jay@npois.UUCP (Anton Winteroak) (02/10/86)
The actual time for the precession of the Moon's orbit around the Earth is 18 years, 6 days, and about 8 hours. Many books about old astronomy confuse this with a cycle of 18 years, seven (lunar) months, in which the lunar and solar calender get synchronized. Some accounts of Stonehenge indicate that it was built with the 54 year 19 day eclipse cycle in mind. (This is 3 times the 18 year 6 and 1/3 day cycle). Otherwise, nice article. With great difficulty, it could be transported east or west, but any North or South movement would require an Engineering Change Order.
msb@lsuc.UUCP (Mark Brader) (02/14/86)
> The actual time for the precession of the Moon's orbit around > the Earth is 18 years, 6 days, and about 8 hours. Many books about > old astronomy confuse this with a cycle of 18 years, seven (lunar) > months, in which the lunar and solar calendar get synchronized. Sorry, Anton, this is quite wrong. I didn't really think Gerald Hawkins would get it wrong after making a special study of it, but I checked with Van Nostrand's Scientific Encyclopedia before posting. The moon actually has THREE cycles in the range 18-19 years. Simplest is the Metonic cycle, which is, as you put it, the lunar and solar calendars getting synchronized. This has to be an exact number of years, therefore! It's 19 years, which is very close to 235 synodic periods (lunar months). Taking the latter as 29.53 days and the average year as 365.2422, the two figures differ by .05 of a day. The other two cycles both involve the "regression of the nodes", or precession of the plane of the moon's orbit. The VNSE gives this this movement as west 19.5 degrees per year, but this must've been rounded, since other figures are consistent with it being 19.34 degrees. Now, the plane of the moon's orbit intersects the ecliptic (plane of the earth's orbit) in a line, which is called the line of nodes. This line's direction moves through a complete circle every 360/19.34 or 18.61 years, which is the period I was talking about in the other article. (I didn't know exactly what it was myself then; thanks for making me look it up.) It should be obvious that it is indeed the plane of the moon's orbit that will determine its azimuth at rising under the constraints described in the other article. The third cycle is the one of just over 18 years, which is called the Saros. Consider the movement of the line of nodes again. The earth-sun line and the line of nodes will be parallel approximately every 6 months (and this is when eclipses happen). It is more convenient to think of the lines as having direction, so that they are parallel (as opposed to antiparallel) about once a year. But it is "about" once a year, because in a year the line of nodes moves 19.34 degrees. Since the earth-sun line is moving around to meet it, the actual period is (1 - 1 / (1 + 360/19.34)) of a year, or 346.62 days. This can be called an "eclipse year". And the Saros refers to the synchronization of eclipse years and lunar months. 19 eclipse years is just .55 day different from 223 lunar months. All three of these cycles are related to repetitions of eclipses. The Saros is most closely related since the orbits are returning to the same configuration. If there is an eclipse on a certain day, there will almost certainly be another one 223 lunar months later, and of the same type (partial, total, annular) too. It is also quite likely that there will be another one one Metonic cycle of 235 months later, and in about the same place, too, whereas the Saros-determined eclipses shift 1/3 of the way around the world each time. For instance, the February 26, 1979, North American total solar eclipse will be followed one Saros later on March 9, 1997, by a total solar eclipse in eastern Asia, and one Metonic cycle later on February 26, 1998, by another one traversing northern South America. As for the third cycle, well, if you consider only the full and new moons nearest a certain date, it is the state of the 18.61-year cycle that will determine whether there is then an eclipse. Mark Brader