is the satellite period of an iron planet calculated?

The satellite period of an iron planet can be calculated using Kepler's third law, which states that the square of a planet's orbital period is directly proportional to the cube of its average distance from the sun. This equation can be applied to calculate the satellite period of any planet, including an iron planet.

What factors can affect the satellite period of an iron planet?

The satellite period of an iron planet can be affected by the mass and density of the planet, as well as the distance between the planet and its parent object. Other factors such as the presence of other satellites or gravitational forces from nearby objects can also have an impact on the satellite period.

Why is calculating the satellite period of an iron planet important?

Calculating the satellite period of an iron planet can provide valuable information about the planet's characteristics, such as its mass and density. This information can help scientists better understand the formation and evolution of the planet, as well as its potential for hosting life.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
784
  • Introductory Physics Homework Help
Replies
12
Views
4K
  • Introductory Physics Homework Help
Replies
1
Views
774
  • Introductory Physics Homework Help
Replies
4
Views
394
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
Replies
1
Views
912
  • Introductory Physics Homework Help
Replies
15
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
993
Back
Top