Before I read that Elon Musk’s insanely-huge satellite fleet was to orbit at around 1100 kilometers above the Earth, I did some back-of-the-envelope math to figure out what satellite altitude would be necessary to carpet the planet with coverage. From this came an interesting little exercise in hypothetical logistics.

First, figuring the minimum altitude of a 4,000 station constellation: We can use a formula for the fraction of the Earth visible from a point:

\(A = \frac{1}{2} \left( 1 – \frac{R_e}{R_e + h} \right)\)

…where \(R_e\) is the radius of Earth, \(h\) is the altitude of the observer, and \(A\) is a fraction of the Earth’s surface area. We can divide up the Earth into 4000 pieces and solve for h to know how high a satellite must be to see its portion of the Earth. When we do this, we get…

1.98 miles high.

What.

If you want to blanket the entire planet with internet coverage, and you’ve got 4000 things to do it with, those things only need to be floating about 2 miles off the ground!

Obviously nobody’s putting satellites in two-mile orbits. And we’d like some redundant coverage, so let’s demand that every point on Earth be covered by at least three stations and try again. What do we get? Continue reading →