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1. Mar 19, 2016

### Physgeek64

1. The problem statement, all variables and given/known data
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

2. Relevant equations
Below

3. 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.

2. Mar 19, 2016

### Guneykan Ozgul

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

3. Mar 19, 2016

### Physgeek64

Absolute star! Thank you!!

4. Mar 19, 2016

### Physgeek64

Sorry - Ive 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

5. Mar 19, 2016

### 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 .

6. Mar 19, 2016

### Staff: Mentor

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 $\eta R$.

7. Mar 19, 2016

### 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.

8. Mar 19, 2016

### Physgeek64

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)

9. Mar 19, 2016

### Staff: Mentor

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

10. Mar 19, 2016

### Physgeek64

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

11. Mar 19, 2016

### Staff: Mentor

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.

12. Mar 19, 2016

### Physgeek64

Thank you- please excuse my handwriting.

#### Attached Files:

• ###### Photo on 19-03-2016 at 14.35.jpg
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13. Mar 19, 2016

### Staff: Mentor

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 Mathjax website.

Last edited: Mar 19, 2016
14. Mar 19, 2016

### tony873004

Your solution looks good. To do Latex, type this
Code (Text):

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

and put tex tags around it.