Tropical timings – the orbit of Saturn

Saturn [credit: NASA/JPL]

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The idea here is to demonstrate that the Saturn orbit period on the solar simulator is in tropical years, using the same process as in our Uranus orbit post (here).

The alternative would be a sidereal year period based on the so-called ‘fixed stars’ as a reference frame. As Wikipedia points out, ‘The term fixed stars is a misnomer because those celestial objects are not actually fixed with respect to one another or to Earth’, but their movement from an Earth perspective is extremely slow due to their vast distances away from us.

From the NASA planetary factsheet for Saturn we find:
Sidereal orbit period (days) — 10,759.22 (S) — 365.256 (E) — 29.457
Tropical orbit period (days) — 10,746.94 (S) — 365.242 (E) — 29.424

The last figure in each row is the time of one Saturn orbit in Earth years. The data can be used on Arnholm’s solar simulator to test planetary motions.

We use the tropical year of Earth as published – 365.24219 days, so the NASA orbit period is:
10746.94 / 365.24219 = 29.42415 tropical years (TY).

Our own ‘tropical timings’ calculation goes like this:
83 TY / 7 = 1 Jupiter (J) orbit = 11.857142 TY.
67 J = 27 Saturn (S) orbits. (See this post for more details).
67 J / 27 = 29.42328 TY = 10746.62 days (~0.3 days less than NASA tropical orbit data).

The period of a Saturn-Earth conjunction using this result is:
29.42328 TY * 1 / (29.42328 – 1) = 29.42328/28.42328 = 1.0351824 TY.

Since 29.424328 * 26 = almost exactly 765 years (765.00528), and 739 (765-26) Saturn-Earth conjunctions = 764.9998 TY, a simple formula to test on the solar simulator is: 26 S = 739 S-E = 765 TY.

On the solar simulator, the note at the top says: ‘Looking down on Sun’s north pole’. This defines its frame of reference. For a first check we compare two Saturn-Earth conjunctions 765 tropical years apart.

That shows 26 Saturn and 765 Earth orbits (= tropical years) is a period when their conjunctions occur in the same orientation to the Sun.

For confirmation we move back 765 TY*2 and repeat the check.

That’s the limit of checks due to the 3000-year window of the simulator. The screenshots show two comparisons of the orientation of Saturn and Earth, using the same calendar dates 765 tropical years apart.

The point is that using NASA’s sidereal year period the 765 years would become 29.457 * 26 = 765.88 years, which is not what the simulator sees. Obviously the tropical year period does give the match to 765 simulator years that we were looking for.
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Image: Saturn [credit: NASA/JPL]
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For other ‘tropical timings’ posts see here:
https://tallbloke.wordpress.com/?s=tropical+timings

More about reference frames: https://boffinsportal.com/non-inertial-frame-of-reference-examples/

Source: https://tallbloke.wordpress.com/2026/04/13/tropical-timings-the-orbit-of-saturn/