Chapter 132: What portion of the night sky have you never seen?

At many points during my road trip this summer I had the opportunity to lie on my back and stare at the unpolluted stars. After spending a minute to find the Big Dipper and follow its handle to the northern star, Polaris, I realized I had never seen the southern star (some punk upstart named Sigma Octantis). For that matter, I hadn’t seen an entire portion of the night sky, merely by virtue of being a resident of the Northern Hemisphere.

Assuming a clear night and an unobstructed view to the horizon, you can see half the sky at night. Part of that sky doesn’t always change depending on what time of year it is (Earth revolves around the sun on a fixed rotational axis), and for us Northern Hemisphere dwellers that includes Polaris.

If I’ve spent my life in the Northern Hemisphere, how much of the sky have I never actually seen?

The answer works itself out nicely if you abstract the nights sky to the inside of a near infinite sphere and calculate the surface area of the cap of the cone carved by your horizon over the course of a year. If that explanation isn’t clear, just spend a little time staring at my diagram and equations. It’ll come to you.

The equation to calculate the portion of the night sky you’ve never seen is on the bottom right, with the only input being your latitude.

That is, to calculate the percentage of the night sky that has remained forever hidden to you by Earth’s mighty bulk, plug your latitude in for theta and get ( 1 – cos ( latitude ) ) / 2. If you prefer Lisp notation, (/ 2 (- 1 (cos latitude))).

The closest I’ve ever lived to the equator for more than a year was hurricane prone Galveston, Texas (latitude 29.28). That means the percentage of the sky that remains unseen to me is (1 – cos(29.28 degrees))/2, or a tiny 6.4%.

A lifelong resident of Wasilla, Alaska(latitude 61.58) who only got their passport last year would have missed out on a full 26.2% of the night sky.

You can use the handy dandy form below to calculate just how much of life you’re missing (needs javascript):

Latitude (in degrees):
Portion of night sky unseen:

There are a lot of reasons to travel around the world, but up until that night of looking up at the cosmos it had never occurred to me that stargazing could be one of them.

Math errors are best reported with smugness in the comments. Thanks.

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