Space Exploration Stack Exchange is a question and answer site for spacecraft operators, scientists, engineers, and enthusiasts. It only takes a minute to sign up.
Sign up to join this community
Wikipedia's Geostationary orbit; Communications says:
Geostationary communication satellites are useful because they are visible from a large area of the earth's surface, extending 81° away in both latitude and longitude.
But how to calculate that above 81° they are not visible? And also how do I know exactly at what height will I see a satellite in some city (ex. Moscow - 55.7558° N, 37.6173° E)?
A diagram showing the cross section (longitudinal section) of the earth at the same longitude as the geostationary satellite is shown below.
A location from the the geo stationary satellite aligns with the horizon is marked. Its latitude is also marked in the picture. At higher latitudes, the satellite is below the horizon.
$$ cos(\mathrm{lat}) = \frac{6400}{36000+6400}\\ \mathrm{lat} \approx 81\deg $$
Instead if we imagine that the view in the picture is by an observer in space above north pole, then the diagram shows longitude and so the 81 deg is applicable to longitude also; but only at the equator since the cross section was made at the equator.
In fact, a tangent line drawn from the satellite to the earth's surface traces out a cone of half angle 90 - 81 = 9 deg.
