Understanding the Moon's Changing Angular Momentum and Its Impact on Eclipses

[Universh13]

I know that the angular momentum of the moon with respect to the Earth can be calculated by L = Iw but if the L of the moon is k * Learth-sun the there will be way more eclipses, one of each every 28 days. So the momentum of the moon must change over time, how does it work?

 

[nasu]

Why does it have to change? And what is I and what is w in that formula?

 

[mfb]

How are eclipses related to the angular momentum of the moon?

So the momentum of the moon must change over time

No.
The orbital planes moon/earth and moon/sun are not aligned, only twice per year they cross at the right place to give eclipses.

 

[Universh13]

The orbital planes moon/earth and moon/sun are not aligned, only twice per year they cross at the right place to give eclipses.

Ok, now I get it, so there are two points every 28 days that are the same for both planes and 2 per year in which those points are aligned forming eclipses. Thank you

 

[nasu]

Well, the orbital planes cross all the time.
The moon will go through the intersection points of the two orbits twice per month but to have a total eclipse the moon has to be full too. So it happens not so often.
It happens twice a year for many years but not as a rule. There will be only one (total) in 2019 and none in 2020. There will be some sort of events, though. Like partial or penumbral eclipses.

 

[Janus]

Ok, now I get it, so there are two points every 28 days that are the same for both planes and 2 per year in which those points are aligned forming eclipses. Thank you

In any given calendar year there will be at least 2 eclipse events (including partial eclipses) and as many as 5.

Eclipses happen during full moons, which are 29.53 days apart, and when the Moon is within 18 degrees of a node( the point where the the orbital planes cross). Now if the planes of the two orbits kept the same orientation, then the Moon would cross a node every 13.66 days ( 1/2 of 27.32 days, which is the sidereal month or the time it takes the Moon to complete one orbit with respect to the stars). But they Don't. Due to the effect of the Sun's gravity on the Moon, the Moon's orbit precesses, and "wobbles" with respect to the Earth's orbital plane. As a result, the nodes slowly shift and the time it takes for the Moon to travel from one node and back to it again (the Draconic month) is 27.21 days.

The end result is that every 173.3 days we enter an eclipse season, where the we have a new moon and the Moon is within 18 degree of an node. What this means is if you have a partial eclipse at the start of an eclipse season, the next new moon can occur before the end of the eclipse season and you can have partial eclipses in consecutive months.
In addition, 173.3 days is ~9 days less than 1/2 a year. This means that it if a calendar year starts with an eclipse season, the next eclipse season will start ~9 days before the midpoint of the year, and you will start a third eclipse season ~18 days before the end of the year. So, it is possible to have two partial eclipses each in the first two eclipse seasons, and have a fifth eclipse occur during the first part of the third eclipse season resulting in 5 eclipses in one year.