Minimum height for a satellite to remain over the same geographical point

1. Feb 12, 2005

F|234K

a.)calculate at what height above the earth's surface a satellite must be placed if it is to remain over the same gerographical point on the equator of the earth. b.)what is the velocity of such a satellite?

i have no idea how to do the question, but i know it has to do with these equations:
Fcent.=Fgrav.
m(v^2)/r=GMm/(r^2)

because my book doesn't have answers for this question, i don't know the answer for this question.

2. Feb 12, 2005

dextercioby

That's the equation u need to use,but under an equivalent form.Now find "r" by plugging the correct numerical values...

Daniel.

P.S.HINT:relate angular velocity to tangent velocity...

3. Feb 12, 2005

F|234K

dextercioby, can you please show me some work or maybe even tell me the answer. i am stuck becuase i found that there are two variables, "v" and "r", are unknown.

4. Feb 12, 2005

dextercioby

Yes.$v=\omega r$.And now u have only one variable,namely 'r'...

Daniel.

5. Feb 12, 2005

F|234K

sorry for my ignorance, but what is the w(or omega) thing stands for?

6. Feb 12, 2005

dextercioby

Angular velocity of the Earth's rotation motion.U can find it knowing the period of rotation ("length" of a mean day) and the value of $\pi$,which can be approximated to $3.14$

Daniel.

7. Feb 12, 2005

F|234K

i found the answer for part a of my question to be 35870 km, can you please approve it. thanks alot so far.

8. Feb 12, 2005

dextercioby

It seems correct.However,for point b) u'll need another number,or u can use this 35870Km,but indirectly.

Daniel.

9. Feb 12, 2005

F|234K

anyways (i have a feeling that you arn't going to do the question for me), thanks very much dextercioby for your quick response, it helps me a great deal.

10. Feb 12, 2005

F|234K

lol....k thanks

11. Feb 12, 2005

dextercioby

Tell me what number you get for velocity...

Daniel.

12. Feb 12, 2005

F|234K

does 3072.6 m/s sounds good?

13. Feb 12, 2005

dextercioby

Pretty much so.

Daniel.

14. Feb 12, 2005

F|234K

k, thanks again.