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Telling Time by the Stars October 31, 2006

Posted by ionicflux in Portals.
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star.pngHowever, learning how to do it is educational. It teaches you a few things about the constellations, and a few things about spherical geometry.

The task requires more skill than you might think. I just checked with google and found a googol of sites that describe what I call the “standard hokey” technique — namely the one that depends 100% on the “pointer” stars: Alpha and Beta Ursae Majoris (Dubhe and Merak). This has the slight problem that it doesn’t work. It has apparently been devised by people who spend too much time looking at star-charts and not enough time looking at the real sky. It works OK at, say, 10PM in late April, when the pointers are high overhead, but it gives the wrong answer 3 months later and/or 6 hours later (because of spherical geometry) and it gives no answer at all 6 months and/or 12 hours later (because you’ll have trouble seeing the pointers).

Typical charts of the circumpolar stars use a polar projection, which doesn’t accurately portray how things actually look. Suppose you are standing at latitude 40 degrees North, and the 0-hour circle (marked by e.g. Beta Cassiopeiae) is overhead. That does not mean that the 18-hour circle (marked by e.g. Gamma Draconis) is a horizontal line 40 degrees above the horizon. It is locally horizontal near the pole, but then it dips quite markedly. If you extend it far enough it dives through the western horizon. Gamma Draconis is halfway along the great-circle route from the pole to the horizon, so its elevation above the northwestern horizon is less than 3/4ths of the elevation of the (since the sine of 45 degrees is 0.7).

I’ve found several on-line star-chart generation sites that get this wrong, but I’ve been unable to find one that gets it right. Can anybody recommend something that works?

Anyway, here is how I do it. This is just a quick overview; you will have to fill in many details on your own. This only deals with the northern temperate latitudes. Also note that tradeoffs have been made between convenience and accuracy: there are simpler methods that are grossly inaccurate, and more-accurate methods that are more complex (using equatorial rather than circumpolar stars).

  1. Memorize four landmarks (skymarks?)
    • The 0-hour circle. This is marked by Beta Cassiopeiae (Caph) which is the star at the bright end of the W, the end with the acute angle. Continuing along, we also have Alpha Andromedae (Alpheratz) and Gamma Pegasi (Algenib) which together constitute the trailing (eastern) edge of the Great Square — hard to miss.
    • The 6-hour circle. This is marked by Delta Aurigae, Beta Aurigae (Menkalinan), and Theta Aurigae.
    • The 12-hour circle. This is marked by point halfway between Delta and Gamma Ursae Majoris, the two non-pointer stars in the bowl of the Big Dipper. (The pointer stars are excellent markers for the 11-hour circle.)
    • The 18-hour circle. This is marked by Chi, Phi, Xi, and Gamma Draconis, the hind feet, chin, and nose (Eltanin) of the Dragon.

    Also remember that the 12-hour circle is the continuation of the 0-hour circle, and that the 18-hour circle is the continuation of the 6-hour circle.

  2. The 12-hour circle is overhead at midnight at the spring equinox. The 18-hour circle is overhead 6 hours later, and/or 3 months later in the year. And so forth. This gives you four “primary” reference pictures, where one of these four circles is overhead.
  3. You can then construct four “secondary” reference pictures, halfway between the primaries. These correspond to the situation where the primary circles form a giant V shape that is symmetrical with respect to the vertical. Do not try to judge the angle that the circles form relative to horizontal, because the perception of horizontal is distorted by the spherical geometry. The perception of vertical is OK, and the perception of symmetry is OK. Anything else you need can be judged by interpolation between the symmetrical picture and the vertical picture.
  4. As you face north, the great clock in the sky rotates counterclockwise1. It moves counterclockwise as you get later in the night or later in the year. The time-of-year contribution is 2 hours per month, or a half hour per week.
  5. Therefore: Suppose it is March 22nd. If you see the 12-hour circle is past vertical, 1/3rd of the way to the symmetrical V position, it must be 1:00 AM. If it is two weeks later in the year, the same picture is only 12:00 midnight (standard time); the advancement is explained by being later in the year, not later at night.
  6. Correct for daylight savings time. If DST is in effect, humans say it is one hour later than the stars say it is.
  7. Correct for longitude. This could be a half hour either way if you are near the edge of your timezone. The correction is zero if you are in the middle of your timezone.