A triangle that creeps three degrees a lap
Jupiter and Saturn meet every 19.87 years, and each meeting falls 243.2° further on. That is nearly two thirds of a circle, so three meetings make a near triangle. Nearly is the whole story: the 3.2° left over is what walks the pattern out of one set of signs and into the next, and it is why anyone was ever able to build a theory of history on two planets.
Anything in a violet panel we computed from DE421 ephemeris data. You can check it.
Anything on a gold rule was said by people, at a particular time. We say who, and when.
The slowest thing a chart tracks
TWO PLANETS, TWENTY YEARSMost of what a chart says changes within a lifetime, and much of it within a week. Jupiter and Saturn passing each other is the exception: it happens about once every twenty years, which means a person sees four or five of them and no more.
Here is every one the app's own ephemeris can reach, with how close the two really came.
| Closest | Where | Separation |
|---|---|---|
| 28 Nov 1901 | Capricorn 13°60′ | 0.44° |
| 10 Sep 1921 | Virgo 26°36′ | 0.95° |
| 7 Aug 1940 | Taurus 14°27′ | 1.19° |
| 19 Oct 1940 | Taurus 12°28′ | 1.23° |
| 15 Feb 1941 | Taurus 9°07′ | 1.29° |
| 19 Feb 1961 | Capricorn 25°12′ | 0.23° |
| 31 Dec 1980 | Libra 9°30′ | 1.05° |
| 4 Mar 1981 | Libra 8°07′ | 1.06° |
| 24 Jul 1981 | Libra 4°56′ | 1.10° |
| 28 May 2000 | Taurus 22°43′ | 1.15° |
| 21 Dec 2020 | Aquarius 0°29′ | 0.10° |
| 31 Oct 2040 | Libra 17°56′ | 1.13° |
12 rows for fewer meetings than that, because a meeting can be counted three times. Separation is the real angle between the two bodies on the sky, which is not the same as the difference in their zodiac longitudes.
That last sentence is worth pausing on, because it is where the obvious measurement goes wrong. A conjunction is defined as equal longitude, so if you measure closeness that way the answer is zero every time and every meeting looks identical. The two are also separated north and south of the ecliptic, and that is what makes one meeting a spectacle and another a pair of stars a thumb's width apart.
The tightest is a well known record: at that separation the two were about a fifth of the Moon's width apart, the closest since 1623. That earlier one stood only thirteen degrees from the Sun and was effectively unobservable, so the last easily visible meeting this close was in 1226.
Why three of them make a triangle
AND WHY THE TRIANGLE WILL NOT STAY STILLEach meeting happens further round the zodiac than the last, and the step is the same every time to within a few degrees. Over the long series it comes out like this.
The individual steps vary by more than forty degrees, so the mean is taken across the whole series rather than a handful. Seven of them are not enough to state an average, and the first version of this article learned that the hard way.
Two hundred and forty degrees is two thirds of a circle, which is the same as one third going the other way. So each meeting lands roughly a third of the way round from the last, and after three of them you are back near where you started. Draw the three points and you have a triangle with its corners in three signs of the same element.
The word roughly is doing the work. The advance is 3.2° more than two thirds, so each triangle sits about 9.6° round from the one before. Slowly, over centuries, the corners walk out of one set of signs and into the next.
Two hundred and forty degrees would have locked the pattern for ever. Two hundred and forty-three lets it walk.
How long a set of signs holds
TWELVE CENTURIES, MEASUREDThe app's own ephemeris covers a century and a half, which is not enough to see this. For the long view we used an independent library, and checked the two against each other where they overlap: across 12 meetings the worst disagreement was 0.7 arcseconds, so the far figures are not a different kind of number.
| Signs like | From | To | Meetings |
|---|---|---|---|
| Taurus | 1206 | 1206 | 1 |
| Aquarius | 1226 | 1405 | 8 |
| Scorpio | 1425 | 1583 | 9 |
| Sagittarius | 1603 | 1821 | 10 |
| Capricorn | 1842 | 2000 | 8 |
| Aquarius | 2020 | 2199 | 9 |
| Scorpio | 2219 | 2378 | 8 |
| Sagittarius | 2398 | 2398 | 1 |
A run holds for 175 years on average and 8.7 meetings, the longest 218 years. The first and last rows are cut off by the ends of the window and are not counted in those averages.
There is one thing here the tradition does not prepare you for. The runs are not clean. Across 61 meetings there are 7 strays, single conjunctions that jump into the next element and then come back, so the boundary between one era and the next is ragged rather than a line. We counted them rather than tidying them away, because a table that showed neat two-century blocks would be a nicer picture of something that is not true.
The current run began in 2020 and the one before it ended in 2000. If you were born between those dates you were born inside a boundary, which is a sentence that means something historically and nothing astronomically.
The meeting that happens three times
WHEN BOTH GO BACKWARDSSometimes the two pass each other, back up, pass again, and pass a third time. That is not the planets circling one another; it is the Earth overtaking them both, which makes them appear to move backwards for a few months.
Both bodies turn retrograde during the same stretch, so the same pair of longitudes is crossed three times over about seven months.
This matters more than it sounds, because a triple conjunction is the thing at the centre of the most famous astrological argument ever made, and we can compute it.
