Satellite period, which equation?

[izforgoat]

Homework Statement

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.

Homework 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

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?

 

[malawi_glenn]

http://upload.wikimedia.org/math/3/5/9/3594c905aef4519555d50788515e4825.png

Keplers third law (the forumula above is for spherical orbitals)

 

[Dick]

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

 

[izforgoat]

thx a lot 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?

 

[izforgoat]

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

I'm using a different value for this problem

 

[Dick]

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

 

[Dick]

I'm using a different value for this problem

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

 

[izforgoat]

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

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.

 

[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.

 

[izforgoat]

thank you