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

1. ### F|234K

74
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. ### dextercioby

12,310
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. ### F|234K

74
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. ### dextercioby

12,310
Yes.$v=\omega r$.And now u have only one variable,namely 'r'...

Daniel.

5. ### F|234K

74
sorry for my ignorance, but what is the w(or omega) thing stands for?

6. ### dextercioby

12,310
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. ### F|234K

74
i found the answer for part a of my question to be 35870 km, can you please approve it. thanks alot so far.

8. ### dextercioby

12,310
It seems correct.However,for point b) u'll need another number,or u can use this 35870Km,but indirectly.

Daniel.

9. ### F|234K

74
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. ### F|234K

74
lol....k thanks

11. ### dextercioby

12,310
Tell me what number you get for velocity...

Daniel.

12. ### F|234K

74
does 3072.6 m/s sounds good?

13. ### dextercioby

12,310
Pretty much so.

Daniel.

14. ### F|234K

74
k, thanks again.