Geostationary satellite orbit radius as a multiple of Earth radius.

[Physgeek64]

Homework Statement

Okay, so the question seems really simple so I don't know what I'm missing

A satellite orbits at a fixed point above the Earth's equator. Assuming the Earth has uniform
density, radius R, and angular frequency of rotation, omega
Find an expression for eta, such that the orbital radius of the satellite is expressed as eta R

Homework Equations

Below

The Attempt at a Solution

Centripetal force= gravitational force

mr(omega)^2=GMm/r^2
r^3=GM/(omega)^2
But I honestly have no idea how to incorporate the Eaths radius. Every time I try it cancels.

Thanks in advance :)

 

[Guneykan Ozgul]

When calculating mass of the Earth you can use density and radius of the Earth so it doesn't cancel out.

 

[Physgeek64]

When calculating mass of the Earth you can use density and radius of the Earth so it doesn't cancel out.

Absolute star! Thank you!

 

[Physgeek64]

When calculating mass of the Earth you can use density and radius of the Earth so it doesn't cancel out.

Sorry - I've just had a thought. That will give me an expression in terms of R^3, not R. This produces the same problem as I had before

 

[Guneykan Ozgul]

I don't understand the problem exactly. Any function dependent on R is actually an expression in terms of R so if you obtain a term with R^3 (you should) don't worry because it means that radius of the sattelite is not dependent on R linearly .

 

[gneill]

There are two different radii involved: One is the radius of the Earth and the other the radius of the orbit. The volume is calculated using the Earth radius R, while the satellite orbit is a multiple of R. Replace the radius in your satellite force balance with $\eta R$.

Can you show more details of your workings?

 

[Guneykan Ozgul]

Ohh, sorry I did not see the part that asks you to write the sattalite radius as eta R. I think you should use @gneill 's argument.

 

[Physgeek64]

There are two different radii involved: One is the radius of the Earth and the other the radius of the orbit. The volume is calculated using the Earth radius R, while the satellite orbit is a multiple of R. Replace the radius in your satellite force balance with $\eta R$.

Can you show more details of your workings?

Ah okay - I think I've got it now. Thank you. Of course- would you like me to upload a photo of my working? (For some reason Latex doesn't work on my computer)

 

[gneill]

Ah okay - I think I've got it now. Thank you. Of course- would you like me to upload a photo of my working? (For some reason Latex doesn't work on my computer)

You can upload a photo if it's easily legible.
What machine/browser are you using?

 

[Physgeek64]

You can upload a photo if it's easily legible.
What machine/browser are you using?

How do I inset a photo? I can't see the button- The only one i can find is the one requiring a URL

A macbook air and safari

 

[gneill]

You can UPLOAD an image file. Check out the UPLOAD button at the bottom right of the reply edit panel.

Ah. I'm not familiar with safari, so I can't help you there.

 

[Physgeek64]

You can UPLOAD an image file. Check out the UPLOAD button at the bottom right of the reply edit panel.

Ah. I'm not familiar with safari, so I can't help you there.

Thank you- please excuse my handwriting.

My laptop is a mystery- I've had many people try to download latex, but no one has had any luck

 

[gneill]

Your solution looks good.

PF's LaTeX does not require any extensions or software to be added to your browser or machine. It's a feature that's managed externally. It may, however, require that certain character set capabilities exist in the browser. You might try testing another browser just to see if it's a browser issue. I think there's versions of Chrome and Firefox for mac.

Edit: You might check your browser version against the supported versions at the http://mathjax.readthedocs.org/en/latest/misc/browser-compatibility.html.

 

[tony873004]

Your solution looks good. To do Latex, type this

\eta  = \sqrt[3]{{\frac{{4G\rho \pi }}{{3\omega ^2 }}}}

and put tex tags around it.