Next message: Frank Reed: "Re: No sextant, no watch, no almanach, nothing"
A few days ago, I wrote:
"Another related game: are there circumstances under which you can navigate
celestially without a sextant, without a timepiece, AND without an almanac (of
any type)? I think the almanac is the "technological artifact" that is most
difficult to do without..."
And Alex has been dying of curiosity <g> assuming that I meant this as a
riddle. No, actually, I meant it as more of a game. And the real point was to
emphasize the necessity of having at least some form of almanac.
Nonetheless, let's "play the game". Latitude is no serious problem assuming
we can remember simple rules for generating the daily declination of the Sun or
assuming that we know the declinations of a handful of stars from memory
(Polaris being the obvious case). But what about longitude? Since antiquity
astronomers and geographers have understood that you need a clock in the sky -- a
clock that reads some "absolute time" that we can compare against the apparent
time given by the positions of the Sun and stars relative to the local
observer's horizon. What absolute clock can we use if we have lost everything (no
sextant, no almanac, no telescope)? Nature hasn't provided us with anything that
would let us read the time to the second or even to the nearest minute, but
there is a clock which beats out the time regularly, its alarm going off like
clockwork every 2 days, 20 hours, 49 minutes. It's the eclipsing binary star
Algol in the constellation Perseus. Visual observers with a little practice can
time the middle of its eclipses to the nearest 30 minutes or so. Not great for
longitude, but if you had absolutely nothing else, it would get you your
longitude to the nearest 7.5 degrees. In an alternate history, that might be worth
something. Note that eclipses of Algol are only visible half of the time (half
occur in daylight), and they are not observable at all for some six weeks
around May 20th.
How would you use Algol in practice to get longitude? First, you would need
to know how to find Algol and estimate its magnitude. Second, you would need
the time of at least one relatively recent eclipse. Maybe you observe one just
before leaving on your round-the-world voyage. Let's suppose you observe the
eclipse that takes place a few days from now centered on 16:55 UT on Nov. 10,
2004. Next, you would need to know the rule for predicting future eclipses. It's
very short and easy to memorize. I have split it up into very small morsels:
1) start with a known eclipse date and time (best if it's a date from August
or February but any will do).
2) add 3 days.
3) subtract 3 hours 11 minutes.
4) every 7 weeks, subtract 1 minute.
5) for the four months centered on May 20, add 7 minutes. for the four months
centered on November 20, subtract 7 minutes. Otherwise, do nothing.
You can generate a list of eclipses for years into the future by iterating
steps 2 through 5. The predicted times will be accurate to +/- 3 minutes which
is plenty good enough given the observational limits of visual magnitude
estimates. When you observe an eclipse of Algol on the far side of the globe, that
immediately gives you Greenwich Time. Comparing that with local time,
determined by observing the stars at the zenith at the time of the observation, yields
the longitude.
Please understand, I am presenting this simply as a way to "play the game"
that I set out earlier. This is not real navigation. But perhaps we can
fantasize about ocean navigators on the sea of a planet in some other star system...
One with a better "Algol" that can be read to the nearest minute or the nearest
second... For them the problem of longitude would never have existed.
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
