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The obliquity cycle refers to the oscillation of the Earth's axial tilt, which has a period of about $41,000$ years.

When the Moon is the main cause of the tilt, and it is receding linearly, how can there be a tilt cycle? The accepted professional opinions lack detail and clarity because they have never given the cause of the 41k obliquity cycle. Evidently, this failure results from the assumption that the cause of the lunar recession is a linear mechanism. Currently, the Moon is receding from the Earth while the obliquity is decreasing. How can the obliquity increase again in the other half of the 41k cycle if the Moon does not approach closer to Earth again? Obliquity varies randomly at various time scales. This fluctuation is cyclical and not random. It has not been explained.

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    $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Gabriel Ybarra Marcaida
    Commented Jun 29 at 22:39
  • $\begingroup$ This might be a better question for Astronomy. $\endgroup$
    – Michael Seifert
    Commented Jun 30 at 23:49

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Milankovitch cycles cannot be calculated just from Sun-Earth-Moon interactions, but must include the effects of the other planets, especially Venus, Jupiter, and Saturn. These are messy multibody interactions, but they are not mysterious and were originally calculated by perturbation methods and now by direct computational integration.

If you want simpler (but not so simple as to be easily summarized here) approximate calculations, look at R. C. T. Rainey's

According to Rainey, the 41k obliquity cycle is primarily due to the first orbital precession mode of the Venus-Earth system.

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  • $\begingroup$ Earth's obliquity is presently decreasing because the Moon is receding. Venus may contribute to the periodicity but cannot change a lessening of the obliquity to an increase. The Moon's pull is the main cause, the Sun is half, and the planets are tiny fractions of that. Then, it is impossible for the planets to tilt the Earth back down. Then, the accepted view fails to explain the cause of the obliquity cycle. Rainey says, "the influence of the other planets being negligible." Then the Moon would have to start approaching the Earth for the obliquity to begin increasing again. $\endgroup$
    – user20333
    Commented Jul 5 at 20:33

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