  Since one satellite can see half of the earth, why do we need more than two satellites in a given network?

Category: Space
Published: May 10, 2013

A satellite in orbit around the earth cannot see half of the earth because of a simple geometric effect known as perspective. As shown in the diagram, when an observer is looking at a sphere, he can only see the portion of the sphere that lies in front of the points where his line of sight is tangential to the sphere. The closer the observer is to a sphere, the less he can see. The line marking the point where the earth begins curving out of view is called the horizon. It is the same horizon that you see when standing on the earth and observing the sky meet the ground in the distance. While hills and other local ground height variations affect the distance to the horizon, these variations are so small compared to the height of satellites that they can be mostly ignored. The distance of an observer from a sphere determines how much of the sphere is visible to the observer, as shown here in red. Public Domain Image, source: Christopher S. Baird.

If the radius of the sphere is R and the distance of the observer from the sphere's surface is d, then simple geometry reveals that the percent of the sphere's surface A that is visible to the observer is: 