Where can you not see a satellite

[solarcat]

Homework Statement

Where on Earth (what latitude/Longitude) can you not see a geostationary satellite, even if it's in the same hemisphere as you?

Homework Equations

The height of a geostationary satellite is 35,860,000 meters
The radius of Earth is 6,371,000 meters.

The Attempt at a Solution

So I guess you can't see the satellite from the poles... I'm not really sure why, but maybe it's because it's as far away as you can get from the satellite. This is the diagram but I'm not really sure if this is correct or how to get the latitude from it,

 

[Orodruin]

It is true that you will not see it from the poles because you would have to look through the Earth. However, it is not only the pole. Think about what has to be true for the position where you just barely see it touch the horizon and make a diagram for that.

 

[solarcat]

SO is the diagram as below...
And the solution is cos (angle of latitude or longitude) = (Height of satellite + Radius of Earth) / Radius of Earth?

 

[jbriggs444]

SO is the diagram as below...
And the solution is cos (angle of latitude or longitude) = (Height of satellite + Radius of Earth) / Radius of Earth?

Close.

But if you try to take the inverse cosine of a number larger than one, what do you get?

 

[solarcat]

Oh, sorry, typed that wrong - it would be cos (angle of latitude or longitude) = Radius of Earth/(Height of satellite + Radius of Earth)
Got it! Thank you!