NavList:

Thanks for all the replies last week on our poor crashed interstellar traveller! Of course I suggested this story because it got me thinking about the fundamentals of celestial navigation in a different way. We're so accustomed to thinking about UT/GMT and longitudes on Earth based on the prime meridian at Greenwich... Removing that historical feature and imagining an unmapped world changes the rules substantially.

Hewitt S and a few others spotted the issue right away and suggested a "zenith star" or equivalent. We have to report this at some specific time on a time standard that we and our potential rescuers can agree on. Without that time standard we would be limited to providing a latitude on the planet. On land an exact zenith star is not rare, but it could be very difficult to identify. To find the zenith, our castaway could hang some weights on strings and sight up along them. Those strings can locate the zenith within as little as half a degree, no problem. If our planet is earth-sized, then that amounts to about +/-30 nautical miles on the ground, as expected. If our planet is smaller, then the position error is also smaller in proportion.

If we're able to measure angles with any skill then we can go beyond the zenith star scenario. Robin Stuart suggested using the sun (the sun of the planet we're crashed on). This would be a good choice, but there might be issues that would discourage our space navigator. It's possible that we're orbiting a "red giant" --a large M-class star. In order for the planet to be habitable, he won't see some enormous star in the sky... Necessarily it would be only a few degrees across, but it might not have clearly defined limbs. Perhaps instead our navigator could use a recognizable star...

In my earlier proposal I suggested sending my estimated latitude and longitude on the planet. Suppose instead I send this message: "crashed on planet five orbiting star SAO 110920. Last night bright star SAO 130408 transited my local meridian 6.50° south of local zenith. Star's meridian transit occurred approximately 6hr 31m 12s ago, as I send this".

That should be enough info. I'm supposing here that the castaway and potential rescuers have some common database of stars available (SAO would probably be "ancient 20th century Terran designations" but they could have some common star designations anyway.

The star designated as SAO 110920 is another "name" for the star Menkar which is also "alpha Ceti", not quite the Trek-ish "Ceti Alpha" but close enough for this scenario. Meanwhile the star that I suggest observing in the sky, SAO 130408, is the star also known to earth-based astronomers as "95 Ceti" which is relatively close to Menkar (in 3-dim space) and would be roughly magnitude 1.8 as seen from a planet orbiting Menkar. It's the sort of star that would be "on everybody's charts" in that interstellar region. [Note: that star, 95 Ceti, happens to be an identifiable double star which was originally discovered to be double by the famous telescope maker Alvan Clark in 1853, presumably from the heart of Cambridge, Massachusetts back in the decades before light pollution... The first white dwarf, Sirius B, was first sighted from the same the same observatory just a few years later... And the designation "SAO" also has its homeport in Cambridge].

I did not need to select a nearby star, as above. Betelgeuse, for example, would have worked just fine. One option that might be unusually convenient would be the star Alcyone, brightest star in the Pleiades. Menkar is about 250 light-years from Earth; the Pleiades in the same general direction are about 440 light-years from Earth. If we visit Menkar, the Pleiades will be visually bigger and brighter. So I might send a message saying "Alcyone transited my meridian 18.3° south of zenith at 13:05:50 Galactic Standard Time."

Whether it's Alcyone, or Betelgeuse, or 95 Ceti, the choice has to be a star that's relatively easy for our castaway to identify and well-known to potential rescuers (that's easy, I would think). Zenith distance at meridian passage effectively yields latitude on the planet, and absolute time of meridian passage yields longitude --no prime meridian necessary.

By the way, what qualifies as "south" of zenith? Presumably some standard would be well-known for different planets centuries from now... maybe based on the usual right-hand rule for angular momentum direction, which makes "north" the direction of positive angular momentum and matches the orientation for the Earth. Or maybe based on the galactic "north pole"...

Do we need meridian transit? No, of course not. But if we stick with arbitrary zenith distances at arbitrary times, then we'll need two known stars. For example, I might report: "Alcyone observed 10.3° from zenith at 10:20:45 Gal Standard on 17 Brumaire 2370, Betelgeuse 45.5° from zenith exactly one minute later". That gets you a fix in the usual way. But how well can we measure angles? It's not at all difficult to construct a manual "device" to measure small-ish angles, say, up to 10 or 15° with good accuracy, but to get to 45° is harder ... which, I think, is why we don't see many homemade cross-staffs anymore! :)

Frank Reed