The movements of the Moon

Initially I only focused on the different cycles of precession/ obliquity/ inclination/ 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 made the calculations for you and the graph looks like this:

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 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  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.

It might also be these smaller movements are just imaginary. I have aligned most movements to the solar eclipse Saros cycles .

The solar eclipses are clearly visible in the Interactive 3D Solar System Simulation as well and more or less match all known ones.

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” that gives all above mentioned numbers and in the TAB “Input 3D model” starting from cell Q155 you can find more background.