Where the theory came from
THE INTERPRETATION, AND ITS HISTORYFrom here down we are reporting rather than measuring.
The idea that these meetings time the rise and fall of dynasties and religions is a specific historical doctrine with named authors. Māshā'allāh ibn Atharī, a Persian Jewish astrologer at the early Abbasid court, wrote the earliest surviving treatise applying Jupiter and Saturn to political change. A generation later Abū Ma'shar al-Balkhī gave it the systematic form that everyone afterwards used, in the book known in Latin as De Magnis Coniunctionibus.
His scheme is the one measured above: the meeting every twenty years, the shift into a new set of signs after a couple of centuries, and the full return after roughly a millennium. It is a real periodisation of history, built out of two orbital periods, four hundred years before anyone in Europe could compute either.
One caution. The tidy English labels for the three levels are a modern convenience; do not put them in a medieval mouth. The distinction by rarity is genuinely his, the vocabulary is ours.
Translated into Latin in the twelfth century, the doctrine became ordinary learned practice, and in 1499 Johannes Stöffler's almanac noted a gathering of the slow planets in Pisces due early in 1524. Pisces is a water sign. A pamphlet by Luca Gaurico in 1512 turned that into a prediction of a second Flood.
The panic was continent-wide and is one of the best documented episodes in the history of astrology, edited by Paola Zambelli in 1986 under a title taken from the period: the hallucinating astrologers.
It is worth saying plainly what happened next. Nothing. The year passed without a flood, and the failure was public, expensive and remembered. We include it because an article that quoted only the impressive parts of this tradition would be selling you something.
The run of meetings in fire signs that our table dates from 1603 is the one Johannes Kepler watched begin. The following autumn, while he was still following the two planets and Mars had joined them, a new star appeared, the supernova that still carries his name.
In De Stella Nova in 1606 he raised the thought that a comparable event might have marked the birth of Christ, and in 1614 he worked the chronology out properly: a triple conjunction of Jupiter and Saturn in Pisces in 7 BC.
That claim is testable, and it is the reason this article was worth writing.
Testing Kepler's claim
SEVENTEEN CENTURIES OUT OF RANGEThe app's own ephemeris cannot reach 7 BC and does not pretend to. The independent library can, and it agrees with the app to a fraction of an arcsecond where both are defined, which is the only reason we are willing to quote it this far back.
A triple conjunction, in the sign he said, in the year he said. Kepler was right about the astronomy.
He was right about the astronomy and that is where it stops. At their closest the two planets were about twice the Moon's width apart, which is a comfortable gap: anyone who could tell Jupiter from Saturn, which is precisely the skill the story credits its travellers with, would have seen two familiar planets near each other for several months, not a star.
That is the standard objection and it is not ours. There is no scholarly consensus on what the Star of Bethlehem was, astronomical or otherwise, and Kepler's version is one hypothesis among several; a different one, put forward by Michael Molnar in 1999, proposes an occultation of Jupiter by the Moon in 6 BC and has nothing to do with Saturn at all. Popular accounts blur the two constantly.
What the computation can settle is the arithmetic. It cannot settle what a first-century text meant, and we are not going to pretend a number does.
What we take from it
OUR OWN POSITION, DECLAREDThis app computes conjunctions and tells you which sign they fall in, and it does not tell you that a dynasty is ending. The measured part of this article, the interval, the advance, the creep, the runs, is astronomy that anyone can reproduce.
The doctrine built on it is a thousand-year-old attempt to read history off two orbits. It produced a serious body of work, one of the most spectacular public failures in the history of prediction, and a chronological argument by Kepler that was astronomically correct and probably still wrong about the thing it was arguing for. All three of those are worth knowing about.
Where Jupiter and Saturn stood when you were born, and where they are now. Computed free.
Compute your chartSources
SO YOU CAN CHECK THEM YOURSELF- Positions: JPL DE421 inside 1 Jan 1901 to 1 Jan 2052; Swiss Ephemeris 2.10.03 outside it. The two were compared across 12 meetings and differed by at most 0.7 arcseconds.
- Abū Ma'shar, The Book of Religions and Dynasties (On the Great Conjunctions), edited and translated by Keiji Yamamoto and Charles Burnett, 2 volumes, Brill, 2000.
- Paola Zambelli (ed.), "Astrologi hallucinati": Stars and the End of the World in Luther's Time, de Gruyter, 1986, on Stöffler, Gaurico and the flood that was predicted for 1524 and did not happen.
- Johannes Kepler, De Stella Nova in Pede Serpentarii (1606), where the idea is raised, and De Jesu Christi Servatoris Nostri Vero Anno Natalitio (1614), where the chronology is worked out.
- Michael R. Molnar, The Star of Bethlehem: The Legacy of the Magi, Rutgers University Press, 1999, for the competing hypothesis.
- The 2020 separation of about six arcminutes, and the 1623 and 1226 comparisons, are as reported by NASA and by Sky and Telescope at the time; our own measurement agrees.
- A note on the history: the doctrine and the 1524 panic are well served by scholarly editions. The modern three-tier vocabulary for conjunctions, and the phrase great mutation, are practitioner usage rather than terms we could trace to a period source, so we have not put them in anyone's mouth.