# Satellite period, which equation?

1. Nov 23, 2007

### izforgoat

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

I'm looking for the period of an orbiting object a certain height from the earth's surface, I am given this height. So I have the total radius of 6,5OO,OOO m, g = 9.81 m/s^2 and the mass of earth = 5.98*10^24 kg

Please note that for this problem G is another constant than what it usually is.

2. Relevant equations

Here is where I am confused I do not know whether to use the T = (2$$\pi$$r)/$$\sqrt{gr}$$

or the T$$^{2}$$ = (4$$\pi^{2}r^{3}$$)/(GM$$_{earth}$$)

where G = 6.67*1O^-7

3. The attempt at a solution

K. So when I use the method of going with T = (2$$\pi$$r)/$$\sqrt{gr}$$

I get about 5114 seconds for the period.

when I use T$$^{2}$$ = (4$$\pi^{2}r^{3}$$)/(GM$$_{earth}$$)
I get 52.13584223 seconds, which doesn't logically seem right but since G is different I don't know.

does anyone know what the right method is?

2. Nov 23, 2007

### malawi_glenn

3. Nov 23, 2007

### Dick

And your value for G is wrong. Though it's hard to really say until you put units on it.

4. Nov 23, 2007

### izforgoat

thx alot for that clarification. Still it doesn't make sense that its period would be 52 seconds here's my work.

T(secs)^2 = (4(pi^2)(6,500,000^3 m))/((6.67*10^-7 N*m^2/kg^2)(5.98*10^24 kg))

are the units for T in seconds? was it alright that I changed km to m for the radius?

5. Nov 23, 2007

### izforgoat

I'm using a different value for this problem

6. Nov 23, 2007

### Dick

G=6.67*10^(-11)*N*m^2/kg^2. Note the exponent.

7. Nov 23, 2007

### Dick

Is it an 'alternative universe' problem? Why would you use a different value for G? It's a 'universal constant'.

8. Nov 23, 2007

### izforgoat

you could say that. But either way I don't think it would have much difference for this equation than the plug and chug. Right now I want to know if I am calculating everything else right. I assume I am.

9. Nov 23, 2007

### Dick

The reason you getting 52 seconds is because you are putting in a value of G that is 10000 times too large. Other than that you are doing fine.

10. Nov 23, 2007

thank you