How do times of lunar standstills vary over time? If we folded them back into a lunar month plot, would they have "prograde and retrograde motion"?

Question

The recent question Are lunar phases and lunar standstills in sync with each other? brought me to a standstill because I don't fully know what a lunar standstill is. It's one of those words like "opposition surge" which sounds exciting but may not be.

@JohnHoltz's answer says:

A standstill occurs when the Moon reaches the northern most declination (or southern) in its orbit. That occurs approximately every 27.3 days.

so I guess the Moon only "stands still" if you project it on to a 1 dimensional declination axis which is definitely not what we see.

and a comment below it says:

...the northern standstill occurs every 27.3 days, and the southern standstill occurs every 27.3 days. They are offset by approximately two weeks. (I'm not sure if it is exactly half the sidereal period!)

Now the Moon's orbit is weird. It's substantially eccentric and inclined and the Earth's equator is bulged, and so the line of apses and the line of nodes both "do their own thing" over time. There's never a dull moment for the Moon's orbit.

So I'd like to ask:

Question: How do the times of lunar standstills vary over time? If we folded them back into a lunar month plot, would they have "prograde and retrograde motion"?

Yes I know there are different kinds of lunar months! I will not pre-specify this, it's completely up to the answer author who knows more about this than I do to decide which folding time is most suitable.

• Is there a timekeeping word for the orbit of a moon?
• How many Moon's Topocentric Conjunction occurs per lunar month?
• Should the synodic period or the orbital period be used to determine the diameter of the Moon?

Answer 1

The lunar standstill or lunistice occurs when the Moon reaches its maximum or minimum declination for the month. Wikipedia says that the term "lunar standstill" was apparently coined by engineer Alexander Thom in his 1971 book Megalithic Lunar Observatories.

As I've mentioned numerous times, the orbit of the Moon is rather complicated. The eccentricity of the orbit, combined with the short nodal and apsidal precession cycles, causes the time between lunistices to vary between ~27.2 to ~27.5 days. The declinations of the lunistices range over a cycle of approximately 18.613 years, or 249 sidereal (or tropical) months, which is approximately the length of the nodal precession cycle.

Here's a Horizons plot of the Moon's declination for 2020 & 2021, with 24 steps per tropical month.

The lunistices occur fairly regularly, with the time from a maximum to the next minimum being a couple of days less than half a month.

Here's a scatter plot showing the time between maxima lunistices for 249 tropical months, from 1900-Jan-12 19:02 to 1918-Aug-02 13:50. The mean is ~27.3217 days, slightly higher than the tropical and sidereal month lengths.

Here's a plot of the maxima lunistices for 750 tropical months from 1900-Jan-12 19:02 to 1956-Jan-24 08:52.

Here's the same data (using the same colour scheme), folded to the tropical month length (by taking the modulus of the Julian day).

Here are the corresponding minima lunistices plots, from 1900-Jan-27 10:09 to 1956-Feb-06 12:52.

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Here's the Sage / Python script that produces the lunistices plots. The start time must be given as a Julian Day number, and it should be close to the time of a lunistice. It finds maxima and minima using sequences of cubic spline interpolation.

Here's the basic Moon declination script, which accepts any of the usual Horizons date & time formats.