Ancient Navigators and the Demon Star

  I just read an article that shows that the Ancient Egyptians knew about the eclipsing binary star Algol back in the 13th Century BC.  It occurred to me immediately that this could have allowed ancient navigators to crudely measure longitude!

   Ancient navigators knew how to measure latitude fairly accurately.  All they needed to do was to figure out the apparent height of the North Star, measure the angle, and bingo, they had an estimate for latitude.  But what about longitude?  The easiest way to estimate that is to know that sunrise and sundown happen at different times depending on longitude (or, as we might think of it today,  what time zone you are in).  So if an ancient navigator knew sunrise was supposed to be a 6:55 AM in Oslo, and instead it happened at 7:55 AM, that would tell him that he was positioned 15 degrees West of the reference location, or out in the Norweigian Sea somewhere.  This can very easily be done today, what with electronic watches, but note that a sundial would not work to measure time, because it is based on the position of the sun, and automatically cancels out the effect that you want to see.  Other forms of ancient clocks were not very good.  It is generally assumed that the ancient navigators had no way to measure longitude until 1773, at which time John Harrison produced an accurate marine chronometer.  

    But wait a minute.  The Demon Star Algol (which actually consists of two stars which rotate around each other, Beta Persei A, which  regularly gets eclipsed by the dimmer Beta Persei B) dims by more than a factor of three for 10 hours at a time, dwindling easily seen with the naked eye.  This was recorded by the Ancient Egyptians according to an article that has just appeared in LiveScience.com, by Charles Choi.  

   I frankly had no idea the effect was visible to the naked eye.    But according to Choi, Algol dims by more than a factor of three for 10 hours at a time, which is easily seen with the naked eye.  

     Jiminy Christmas, this is a huge effect, and I can't believe none of us apparently put two and two together before.  The clues are staring us in the face.   Algol, known as the Demon Star, represents the eye in Medusa's head!  Doesn't this suggest that ancients thought this star was a bit unusual??

    The period is 2.867 days now, but back in the 13th century BC it may have been closer to 2.85 days. The slowing is consistent with calculations of the change of mass of the binary as it spirals out.  
      The salient point is that if you know the period accurately, it becomes a universal clock that can be used from any point on the earth (as long as the weather is clear and if the eclipse occurs at night).  That allows the navigator to calibrate his hourglass and get a true calibration to measure longitude.  That could allow trans-Atlantic or trans-Pacific navigation.
     An observer could detect up to four events, depending on the sensitivity of the instrument (in this case, the human eye):  the beginning of the dimming phase; the end of dimming, the beginning of the brightening phase and the achievement of maximum brightness.  
    Over many cycles, it is possible to determine the period with great accuracy.  But how accurately can the magnitude or change in magnitude be estimated by the naked eye over a single cycle?  
   An upper bound exists from the ancient Greeks, who classified stars over six magnitudes.  Algol is normally magnitude 2.1, but decreases to about 3.3 and the back to magnitude 2.1 over 10 hours. The change rate is thus 1.2 magnitudes per 5 hours, or 0.24 magnitudes per hour. In recent times, naked-eye astronomer Alan MacRobert describes how to estimate magnitudes by eye to roughly within 0.1 magnitudes.  If so, a sunset-calibrated hourglass could be used to plausibly determine the minimum brightness of Algol within about 24 minutes, allowing a crude estimate of longitude, accurate to some 6 degrees, corresponding to 600 km at the equator.  At northern latitudes, this is roughly the difference between Dublin and London. 

Data from the Northern Houston Astronomy Club  indicate that it is possible to trace the light curve of Algol.  By extrapolating the shape of the curve and directly measuring the time of the minima, it is possible to estimate the time of minimum brightness to within about 0.01 to 0.02 periods, or plus or minus 20 to 40 minutes, or 5 to 10 degrees of longitude. If a highly skilled stargazer were able to improve upon the accuracy demonstrated by the North Houston Astronomy Club, better precision might be obtained. 

    Now, there is absolutely no evidence, as far as I am aware, that the ancients actually used this method to navigate.  The key would have been for ancient astronomers to realize that the brightness variations occur independent of longitude.  But if someone had made that connection, it is clear enough that longitude could have been crudely estimated in ancient times.

For Additional Reading

History of Longitude, Wikipedia, http://en.wikipedia.org/wiki/History_of_longitude 

L. Jetsu, S. Porceddu, J. Lyytinen, P. Kajatkari, J. Lehtinen, T. Markkanen, J. Toivari-Viitala, Did the ancient egyptians record the period of the eclipsing binary Algol - the Raging one? (Submitted on 27 Apr 2012)

http://arxiv.org/abs/1204.6206