Popular media are discussing the “super blue moon” this week. I read their facts and figures, but I’m curious what the Tychos take would be. For one, what is the cycle of moon’s perigee/apogee to earth? I read the portion in the book on the shift of moon’s perigee/apogee, but as I understand it, that is a very slow shift of each respective cycle over 5,000 years. The articles seem to suggest the moon is fluctuating on a 14 year cycle. The media again say the next super blue moon (in which a full occurs twice in one month) will be in 2037, or, in 14 years. I would like to understand moon’s ‘apsidal precession’ and the significance of 8.85 years.

NASA say the “blue supermoon” occurred in 2009, this week in 2023, and will occur in 2037. This is an interval of 14 years. Any idea what they’re getting at here, in Tychos terms? I’ve seen bigger moons than this one, so I’m wondering what’s going on.

/Meant to add that I’d also like an explanation as to the trochoids in the image; how many trochoids are occurring in one revolution of moon around earth? if this is how moon rotates, then is this an explanation for the relative closeness or distance of the moon on a given month?
Thanks Simon and Patrick.

That’s quite a bunch of questions in one single post!

Firstly, let me just direct you to this Wiki page which goes to show that the “blue moon” phenomenon doesn’t actually seem to be fully understood: Blue moon - Wikipedia

As for this query of yours…

“I would like to understand moon’s ‘apsidal precession’ and the significance of 8.85 years.”

… let me just copy/paste here the following section from Chapter 13 of my book:

“TESTING THE MOON’S PERIGEE PRECESSION - IN THE TYCHOS”

The above graphic depicts the current astronomical understanding of the Moon’s perigee precession (a.k.a. the Moon’s “apsidal precession”). It is observed that our Moon’s perigee precesses by 0.1114° per day:

“The lunar perigee precesses in the direction of the moon’s orbital motion at the rate of n−n˜ = 0.1114 ◦ per day, or 360◦ in 8.85 years.”

Since our Moon’s perigee precesses by 0.1114° daily, it will complete one full 360° revolution in 8.8476327 years - or 3231.5978 days.

In fact: 0.1114° X 3231.5978 days ≈ 360°

The Moon’s perigee thus precesses annually by

0.1114° X 365.25 = 40.68885° (or ≈ 146480" arcseconds)

As we compare this empirically-observed annual precession of Moon’s perigee with our ACP (Annual Constant of Precession) of 51.136”, we see that the Moon’s perigee precesses 2864.5 X faster than the stars (i.e. our entire firmament).

146480" / 51.136" ≈ 2864.5

(Remember that our ACP of 51.136" x 25344 y adds up to a full 360° precession of our firmament - i.e. our “Great Year”).

3231.5978 days / 29.22 days(the TMSP) ≈ 110.5954

There are 110.5954 TMSPs in 3231.5978 days (i.e. one full perigee precession of the Moon around Earth).

110.5954 X 2864.5 ≈ 316800 (i.e. the number of TMSP’s completed by our Moon in 25344 years)

In other words, the Moon’s empirically-observed perigeal precession is in agreement with the TYCHOS-computed duration of a “Great Year” (25344 solar years).

For now, this will be my best reply to (some of) your queries - as I’m not sure if I understand them all.

But I have more questions if you find time to consider!
Does the moon revolve on it’s axis as the sun and earth do?
I don’t think I found a mention of this when searching the book but it’s possible I overlooked it.

Do you have any good reference material on why the moon shows roughly the same face every 27 days? Do you mention this at all?

This is what I was wondering when seeing the trochoids in the simulator I posted above showing several years’ orbits with the trace feature - actually around 8 years to be completed. So I realized that the pattern of trochoids was created by the slight precession of the moon 8.85 years; the ‘orbit’ itself while precessing is creating the trochoidal patterns.

Yes, the Moon revolves around its axis in about 27.3 days - which is the same time it employs to revolve around the Earth. More remarkably still, 27.3 days is also the time that the Sun employs to revolve around its own axis (the so-called ‘Carrington’ number)!

“The Carrington rotation number identifies the solar rotation as a mean period of 27.28 days, each new rotation beginning when 0° of solar longitude crosses the central meridian of the Sun as seen from Earth.”

As for WHY this Sun-Moon resonance exists, no one really knows, but you may agree that the question becomes considerably less mysterious in the TYCHOS model - where the Moon is located in the ‘centre’ of the Sun’s orbit (rather than just being an appendage of the Earth, the two of them orbiting around the Sun)…

You may find more info about the Moon’s axial rotational speed (16.65 km/h) as compared with Venus & Mercury (i.e. the moons of the Sun) in this section of Chapter 3 of my book: Chapter 3: About our Sun-Mars binary system – Nextra

Thanks, I was having trouble finding those excerpts. But can you elaborate on the truth or falsity of the moon coming closer or farther to earth? I’m not a mathematician or astronomer - going back to precession of the moon, is the idea that in about 8.85 years the moon will return to a uniform distance from earth? If the moon precesses 146,480 arcseconds in one year, that is 2.32 ft/1 year or 20.6 ft/8.85 years which is not much. So surely this small amount of precession wouldn’t be visible to the naked eye?
Thanks again Simon.

Aha - looks like you’re quite confused there, my dear babayaga !

That value of 146480" arcseconds does not represent the actual / physical distance covered by the Moon’s perigee in one year: it is the annual ANGULAR displacement of the Moon’s perigee - as seen from Earth!

Now, if you multiply 146480" by 8.8476327y you obtain 1296000" arcseconds (which equals 360°).

So yes, the Moon does indeed return closest to Earth every 8.8476327 years, as its orbit oscillates back and forth over time. You may even see this oscillation with your own eyes in the Tychosium simulator:

Open the Tychosium and enlarge at maximum the view of the Earth & Moon (using the scroll wheel of your mouse). In the ‘Controls’ menu, set “1 second equals” to 1 YEAR. Then, click the “Run” box and watch the Moon’s orbit as it oscillates back and forth, the Moon returning closest to Earth (i.e. to its very closest perigee) every 8.85 years or so.

However, this doesn’t mean that the Moon only comes close to Earth only every 8.85 years: this is just the period separating two VERY CLOSEST lunar perigee passages (circa 356000km). As it is, the Moon only needs about 14 days to go from perigee to apogee. Example:

On January 21, 2023 the Moon was at a perigee of 356570 km
On February 4, 2023 the Moon was at an apogee of 406476 km
Source: Moon at Perigee and Apogee: 2001 to 2100

Simon,
I think this really elucidates the issue. Thanks. I’m finding that using an interval of 9 years shows the moon’s orbit relatively identical in relation to earth, skipping from 2023 to 2014 to 2005, 1996, 1987, 1978, etc., which also makes this easier to understand.

Now 146480" x 8.847 is the amount of displacement that occurs in a full revolution, correct? In other words the moon’s orbit will revolve fully in 8.85 years?

My next question has to do with your last point about the moon traveling from perigee to apogee in 14 days. Wouldn’t it be that we rely on calendar(s) to know when we see the moon at the perigee or apogee phase of its monthly orbit?
For example, when I checked in the simulator, it seems that we will be entering the apogee segment of the moon’s 27 day cycle. Forgive my sense of shock - this really elucidates why the moon would have a phase in the first place, no? So the “phase of the moon” is really a phase within the larger 8.85 year orbital phase.
Anyways
Thanks again - this is a bit of a revelation!
Appreciate your time.