# Geosynchronus Sattelite Question

1. Nov 12, 2009

### bleedblue1234

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

A satellite that stays over the same spot on a planet as it rotates is called a geostationary satellite. (Geostationary satellites must be positioned somewhere over the equator of the planet.) What is the average orbital radius of a geostationary satellite for a planet with a mass of 4.82 x 10^24 kilograms and a period of rotation of 14.0 hours?

2. Relevant equations

3. The attempt at a solution

F = ma
Fg = GM1m2/r^2
Gm1m2/r^2 = m2(v^2/r)
GM1/r = V^2
GM1/r = (2(pi)/T)^2
GM1/r = 4(pi)^2r^2/T^2
GM1T^2/4(pi)^2 = r^3
r = approx 1.26E8 m

but i am getting it wrong

Last edited: Nov 12, 2009
2. Nov 12, 2009

### cepheid

Staff Emeritus
Looks like a computation error? I get a different answer using that same formula with those same numbers.

3. Nov 12, 2009

### bleedblue1234

its 10^24... see my post again i edited the question to include the ^

edit... i got 3.34E8 now...

nvm back to 1.26E8

4. Nov 12, 2009

### cepheid

Staff Emeritus
Yeah, I assumed that's what it meant, but I still got a different answer from you.

5. Nov 12, 2009

### bleedblue1234

hrm so

(6.67E-11) * (4.82 x 10^24) * (14*60*60)^2
/
(4(pi)^2)

so doing the math i get approx
2.01E24 ish

then do the third square root of that to get r...
and i get 1.26E8

6. Nov 12, 2009

### cepheid

Staff Emeritus

I get approx. 2.06e22.

Do you mean the cube root?

It looks like there could be at least two problems with your calculation...

7. Nov 12, 2009

### bleedblue1234

yes.... i meant the cube root

but i am doing the calculation right and i keep getting 2.014E24

(are you doing 14*60*60 to convert hours to seconds?)

8. Nov 12, 2009

### cepheid

Staff Emeritus
9. Nov 12, 2009

### bleedblue1234

10. Nov 12, 2009

### cepheid

Staff Emeritus
Yes, that's about what I got.

11. Nov 12, 2009

### bleedblue1234

about or is.... i have 1 submission to get it right... :tongue:

thanks

edit: nailed the problem, much thanks

12. Nov 12, 2009

### cepheid

Staff Emeritus