Tropical Timings: Precessions of the Earth and Moon

Precession of Earth’s axis [credit: NASA, Mysid @ Wikipedia]

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‘Small cyclical variations in the shape of Earth’s orbit, its wobble and the angle its axis is tilted play key roles in influencing Earth’s climate over timespans of tens of thousands to hundreds of thousands of years’ says NASA.
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In this post we analyse the periods of axial and perihelion (or apsidal) precessions, giving a perhaps surprising result.

Axial precession is described as ‘precession of the rotational axis’ and is often given the period of 25771.5 years. We take this as tropical years (TY) with an equivalent of 25770.5 sidereal years (SY), SY being one less than TY by definition of this precession cycle itself.

The three orbital precessions occur in periods when –
Axial: Tropical Years (TY) less Sidereal Years (SY) = 1
Perihelion: SY less Anomalistic Years (AY) = 1
Combined: TY less AY = 1

(Note: to skip the analysis, scroll down to Results.)

Earth analysis
Referencing our Jupiter-Earth-Mercury post, we showed there a repeating cycle of triple conjunctions, occurring 19 times every 1079 (83*13) tropical years, which we use here.

To get a whole number of years for axial precession, multiply by 2:
25771.5*2 = 51543 = 83*621.
To extend that to multiples of 1079 TY, multiply by 13:
13*83*621 = 670059 TY

Having multiplied by 2*13 = 26, it follows that the number of sidereal years = 670059 – 26 = 670033 (= 26 axial precession cycles).

To find the equivalent in anomalistic years:
670059 * (TY/AY) = 670027 AY
Calculation check:
(670059/670027 * TY(365.24219 days) = 365.2596337 days.
The link gives 365.25964 days for one AY. Check passed.

Results
These long periods may seem hard to relate to, but the interest for now is in the differences between the numbers. Given that a difference of 1 between two types of year is going to mean one orbital precession cycle we get:
670059 – 670033 = 26 axial precessions
670033 – 670027 = 6 perihelion precessions
670059 – 670027 = 32 combined precessions (26+6)
The period of each in tropical years is:
670059/26 = 25771.5 TY
670059/6 = 111676.5 TY
670059/32 = 20939.34375 TY

Confirming 6 perihelion precessions:
670033 / 6 = 111672.1667 SY
670027 / 6 = 111671.1667 AY
Difference = 1 between sidereal and anomalistic years.

Comparing the number of perihelion and axial precessions, the ratio in the full period is exactly 6:26 (32 combined) which reduces to 3:13 (16 combined). That’s the key finding in this post.

This is all based on accepted data for the year periods, plus the ephemeris used in Arnholm’s solar simulator for the 1079 TY cycle. We could call the full period the Great Precession Cycle (GPC), which also applies to the Moon judging by the data.
GPC lunar

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Lunar analysis:
The graphic on the right contains the full descriptions of the lunar periods shown below (click on image to enlarge).

670059 TY – the Great Precession Cycle (GPC – see above)
75734 LAC (GPC/LAC = 8.847532 TY)
35999 LNC (GPC/LNC = 18.613267 TY)
594325 FMC (GPC-LAC) = 1.1274286 TY)
706058 DY (GPC+LNC) = 0.9490141 TY)
111733 de Rop cycles (670059/dRC = 5.996966 TY)

More about what we mean by the de Rop cycle can be found in this Talkshop post, which has a link to astronomer Willy de Rop’s own short paper (2 pages including 3 diagrams).

Note – these results are as expected:
FMC/LAC is 1 less than TY/LAC (anomalistic).
DY/LNC is 1 more than TY/LNC (nodal, aka draconic).
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Based on these results we’ll extend the analysis to other aspect of Earth’s orbital parameters using ‘tropical timings’, and try to put forward something new in the next post.
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Image: Precession of Earth’s axis [credit: NASA, Mysid @ Wikipedia]
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Footnotes
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Some typical definitions of the three types of year:
TROPICAL YEAR: The time it takes for the Sun to return to the same position along the ecliptic, as viewed from the Earth.

SIDEREAL YEAR: The time required for one complete revolution of the earth about the sun, relative to the fixed stars.

ANOMALISTIC YEAR: The time of the earth’s revolution from perihelion to perihelion again.

(There are other wordings to define these periods, but no need to study them all as they amount to the same thing.)

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Source: https://tallbloke.wordpress.com/2025/03/18/tropical-timings-precessions-of-the-earth-and-moon/