Refining the Technique
These figures gives us an idea of the variation in the speeds of retrograde motions:
Average Retrograde: 122 days
Fastest Retrograde: 116 days 18 hours, Jupiter at perihelion, Earth at aphelion
Slowest Retrograde: 122 days 12 hours, Jupiter at aphelion, Earth at perihelion
It so happens that the perihelion of Jupiter was fixed in the constellation of Pisces 2000 years ago (352 degrees ecliptic longitude). This location, of course, slowly changes due to the precession of the perihelion. But it was so slow it would not throw off the historical usefulness of the Magi’s tradition. Earth also has a perihelion. In 2 BC, Earth was at perihelion on December 4. That means it was at its closest point to the sun. At its closest point, the earth moves the fastest. The aphelion of Jupiter was at RA 11h 31m. These positions are fairly close to accurate. The Magi did not need to know about them. But they had figures reflecting them. By finding the averages of many observations they knew the number of days between the first station and the second station of Jupiter for every constellation and month of the year using the accumulated observations of almost 500 years. That is they noticed that their results were fixed according to the month of the year and the constellation that Jupiter was in.
Accordingly their data will tell them that a retrograde that begins in Leo in late November will last 122 days. This is because in November 3 BC, Jupiter was in Leo about 1.5 hour circles before aphelion, and earth was approaching perihelion. The Magi measure all the longitudes of Jupiter from the first to the second station noting the dates as they go. For the longitude of the first station, they will obtain the equivalent of the modern figure: 129.76°± 0.06° (4 arc minute accuracy). The width of the moon is about 30 arc minutes. So we can expect them to be at least accurate enough to detect angle distances of 1/8th the moon’s diameter. A modern sextant can measure 1/64th degree (0.015°). Some such instruments may have existed in ancient times. Modern Experts are sometimes snobbish or arrogant and like to insist that ancient man did not invent any precision instruments. That’s because they think they are at the pinnacle of evolution. The Magi don’t actually need anything too fancy in this case. They measure the second station at: 119.75° ± 0.06°. They then calculate the midpoint: 124.76° ± 0.12°. They then check their notes to see what date Jupiter was at that longitude. They find in modern terms that it was JD: 1720718.40. From this they subtract 1/2 of 122 days, i.e. 61. The result is JD: 1720657.4, the date of the first station. The actual figure is 1720657.49, which is within the stated error. The error is about 2 hours. If they used this method, they were close. Actually, they would be lucky to be that close.
This method, however, often results in a much greater error, up to three days. This is due to the long arc of the calculation. A better method is to use guide stars conveniently near the the first station. We will apply this in a bit.
The Magi also have figures for the time between two first stations. It so happens that every twelve years Jupiter does a run from Leo to Virgo between two first stations in 395 days. The reason this is faster than the synodic period (398.88 days) is that when Jupiter is moving near aphelion it is more easily caught up with by the earth. In 50 BC the dates of two first stations are:
First Station Leo: 1703504.39166 142.7121° -49/12/10 23:44:59
First Station Virgo: 1703899.43332 172.8122 -47/01/09 00:44:59
Difference: 395.04166 days
And in 39, 15, and 3 BC:
First Station Leo: 1707496.34999 116.4475° -38/11/14 22:44:59
First Station Virgo: 1707891.34999 147.0321° -37/12/14 22:44:59
Difference: 395.00000 days
First Station Leo: 1716271.22499 125.4197° -14/11/23 19:44:59
First Station Virgo: 1716666.26666 155.7817° -13/12/23 20:44:59
Difference: 395.04167 days
First Station Leo: 1720658.30832 129.7575° -02/11/27 21:44:59
First Station Virgo: 1721053.38123 160.0087° -01/12/27 23:29:59
Difference: 395.07291 days
Therefore, if one can figure out the date of the first station in Leo then all one has to do to figure the first station in Virgo is to add 395 days. So let’s take a crack at each of these calculated dates and see if we can simulate a way how the Magi figured them. I should note that the Magi would have a great many more years of data than I listed above for the 395 days. They would make mistakes, but by averaging a large amount of data they would end up with that figure. In a similar fashion, by averaging 365 day ordinary years, and 366 day leap years, one will see that over time a year is 365.25 days, and with even greater amounts of data 365.2422 days! Once the constant is known, it becomes quite useful for predicting the dates of equinoxes.
So lets see how this works with a simulation. On -14/10/7 @ 5:30 JMT Jupiter is in conjunction with Regulus (JD: 1716223.63). On -13/1/10 @21:30 JMT Jupiter is again in conjunction with Regulus (JD: 1716319.3) after having stopped and begun retrograde motion. The midpoint date is the first station (stopping point): JD: 1716271.47. The actual time of the first station is 1716271.22499 (see above) with an error of 5.8 hours. About 399 days later we repeat the procedure. -13/10/15 @ 3:21 JMT Jupiter lines on a line between Zavijava (β Vir) and b-Vir (mag 5.90). (JD: 1716596.54). -12/3/4 @ 20:21 JMT Jupiter is again on a line between Zavijava (β Vir) and b-Vir (JD: 1716738.25). The midpoint date is: 171667.4. The actual time of the first station was 1716666.26666. The error is 1 day. The difference between the figures calculated in the simulation is 395.93 days. The actual difference is: 395.04167 days.
