Calculating the Height and Speed of a Stationary Satellite | Help Needed

[phys1618]

Please help! circular motion

Homework Statement

At what height above the Earth's surface would a satellite have to orbit in order that it be stationary in reference to a point on the earth? b. what would be it's speed? c. How would you describe the general location of that point in relation to the Earth's surface?

Homework Equations

Fg= (G)(M₁M₂)
r²
G=6.67x10^-11Nm²/kg²
Fw=Mg
Fc=M v²
r
a=v²
r
Earth mass=6x10²⁴kg
Earth radius=6.4x10⁶m

The Attempt at a Solution

Can someone help me and let me know where to start? I know how to find the velocity, but seems like i don't have enough information? is there something I'm missing?? please help!

 

[Redbelly98]

The whole key to this problem is to think what the orbital period would be, if the object is to be "stationary in reference to a point on the earth".

That, plus an equation relating the orbital period to v and r.

 

[phys1618]

thanks for the clue...but is it a day??

 

[Redbelly98]

Yes.

 

[phys1618]

thank you thank you redbelly! now i can starting working on the problem!
but one more question if you don't mind...after i get all the answr i get how would i describe the general location of that point in relation to the Earth's surface?
to be more clear, what is that question asking for?? again thank you for your help! greatly appreciates it

 

[Redbelly98]

The question is asking for the height or altitude of the satellite above the Earth's surface. In other words, the distance from the satellite to the surface directly below it.

Note however that "r" in these equations is distance from the satellite to the center of the Earth.

 

[phys1618]

using period (T) as one day, which is 86400sec. In order to find "r" i used Fg=Fcp, which cancels out the mass of the shuttle:
(6.67x10^-11 Nm²/kg²)(6x10²⁴kg/r²) = 4pie²/(86400s)², after all the math is done i have r=4.23x10⁷,so is this the height from Earth's surface and shuttle , or do i have to add or subtract that number from the Earth's radius??
if r is correct, v=3076.14 m/s
What does this sentence mean?"How would you describe the general location of that point in relation to the Earth's surface?"
would i say like north,south, west, east, or what kind of answer is it asking for?

 

[Redbelly98]

... after all the math is done i have r=4.23x10⁷,so is this the height from Earth's surface and shuttle , or do i have to add or subtract that number from the Earth's radius??

That's the distance from the satellite's orbit to the center of the Earth.

What does this sentence mean?"How would you describe the general location of that point in relation to the Earth's surface?"
would i say like north,south, west, east, or what kind of answer is it asking for?

I'm not sure. Does anybody else have an idea?

 

[phys1618]

Thank you Redbelly98 for answering my questions...I really appreciates your consistent help and patience. Thank you.
At what height above the Earth's surface would a satellite have to orbit in order that it be stationary in reference to a point on the earth?
So i would take r=4.23x10^7m and substract that from Earth radius=6.4x10^6m to get the height aboe the Earth's suface to the satellite right??
sorry for keep bothering

 

[Redbelly98]

So i would take r=4.23x10^7m and substract that from Earth radius=6.4x10^6m to get the height aboe the Earth's suface to the satellite right??

Yes. (Assuming you really mean to subtract r_Earth from r)

 

[phys1618]

yes, that's what i meant redbelly...thank you thank you

however, does anyone know What does this sentence mean?"How would you describe the general location of that point in relation to the Earth's surface?"
would i say like north,south, west, east, or what kind of answer is it asking for?

 

[Redbelly98]

They might be asking about where such a satellite could be located. For example, it could not be located directly over the North or South pole, even if it's at the correct height. Do you see why?

 

[phz]

Maybe they are searching for the term used to describe satellites that are kept stationary above the Earth's surface. There is a special word for this. It is a bit of a strange question if they mean it like that though, but that would be my guess.

 

[phys1618]

thank you thank you for all help!
the answer was the a point above the equator...

Thank you all!