Satellite height from earth Question

[thomasrules]

I hate this question:

I don't know if I'm doing something wrong because it seems so hard. Can i get someones way of doing this question...

Communications satellites are placed in orbit so that they remain stationary relatice to a specific area on the Earth's surface. They are given the name synchornous satellites because, to maintain such a position, their period as they orbit must be the same as the Earth's.
What is the height of such a satellite measured from
a) the centre of the Earth, and
b) the surface of the Earth

 

[vincentchan]

If you hate it, then don't do it...
read the sticky

 

[dextercioby]

They are called geostationary satellites.

Their trajectory can be a circle.Apply the 2nd law to the satellite in the inertial frame given by the center of the Earth.

Daniel.

 

[thomasrules]

I'm not given an acceleration though

2nd law:?

net f=ma

ma=M(4pi^2r)/T^2

is that it?

 

[dextercioby]

Okay,now use the fact that the movement is not in a straight line,but on a circle...

What is the RHS of your equation??

Daniel.

 

[thomasrules]

man you've got to help me here...Okay I'll tell you what I've done...

i got (r+x) as my radius...x being the distance from Earth surface to satellite. therefore

4pi^2(r+x)/T^2=GM/(r+x)^2

I continued after that but this is probably all wrong please help...:)

 

[dextercioby]

Perfect.Your equation is good.Now just plug in the numbers and tell me your result.Total distance (from the Earth's center).

Daniel.

 

[thomasrules]

LOL that can't be right dext. I mean I get cubes when i cross multiply and it's all messed up...I get stuck later i can't find x

I got stuck at

x=7.51(10)^22/(1.2E14+1.9E7x+x^2)

THATS so wrong ain't it

 

[dextercioby]

You needn't solve for "x".Your unknown is not necessarily "x".Think about it.

Daniel.

 

[thomasrules]

dexter i need to know r+x which is equal to height but in order to know that I need to solve for x right...then add x with r which i have already...

I'm sorry but my iq is nothing compared to yours

 

[dextercioby]

How about this equation??Can u solve it...?

$$(R+x)^{3}=\frac{T_{rot}^{2}GM_{E}}{4\pi^{2}}$$

Daniel.

P.S.How about "thinking out of the box"?

 

[thomasrules]

OMG ! HAHAHAHAHAHA DEXTERCIOBY...I'm so Amazed...seeing that equation was like magic to me...like how the hell OMG
you know what I did was the following ! :
4pi^2(r+x)(r^2+2rx+x^2)=Gmt^2

and then multiplied each one

THANK YOU OMNISCIENT ONE