Tropical timings: a new Jupiter-Saturn model

Jupiter and Saturn

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In this post we propose a heliocentric view of solar system planetary motion based on Arnholm’s Solar Simulator 2, data provided by Jean Meeus and his collaborators. On the screen it says: ‘Looking down on Sun’s north pole.’

We refer to the tropical orbit data in NASA’s Planetary Fact Sheets for the main planets in the solar system, which says:
Jupiter = 4,330.595 days
Saturn = 10,746.94 days

Ratio calculation:
10746.94 / 4330.595 = 2.48163
2.48163 * 27 = 67.00404
A ratio of 27S:67J is almost 100% accurate (99.994%) so we proceed with that. The number of J-S conjunctions in the period of those orbits will be 67-27 = 40.

(Incidentally, in earlier Talkshop posts e.g. here we’ve defined the Jupiter tropical orbit as 83/7 tropical years = 4330.728 days, almost the same as the NASA figure.)

Degrees of orbital motion in the period:
Saturn = 27*360 = 9720 = 243° (9720/40) per J-S conjunction.
Jupiter = 67*360 = 24120 = 603° (24120/40) per J-S conjunction.

Each conjunction occurring when Saturn has moved 243° and Jupiter 603° (243° + 360°) means an ‘extra’ 3° each per conjunction compared to a 2:5 (= 600:240) theoretical orbit ratio model. The absence of such an exact orbit ratio is sometimes described as ‘The Great Inequality’ of Jupiter and Saturn. It leaves both planets 117° short of a whole number of orbits (1 for Saturn, 2 for Jupiter).

The difference of 40(67-27) * 360° = 40 J-S conjunctions, and also 13 precessions of their conjunction axis since:
40*117° = 13*360°.

This can be seen in the graphics here…

To confirm the consistency of these motions, here are the planet positions at 40 Jupiter-Saturn conjunctions earlier (left), and later (right) than the dates in the graphic above…

We can see the Sun-planets(J,S) line orientation is the same for all four dates, or almost so. In the second graphic the time interval of 2383.29~ years is equivalent to the well-known Hallstatt cycle, or 120 (40*3) J-S conjunctions. We’ll explore this further in another post.

[NB there’s nothing special about the dates we’ve used in those graphics, other than being intervals of 40 J-S conjunctions. Any initial J-S conjunction date with the same intervals should give the same outcome, although the orientation will depend on that date. On the solar simulator the last J-S conjunction date allowing a full Hallstatt cycle to be shown is in July 610, ending in December 2993.]
Credit: Sky & Telescope

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These closely aligned J-S conjunctions occur every 20 J-S or ~397y, as described in this article from Sky & Telescope: The 400-Year Rhythm of Great Conjunctions (see chart, right). Reason: 20*117° = 13*180° (i.e. halves of the conjunction) as the chart in effect shows, with the highlighted ‘great conjunction’ years alternating between rising and falling parts of the waves (1563-2020 = 397~ years). Our earlier graphics hint at the reason for the three overlapping waves, to be explained in a follow-up post.

The caption says: ‘In this chart, each small square represents a Great Conjunction.’

See also: 2020, November 2: Jupiter – Saturn Heliocentric Conjunction at the site ‘When the Curves Line Up – Watching the Sun, Moon and Planets’.

The graphic in that article has the caption:
‘2020, November 2: Jupiter passes Saturn in a heliocentric conjunction, as viewed from outside the solar system.’
Arnholm’s solar simulator also shows the conjunction on the same date (right), confirming the heliocentric view.

Note that NASA’s article: The ‘Great’ Conjunction of Jupiter and Saturn says that viewed from Earth the same conjunction peaked on December 21, 2020. This date is an outcome of Earth’s offset orbital position relative to a line between the Sun and the two big planets at the time (as ‘When The Curves…’ shows).

In a future post we’ll expand on some of the points raised here.
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Note on tropical orbit periods –
In a recent Talkshop post: Tropical timings – the orbit of Neptune, we showed that Neptune’s orbit is 163.73~ TY (as in the NASA factsheet) in the reference frame of the solar simulator, just over a year less than the sidereal orbit period quoted by NASA. The solar simulator clearly uses the tropical year, otherwise the 18.25 orbits shown (2988 TY) wouldn’t fit into its 3000-year ‘window’ (18.25 * 164.79~ sidereal years = 3007.4~).

Source: https://tallbloke.wordpress.com/2025/05/30/tropical-timings-a-new-jupiter-saturn-model/