The movements of the Moon

The moon is most probably the most studied celestial body in our solar system. There are a lot of great sources (opens in a new tab) that describe the movements of the Moon. These movements are however described, as if Earth is orbiting the Sun and the Moon is orbiting the Earth. In the dummy universe model the Sun is orbiting (a point close to) Earth but still the Moon is orbiting Earth (off course). The movements of the Moon can therefore be seen as something like this:

Besides the feature of the Moon always orbiting Earth with the same side facing Earth, there are basically two fluctuations in Moon’s orbit that are most important:

• The Moon’s nodal precession duration is 18.59967151 years against ICRF and 18.61439182 years experienced on Earth.
• The Moon’s apsidal precession duration is 8.846966234 years experienced on Earth and 8.850295241 against ICRF.

Although studied intensively by astronomers I could not find one single source that clearly describes these orbits both against ICRF and as experienced on Earth. All sources are just repeating the rough estimates (e.g. ~18.6 years) without making this clear distinction.

An informed observer might also notice the duration experienced on Earth is longer against ICRF for the nodal precession but for apsidal precession it is exactly the other way around. The reason for this behaviour is the nodal precession runs in the direction opposite to Sun’s orbit around Earth, but the apsidal precession runs in the same direction to the Sun's orbit (and Moon’s orbit) around Earth.

These kind of basic facts are missing in the current explanations for the movements of the Moon.

The Moon’s Nodal precession causes the so called Lunar standstill moments (opens in a new tab). The Lunar standstill dates can be calculated with Webgeocalc (opens in a new tab) data. The way to calculate it is described here (opens in a new tab). I made the calculations for you and the graph looks like this:

Additionally in order to get all Moon’s movements correctly in the 3D dummy universe model, there was a duration missing which I somehow found on this website (opens in a new tab). I call this duration the Moon’s Royer cycle and it has a duration of 16.88535454 years. Without this figure the Moon’s orbit can’t be explained/ modelled.

Perhaps it is best to just open the 3D dummy universe model so you know what I am talking about by observing CENTER and run the motion with “1 second equals” “1 year” and just see for yourself.

All durations of the different kind of movements of the Moon are coming together in the Great-Great-Year cycle of 305,760 years. Below you can find all Moon movements:

• Mean Sidereal month : 27.3216596085109 days (305,760 / 4,087,470)
• Mean Rotational period (around its axis) : 27.3216596085109 days (same as sidereal period due to tidal lock)
• Mean Synodic month : 29.5305774642934 days (305,760 / 3,781,723)
• Mean Anomalistic month : 27.554555454065 days (305,760 / 4,052,922)
• Mean Draconic month or nodal period : 27.212217424899 days (305,760 / 4,103,909)
• Mean Tropical month : 27.3215727135746 days (305,760 / 4,087,483)
• Mean Full Moon cycle (ICRF) : 411.7681519 days (305,760 / 271,212)
• Mean Full Moon cycle (Ecliptic): 411.7878901 days (305,760 / 271,199)
• Mean Draconic year (ICRF): 346.6071093 (305,760 / 322,199)
• Mean Draconic year (Ecliptic): 346.6210946 days (305,760 / 321,186)
• Mean Apsidal precession (Ecliptic) : 3231.285669 days = 8.846966234 years (305,760 / 34,561)
• Mean Apsidal precession (ICRF) : 3232.501563 days = 8.850295241 years (305,760 / 34,548)
• Mean Nodal precession (ICRF) : 6793.385486 days = 18.59967151 years (305,760 / 16,439)
• Mean Nodal precession (Ecliptic) : 6798.761963 days = 18.61439182 years (305,760 / 16,426)
• Mean Nodal meets Apsidal precession every : 2190.292898 days = 5.99682272 years (305,760 / 50,987)
• Mean Royer Cycle : 6166.90397 days = 16.88442211 years (305,760 / 18,109)

I have set the initial startpos figures in the 3D model as followed:

• Moon Apsidal Precession - 340
• Moon Apsidal meet Nodal Precession - 90 (also the negative, so effectively this setting is not needed)
• Moon Royer Cycle - -44.1
• Moon Nodal Precession – 64.1
• Moon – 126.22

These setting can be further refined. You can use this site (opens in a new tab) as reference but I do not know if these are official observations or – just like most of the planet figures – are calculated in some model. And additionally, IF they are observed, in which location and at what UTC time. It’s hard to compare numbers this way.

Additionally the Moon’s movement is very complex and contains many small motions according to Wikipedia (opens in a new tab) like Equation of the center, Evection, Variation, Annual equation, Parallactic inequality, Reduction to the ecliptic, etc. See also here. These motions are not added to the model (yet).

It might also be these smaller movements are just imaginary. I have aligned most movements to the solar eclipse Saros cycles (opens in a new tab).

NOTE: These saros cycles startdates are calculated with yearlengths of 365.2425 years instead of the real yearlength ~365.2422 and therefore might differ a bit especially on the longer term. Also have a look at Catalog of Lunar Eclipses 2001 to 2100 (opens in a new tab) or Catalog of Lunar Eclipses 1201 to 1300 (opens in a new tab).

The Excel has more background information on the Moon’s movements around Earth. There are 2 TAB’s: There is a separate TAB “Chapter 8” in the Excel that gives all above mentioned numbers and in the TAB “Chapter 3-4-5-6-7-8-9” starting from cell P153 you can find more background.

I might elaborate on the Moon cycles a bit more in the future but for now let’s move to the planets orbits.