NavList:

Martin C, you wrote:
"Let’s assume that your starship’s advanced navigation system includes a nautical almanac for the alien planet you have crash landed on. Also, let’s assume that the alien planet shape is close to a sphere, so the spherical triangulation principles work."

Thank you for pondering this sci-fi scenario. You have raised some really great points!

I agree that we have to assume that we have a current database of stars, equivalent to a nautical almanac, with some ability to adapt it to our new-found home planet. Unless all our data devices are dead, this seems like it would be a standard feature for any imagined "interstellar shuttle" in a distant century. We could even imagine using that to figure out what star we're orbiting if somehow we do not know that detail (maybe our interstellar shuttle pilot was unconscious for days before crashing...). Any interstellar nautical almanac would be fundamentally three-dimensional so we could adjust our coordinates until the apparent, visible constellations "look right".

But do we need the planet to be a sphere? I say no. It doesn't even need to be close to a sphere. Any natural planet will become spheroidal by gravitation, but suppose, just for thought experiment, we crash on an artificial planet that has the physical shape of a giant cube. Celestial navigation would still work fine on a world like that. Its gravitational field would have a roughly spherical form, and even if it deviates significantly from a spheroid, we really do celestial navigation "on the celestial sphere" (which, of course, is a perfect sphere, because we define it that way...). We "drag" our coordinates down from the celestial sphere along the local zenith lines, and they fall where they will, giving us our astronomical latitude and longitude grid on our planet. This principle only runs into trouble if we attempt to build a second grid of latitude and longitude based on physical measurements. That's why surveyed coordinates on the Earth today, including GPS/GNSS derived coordinates, differ slightly (up to a few miles) from celestial fixes. It's also why our common "latitude" on Earth is not a simple spherical coordinate, like it could be... if we started history over again...

You added
"With some luck, you have landed on a planet with a lot of moons, so you can start by calculating the time using all you have learned at Frank’s Lunar classes."

Heh. I appreciate the plug for my classes! :) But would it work? It's quite possible that our navigator would have a head-count on the number of moons orbiting his new home, but any "lunars almanac" would only give us some type of time standard. And then the navigator would have to translate that to a time standard that potential rescuers would be able to use. This might not be possible...

You wrote:
"You would need to define your own Greenwich meridian on the alien planet and communicate that to your rescue team. Not sure how to do that."

Yes. That's the tricky part, and I think it's what makes this an interesting scenario. We could define our own prime meridian on this planet, but that wouldn't be much use for communication. So we're better off stepping back a bit and just reporting something like a star's meridian transit [please see my earlier post, for example] in some established time standard. If we don't have an established time standard, then we're out of luck on planetary longitude. Myself I can't imagine a viable "futuristic" scenario where I have a functioning communication device that does not have a functioning clock on some well-known time standard built into it.

Martin, you continued:
"Without knowing the size of the alien planet, you cannot calculate the dip correction. You will not be able to calculate refraction if the alien planet has an atmosphere."

I'm glad you brought this up. What would we do without knowledge of dip and refraction corrections? One solution: ignore them! Since we're on a beach, we could arrange to measure angles from the zenith and limit observations to altitudes above, maybe, 30° (zenith distance 60°). Since the air is breathable and not under horrible pressure, we can make some assumptions about composition and refraction properties so it would not be unreasonable to zero out the refraction. Even if we're stuck using the sea horizon, we can measure dip under the right circumstances. This works on Earth, too...

To measure dip: suppose you're back on that cruise ship from last year (when was that? January?). Imagine you're on the vessel's top deck, and you're able to walk from one side of the vessel to the other, or you're able to find a spot where you can see horizons in both directions, port and starboard. You see a bright star at a high altitude, let's say it's above 70° altitude off the port side. Maybe it's Capella. You shoot a series of three or four standard altitudes of Capella, facing it. Record each altitude and the time of the sight (this can be "stop watch" time --doesn't have to be on any particular time scale). Alternate those standard sight with an equal number of "back sights" from the opposite horizon, towards starboard. These will be altitudes greater than 90°. As with the direct sights, you record each altitude and the time of each sight. Graph the direct (port side) sights against time. Graph the back sights (starboard side). Pick some time in the middle of the graphs that looks good, and read off the direct altitude and the back sight altitude for that time. These are simultaneous direct and back sight altitudes, and if there's no dip, they add up to 180°00.0' exactly. Instead you might find that they add up to 180°18.6'. Half of that difference, or 9.3', is the dip. Notice that this will work under conditions where the planet is of unknown size, the atmospheric refraction near the horizon is anomalous, or other unknown altitude corrections are involved. Nice, right? :)

You added:
"You cannot determine your assumed position so the LOP method will not work."

That might be a problem, but maybe not. Have you ever tried a random AP? You pick a random spot, try for a fix. It's a long way off with crazy intercepts, but it gets you closer. So you use that "fix" as a new AP and repeat the calculation. Supposedly in three or four trials, you get yourself into the normal range for ordinary AP-based fixes. I'm repeating other people's stories here. I almost never use AP's or the intercept method. While celestial LOPs are fundamental, intercepts are not. The intercept method if just a math trick... and there are other math tricks!

And basically, you said the same thing by writing:
"However, you can still resolve your position by measuring at least two celestial bodies (your sun, moons, and stars) and resolve both spherical triangles together, as you would do on Earth. "

Yes, exactly. That's the key.

You concluded:
"Lastly, If the alien planet has a gravity lower than the earth, your arms will notice and enjoy that when taking the sights, particularly the lunar’s ones."

Ha ha ha! Yes. We need to add some buoyancy to our sextant. Maybe fill the relatively unimportant battery chamber in the handle with compressed helium. Press the little button, and, ta-da!, a 10-meter balloon blossoms out of the top of the handle filled with now-buoyant helium. And that sextant is then light as a feather. :)

Thanks again for contributing on this little sci-fi cel-nav story. Many of the points you have raised are exactly the sort of thing I was hoping we would all get into. What is essential to modern (terrestrial!) celestial navigation? And what aspects are accidents of history that we can live without?

Frank Reed