Tropical timings: Jupiter-Earth-Mercury repeating triple conjunctions
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This builds on our earlier analysis: Jupiter, Earth and Venus’ tropical alignments point to the mean solar cycle length.
That had a 996 (83*12) tropical year cycle (graphic here).
We find that Jupiter-Earth-Mercury also has a tropical year cycle, this time it’s 1079 TY (83*13) as shown in the graphic (right).
Since all three of the two-planet conjunctions occur a multiple of 19 times in the full period, as per the graphic, a Jupiter-Earth-Mercury alignment with the Sun should occur every 1079/19 tropical years (almost 56.79 TY).
The solar simulator by Carsten Arnholm (link here) shows this. In its 3000-year window (0-2999) there are 53 J-E-Me alignment possibilities, meaning 52 periods of 1079/19 TY. The first one occurs in year 0, and the last one that can be viewed is in year 2953.
Some alignments are exact, some nearly so, and some less so but not by much (a few days). The eccentricity of the orbits, especially that of Mercury (over 12 times that of Earth), probably has an effect there.
Examples of very good alignments include those of years 0, 1079 and 2158 (= 1079*2).
Analysis shows that of the 53 alignments available on the simulator (which has a 3000 year window), about 1/3 are near-perfect, 1/3 very good and 1/3 moderately good. The ‘best’ ones fall roughly between November and February, and the least exact ones roughly between May and August, the rest mainly in the other months.
It’s not clear why that is, but might be related to Mercury’s large eccentricity (see graphic at top of post). Earth’s perihelion is in early January so its orbit speed is at maximum around then, with a minimum in July.
In any case the triple conjunction dates don’t ‘slip’ against the 1079 tropical year cycle, even after two millennia or more.
Here’s another repeating 1079 year cycle example.
The dates of any J-E-Merc triple conjunctions can be calculated by adding or subtracting multiples of nearly 56 years 10 months (56.79~ TY) from the dates of examples published here (via Arnholm’s SIM2 software).
This confirms that the solar simulator recognises Earth is operating in a rotating reference frame (as noted in the introduction to an earlier post, here).
Further analysis, building on this, to follow.
Source: https://tallbloke.wordpress.com/2025/03/12/tropical-timings-jupiter-earth-mercury-repeating-triple-conjunctions/
