The movements of the Moon

Initially I only focused on the different cycles of precession, obliquity, inclination, and eccentricity for Earth. The movements of our Moon and the planets are however also added to the model.

The moon is most probably the most studied celestial body in our solar system. There are a lot of great sources  that describe the movements of the Moon.

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 18.5999625725 years against ICRF and 18.6150580597 years experienced on Earth.
• The Moon’s apsidal precession duration is 8.8469024448 years experienced on Earth and 8.8503161082 against ICRF.

Although studied intensively by astronomers I could not find one single source that clearly distinguish 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 split.

An informed observer might also notice the duration experienced on Earth is longer against ICRF for the nodal precession but for the 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 quite hidden in the current explanations for the movements of the Moon.

The Moon’s Nodal precession causes the so called Lunar standstill moments . The Lunar standstill dates can be calculated with Webgeocalc  data. The way to calculate it is described here . I ran these calculations myself, and the pattern that emerged is quite clear:

Additionally in order to get all Moon’s movements correctly in the Interactive 3D Solar System Simulation, there was a duration missing which I somehow found on this website . I call this duration the Moon’s Royer cycle and it has a duration of 16.8842582106 years. Without this figure the Moon’s orbit can’t be modelled.

All durations of the different kind of movements of the Moon are coming together in the Holistic-Year cycle of 298,176 years.

In the Interactive 3D Solar System Simulation you can find all details.

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

• Moon Apsidal Precession - 330
• Moon Nodal Precession – 64
• Moon – 126.19

These setting can be further refined. You can use this site  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 IF they are observed, in which location and at what UTC time. It’s hard to compare numbers this way.

The Moon’s movement is very complex and contains many other small motions according to Wikipedia  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.

I have aligned the movements to the eclipse cycles  of the moon for most parts as well. The most famous eclipse cycle being the Saros cycle . For instance you can have a look at Catalog of Lunar Eclipses 2001 to 2100  or Catalog of Lunar Eclipses 1201 to 1300 .

So far as I know, there are currently no tools available that could display all solar eclipses  and lunar eclipses . There are simulations of a single event but never in a live environment where you can go through just a random eclipse. So all eclipses are well documented, but they are never shown in a 3D space environment.

Although not 100% aligned yet, they are all made clearly visible in the Interactive 3D Solar System Simulation. This is just done with the lighting and shadow simulation function of Three js .

The fit varies between eclipses — some align remarkably well, others less so. To give you a sense of the current accuracy, I’ve documented three recent examples:

1. Example Lunar eclipse

   The 2025 September 7th (JD 2460926) lunar eclipse is documented here on wikipedia . The Wikipedia page unfortunately only mentions local time. If you search for UTC times the times mentioned are from 17:30 UTC till 22:00 UTC.

   

   Earth is in total darkness in the Interactive 3D Solar System Simulation somewhere between 15:00 UTC to 22:00 UTC.

   In the 3D model we can only show the Lunar Eclipse Penumbra  and not the umbra.

   In this animation  the actual duration from start till finish on 7th of September is from 15:30 UTC till 21:00 UTC.

2. Example Solar eclipse I

   The 2025 September 21st (JD 2460940) Solar eclipse is documented here on wikipedia . The Wikipedia page mentions the maximum eclipse occurred around 19:45 UTC.

   

   In the Interactive 3D Solar System Simulation the maximum eclipse occurred on 22nd of September around 01:00 UTC.

   In the 3D model we can only show the Solar Eclipse Penumbra  and not the Umbra.

   In this animation  the actual duration from start till finish on 21st of September is from 17:30 UTC till 22:00 UTC.

3. Example Solar eclipse II

   The 2025 March 29th (JD 2460764) Solar eclipse is documented here on wikipedia . The Wikipedia page mentions the maximum eclipse occurred around 11:00 UTC.

   

   In the Interactive 3D Solar System Simulation the maximum eclipse occurred on 29th of March around 10:00 UTC.

   In this animation  the actual duration from start till finish on 29th of March is from 09:00 UTC till 13:00 UTC.

As can be seen the eclipses are quite close but not a complete fit yet. Some eclipse dates match more than others. I just took three recent examples but check for yourself other dates as well.

The reason why they are not matching yet is because Earth’s movement around the Sun is added circular instead of elliptic and the smaller movements of the Moon are not added as well which might have an effect. I am sure that with enough effort of the community – for the first time in history of mankind - we could make it a 100% fit in the end FOR EVERY LUNAR & SOLAR ECLIPSE.

The Excel has more background information on the Moon’s movements around Earth. There are 2 TABs: a separate TAB “Chapter 8” that gives all above mentioned numbers and in the TAB “Input 3D model” starting from cell Q155 you can find more background.

Now that we’ve covered the Moon’s complex orbital dance, let’s turn our attention to the movements of the planets in the next chapter.