Satellite latency

Remember that a geosynchronous satellte must orbit the equator.
Let's say for the sake of argument it's over mexico, you're in New
York, and the downlink station is in San Diego. The 36,000 is the
distance straight "down" to mexico, It's probably more like 50,000
to New York, and 45,000 to San Diego.

The radius of the earth is about 6400km. Geostationary orbit is, as
you note, 36000km above the equator. The path from the satellite to
the North Pole is the hypotenuse of a right triangle with legs of
6400km and (6400+36000)km. That gives a distance from the North Pole
to the satellite of 43000km. It's reasonable to conclude that the
distance from either New York or San Diego is less than that.

     -- Brett