Tropical Timings: Earth’s two eccentricity cycles

Here we’ll look at the relationship between the long and short eccentricity cycles of the Earth, and how it might be related to known orbital periods, with hopefully interesting results.

In Figure 1 of the paper: ‘Pacemaking the Ice Ages by Frequency Modulation of Earth’s Orbital Eccentricity’ by J.Rial (shown below with Talkshop highlighting in red), part (C) has a main peak of 95 kyr. The caption for (C) describes this as a ’95-ky eccentricity component’ and says it’s ‘frequency-modulated by a 413-ky modulating signal’.

Another paper – Rial et al (2013): Synchronization of the climate system to eccentricity forcing and the 100,000-year problem, also defines 413 kyr as the LEC period: ‘Here we show that climate oscillations over the past four million years can be explained by a single mechanism: the synchronization of nonlinear internal climate oscillations and the 413,000-year eccentricity cycle.’

In this post we’ll refer to long eccentricity (~413 kyr) as LEC and short eccentricity (~95 kyr) as SEC.

Since 413/95 = 4.4347 and the possible ratio we’re investigating with LEC:SEC is 13:3 = 4.333:1, we have a near-match already (~99.68%).

In the previous post on precessions (here) we found a Great Precession Cycle (GPC) of 621*1079 tropical years (670059 TY). For eccentricity we’ll refer to another Talkshop post which described the Jupiter-Earth-Venus (JEV) 996 tropical year (TY) cycle, confirmed using Arnholm’s solar simulator app.

The GPC is a period of 6 perihelion precessions. An equivalent period using the JEV cycle would be 621*996 TY. Dividing 996 by 6 gives 166 TY, then:
621*166 TY = 103086 TY (‘103 kyr’ for short).

This is 12/13ths of a perihelion precession because:
996 = 83*12 and 1079 = 83*13.
It’s also 4 axial precessions:
103 kyr/4 = 25771.5 TY

We can now propose that:
(1) the LEC = 4*4 axial precessions = 4*103 kyr = 412344 TY (414*996).
(2) the SEC is 12/13ths of 103 kyr = 95156.30769 TY
Result: 412344/95156.30769 = 4.33333 = 13/3.

Another outcome is that the 103 kyr period is the geometric mean (the ‘n’th root of the product of ‘n’ numbers; in this case n=2) of both:
1) axial precession (AP) and long eccentricity (LEC)
2) perihelion precession (PP) and short eccentricity (SEC).

Analysis
1) The LEC:SEC ratio is 3:13 = PP:AP ratio [link to post]
2) The SEC:PP ratio is 13²:12².
3) The LEC:AP ratio is 1:16 (= 1²:4² in this process).
4) The 103 kyr ratios are as follows:
– 4:1 with LEC
– 1:4 with AP
– 13:12 with SEC
– 12:13 with PP

The geometric mean of 1² and 4² is 1*4 = 4.
The geometric mean of 13² and 12² is 13*12 = 156.
[Note: (4/1)*(1/4) = 1 = (13/12)*(12/13)].

Therefore to make all the periods match (Fibonacci equivalents in brackets):
156/4 = 39 LEC (3*13)
156*4 = 624 AP (3*13*8*2)
13² = 169 SEC (13*13)
12² = 144 PP (144 or 8*3*3*2)
(See diagram).

Using those results, it then follows that LEC*AP = SEC*PP:
39*624 = 156² = 169*144 (= 24336)
The period of one of each can be substituted for the numbers of occurrences, and the equation still works:
412344(LEC) * 25771.5(AP) = 95156.30769(SEC) * 111676.5(PP)

The diagram covers over 16 million years: 39*412344 TY.
It’s also 24 Great Precession Cycles.
Ratio of 39:24 = 13:8 (Fibonacci numbers).

The same period is also a multiple of both Jupiter-Earth-Venus (996 TY) and Jupiter-Earth-Mercury (1079 TY) long-term cycles (as per the above-linked Talkshop posts):
24*621*1079 = 24 GPC = 26*621*996 = 39*412344 TY.

Next post: obliquity (tilt) and other orbital parameters, linking to the diagram above.
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Image credit: BBC

Source: https://tallbloke.wordpress.com/2025/03/23/tropical-timings-earths-two-eccentricity-cycles/