コメント１　・　COMMENT 1
石川源晃著

Dear Gen,

It is nice to hear from you. I have looked at your website. Very nice. I can say a little about the precession of the equinoxes. The equinoxes are the points of intersection of two planes: the plane of the ecliptic (the earth's orbit about the sun) and the plane of the earth's equator, which is inclined to the ecliptical plane at about 23 1/2 degrees. The combined gravitational action of the moon and the sun and the planets on these two planes cause both of them to shift slowly in space. Therefore, their points of intersection also shift slowly. This causes the vernal equinox to move backward by about 50 seconds of arc per year. The exact rate of precession is determined by observation of the fixed stars over an extended period of time. Fairly accurate observations of the fixed stars were made in the early 1800's, and by comparing those with observations made today, there is a period of about 200 years between the earliest and the latest observations. It is possible then to use these observations to determine the amount of precession during that 200-year interval. The equations of celestial mechanics give the variations of the precession with great precision. Combining those variations with the actual rate of precession determined from the observations, it is then possible to write equations that define the rate of precession accurately at any time within a few thousand years before or after the present time. The latest equation for the precessional motion is this:
P = 5029.0966 x T +1.11113 x T2 -0.000006 xT3
where T is the time in Julian centuries (36,525 days) from Greenwich Mean Noon on 1 January 2000, T2 is T square and T3 is T cubed, and the coefficients are in seconds of arc. This equation is valid for several thousand years before and after the year 2000. But it is an approximation to a complicated cyclic motion that takes many tens of thousands of years. So if you wanted to know the true value of the precession in 15,000 B.C., you would have to use much more complicated expressions to determine it with precision.
If you want to know what the instantaneous value of the precession was at any particular time, you must differentiate that equation with respect to the time, and you have:
P = 5029.0966 +2.22226 x T - 0.000018 x T2
Hipparchus, who lived in the second century B.C. is credited with the discovery that the equinoxes moved. The Babylonians before him used a fixed zodiac and noticed that the vernal equinox occurred when the sun was in the vicinity of 8 Aries in the late third century B.C. By comparing some of their observations made a century or two before his own time with observations that he himself made in the last half of the second century, Hipparchus estimated that the equinox was actually moving at the rate of about 45 second of arc per year (three hundred years later, Ptolemy reduced that estimate to 36 seconds per year). If we set T = -21, we can find from the preceding eqution that the instantaneous value of the precession at 100 B.C. was 4982.42 seconds per Julian century or 4979.01 seconds per Egyptian century (which had only 36,500 days per century). So, Hipparchus's original estimate of 45 seconds per year (4500 seconds per Egyptian century) was fairly close. (It is not clear why Ptolemy thought that 36 seconds per year was better than 45 seconds per year.)
The Alexandrian astrologers who lived in the early part of the second century B.C. invented horoscopic astrology. They were earlier than Hipparchus, so they did not know about his discovery of the precession. They adopted a fixed zodiac that was a few degrees different from the Babylonian fixed zodiac. And they made tables of the sun, the moon, and the planets that gave positions referred to their fixed zodiac. The Greek astrologers of the classical period used those tables and that fixed zodiac until the fourth century A.D. when Ptolemy's tables became available. His tables gave positions referred to a tropical zodiac that was already about 2 degrees different from the truth. this was because Ptolemy had taken the position of the equinox with respect to the fixed stars to be approximately what Hipparchus had determined in his star catalogue, whose epoch was around 130 B.C., and which was approximately correct; but then Ptolemy reduced the precession to 36 seconds per year, when, as we saw above, it was really about 49.8 seconds per year. If you multiply (36 - 49.8) by 430 years, you get -5934 seconds or -1 degree and 39 minutes. so when the astrologers began using Ptolemy's "tropical" tables, they got longitudes that were nearly 2 degrees in error. This discrepancy was not corrected until the Arabs became interested in astrology in the eighth century A.D., by which time the error had increased to about 3 1/2 degrees. They were good enough astronomers to correct this error in the position of the equinox and make a new estimate of the value of the precession that was close to 50 seconds per year. Thereafter, we Western astrologers have used a correct tropical zodiac.
The Hindus on the other hand, who had learned horoscopic astrology from Greek books in the second century A.D. began to use a fixed zodiac, because that was what they found in the Greek books. (Remember that Ptolemy's "tropical" tables did not become available in the West until the fourth century, so the Greek astrology books of the second century were still using the Alexandrian fixed zodiac. Western astrologers switched from a fixed zodiac to a tropical zodiac in the fourth century, but the Hindus had lost contact with the astrologers of the Western world before Ptolemy's tables became known in the West, so the Hindus never changed from a fixed to a tropical zodiac.

I hope that this little bit of historical information is helpful. And again, it is nice to hear from you.

Best regards,

Jim Holden

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