Why is there a larger error here? The answer is that a larger distance between the marker star and the station the greater the error. The Magi, therefore, will seek to reduce the error by picking a marker star close to the longitude of the first station. If there is no marker star close by enough that can be seen, then the Magi may have to resort to calculated figures based on the last station before it, or they may not be able to give an exact date for a particular station in a given year. Let us redo the last calculation using 10-vir as the marker star. It is magnitude 5.95, extincted to 6.09. Here is the marker data:
10-Vir 6.09 x Jupiter: -13/11/14 05:44:59 JMT 1716626.64166
10-Vir 6.09 x Jupiter: -12/02/01 01:44:59 JMT 1716705.47499
Midpoint date: 1716666.058325, i.e. 1716666.06. Error: 4.8 hours
We see a greatly reduced error by using a marker nearer the station point. The reason for this is that the midpoint is taken based on a shorter arc of the earth’s orbit, and any irregularities in Jupiter’s apparent motion have less effect.
Let us now take a look at 3 BC in Leo and see what markers are available for the Magi, so that they can figure the first station date, and then use their historic 395 day figure. There is unusually close to the station point a sufficiently bright star ρ-Leo (47 Leo - HIP 51264 - SA0 118355 - HD 91316 at RA on date 131.05/+18.36). This star in the presence of the moon is extincted to a magnitude of 4.00 when in conjunction with the moon and Jupiter. The situation is shown in the image at the left taken from Stellarium 0.14.1. The moon is about to cover up the star ρ-Leo, i.e. as the minutes are incremented the moon moves down in the picture to occult the star. The terminator of the moon ends up pointing right at Jupiter. Here is the marker data:
ρ-Leo 4.00 x Jupiter x Moon: -02/10/31 03:44:58 JMT 1720630.55831
ρ-Leo 4.29 x Jupiter x Moon: -02/12/24 21:08:58 JMT 1720685.28331
Midpoint date: 1720657.92081, with an error 9.6 hours under the actual.
Using the figure 395.05 days the predicted time of the first station in Virgo is: 1721052.921, i.e. 12/27/2 BC @ 12h 27m. This is just 10 hours under the actual time at 22h 30m, which is just carrying through the error from the marker star. According to the text, the star stopped BEFORE they found the child (Matthew 2:9-10). They saw the stopped star when it rose in the evening on 12/27 at 22h 30m. About 4:30 a.m. JMT, the next morning it stood in the south over Bethlehem. This is when they set out in the morning after the secret meeting with Herod the night before.
I don’t know if the Magi had a way of eliminating 1/2 day errors. However, the first chance they had to see the stopped star over Bethlehem was near dawn on 12/28. This means their error does not matter. The earliest they could go was in the morning in any case.
In the first alignment with ρ-Leo, the moon occulted the star, that is, it covered it up. I have not showed an image of the occultation. However, anyone with Stellarium can reproduce it. The moon was half full, phase .48, 47.7% illuminated. The terminator line was pointing right at Jupiter. And just as amazingly, and the second time mark with ρ-Leo, the star lies exactly between the moon and Jupiter. This image is shown to the right here.
Conclusion: Could the Magi predict the stopping date? Yes, within about ±½ day, which is close enough to say it happened just before they found the child. They might even consider the double moon with the marker star propitious to their quest, though I really hope they realized the difference between their astrology and the divine intervention here in their art and realized it was no contest between them and God. Astrology simply cannot measure up the the one time scripture implies that God had something to do with the positions of the stars and the birth of his Son. It means that astrology is superstition and that the Almĭghty simply borrowed its astronomical nomenclature and metaphors to do something real. For example calling the heliacal rising the birth of a star, or the rebirth of a star is a nice metaphor. Everyone realizes stars do not die and are not born when they go behind the sun. It just appears so. Astrology is trying to say that a particular rising is tied to a human birth or influences the destiny of the human. There is no scientific connection. And false gods certainly are not powerful enough to move planets or change biology. But they might deceive people by arranging the fate of the person according to their horoscope. This is all bunk because the causes are not scientific. However, when the true Gŏd of heaven steps into the picture, and decides he will move the stars to mark an event (just one event), then there is no scientific problem. He really does have the power to make it happen. And I think in the end the Magi got this message and gave up their astrological speculations after that and devoted themselves to the astronomical aspects of their trade. This is because the Star of Bɛƫleɦem was real and put the whole trade to shame by showing the real stuff from heaven. We have to remember that modern astrophysics scientists are just as full of another kind of cosmological superstition, and that is stellar evolution. In their case the Almĭghty is going to roll up the heavens like a scroll.
The Magi might not think the star stopping on any random date except just before they found the child was particularly important. They probably would not have mentioned it to Yeshu‘a’s parents, and Matthew probably would not have recorded this detail. That the Magi more than vaguely knew which day the stopping took place on makes it reasonable for them to resume their journey after the meeting with Herod on the morning of December 28th. They find the child that day or evening. In the night they dream that they should not go back to Herod, and Yosɛf dreams he should take the child and his mother and flee to Egypt. Sometime on the 29th day of the month, and perhaps the next day (2 Sheνat) Herod sends his soldiers to murder all the boys under 24 months in Bɛƫ-leɦem and the surrounding district.