Sextants in space

For November, I’m writing a low-tech, retro science fiction. In this universe, AI almost destroyed everything, so now nobody uses computers. They get to orbit by space by an ancient space elevator and sail the solar system using vast sails.

It was meant to be soft scifi, but it turns out I can’t make a world without researching exhaustively to find out if it’s scientifically possible, so I have been figuring out low-tech ways to manage everything in space. Algae tanks to recycle air. Hand operated levers to spread the sails. Fans operated by spring-loaded cranks.

The big issue is navigation. Not that computers would help with that as much as you’d think. On Earth we navigate by GPS now, but that only works because Earth is surrounded by satellites. In deep space, we couldn’t use that method anyway.

So what other way is there to navigate? On Earth, if your GPS is out, you can use celestial navigation. This is a way of navigating using the stars and a sextant.

It turns out that every star is directly over a specific point on the planet at any given time, so that a line from that point on Earth to that star would form a right angle. Say you have a table saying that right now, Sirius is directly over New York. You take a sextant and measure what angle the star makes with the horizon from where you are. With that angle, you can now construct this triangle and use trigonometry to find out how far away from New York you are.

Of course knowing your distance from New York doesn’t tell you where you are. You’ll have to find your distance from another location using another star. That gives you two circles showing your distance from each location. Where they intersect are the only places you could be. A third star will narrow down the possibilities to one.

I thought for awhile that you could do this in space. Maybe it would even be easier, because the stars are always out and the Earth is never in the way.

But it’s actually impossible to do it quite this way. The Earth is really essential to celestial navigation; by cutting off half the stars, it’s doing you a favor. The horizon gives you something to measure angles off of.

I know Apollo 11 famously got its course with a sextant. (So do the Mars astronauts in The Fated Sky, an meticulously researched book by Mary Robinette Kowal which I highly recommend. If Kowal says something is possible, you can take that to the bank.) But it turns out all the Apollo astronauts used it for was to work out which way they were pointed, not where they were. I wanted to know if you could figure out where in the solar system you were with the stars alone.

It turns out you can’t. The stars are so far away that no matter where you are within the solar system, they’ll all seem in the same place, relative to each other. You’d need something much more precise than a sextant to tell any difference.

Good news though, there’s more in the solar system than stars. There’s the sun and all the planets! These will appear at drastically different angles depending on where you are. If you know where the planets are all supposed to be, and you know what their angles to each other are from where you are, you can find out your position.

You wouldn’t do it the same as in the celestial navigation example above. Instead you would get a bearing as in this trigonometry problem:

Luckily my characters, unlike me, have actually taken trigonometry and know how to do this. It helps that they’ve been genetically selected for hundreds of years as math and science geniuses. They simply work out the necessary angles, look up the distances in the charts, and calculate the missing distances till they know where they are.

With precise enough measurement, they could even work out their distance from the sun or any planet by measuring how big it is from where they are. No computer or GPS required.

Did I need to spend hours studying this topic to write a book about sailing on the solar wind? No, I did not. But I enjoyed doing it. And now I have an answer for any random reader who tells me, “Um, actually, that wouldn’t work, your sailors would be lost in space.”