Something I don't understand about Moon phases

[BrendanC]

Hi all,

I'm building a spreadsheet to help me with planning sessions, and I'm incorporating moon phases as part of this.

I reasoned that, to calculate the phase, it basically follows a sine wave, the period of which is the lunar month ie 29.53059 days.

After a bit of jiggery-pokery involving PI, sine functions and offsets, it worked. Mostly.

All my new moons and full moons correspond with what I can see from sites online such as https://www.timeanddate.com/moon/uk/aylesbury

However, I just noticed something: the phases in between the maxima and minima don't quite match up.

This is what it looks like for December 2020:

As you can see, the actual phases in orange, aren't actually constant increments or decrements, because they don't quite match the calculated, constant phases in blue. They're not quite an exact sine wave.

They're a bit slower at the extreme end of each turning point and accelerate a little midway. There's something else going on here.

I'm kind of ok with what I have, as it's usually within 5% of actuality, but I'm intrigued as to why this should be.

Any takers? I'm just curious!

Thanks, Brendan

[Waddensky]

I guess it's mostly because the orbit of the Moon is not a circle, but an ellipse.

[BrendanC]

Ah, nice one! Very good. That's probably it. Thanks! Very good insight there.

So, I need to include the eccentricity of the lunar orbit to calculate this more accurately. Hmmmm.... strokes chin...

Edited November 16, 2020 by BrendanC

[wulfrun]

The moon also doesn't orbit directly above the equator, in addition to being in elliptical orbit. The motion is complex and not a sinewave, even though the deviation isn't huge. It's enough to throw a "simple" analysis off though.

[Waddensky]

26 minutes ago, BrendanC said:

So, I need to include the eccentricity of the lunar orbit to calculate this more accurately. Hmmmm.... strokes chin...

Yes, but there's a lot more to it, like there always is in astronomy 😉. The Moon's orbital speed is perturbed by (mainly) the Sun and Jupiter, and there's the orbital inclination, as wulfrun says, and the precession of both the nodes and the line of apsides. It all depends on the amount of accuracy you wish to achieve and the date range of the graphic.

Chapters 47, 48 and 49 of Astronomical Algorithms (2nd edition) by Jean Meeus have some in-depth information and formulae to calculate the position and illuminated fraction of the Moon accurately. Be careful - it's addictive.

[Peter Drew]

The above is why the Moon is the hardest object for a goto to find.         🙂

[BrendanC]

All very interesting stuff! This is one of the reasons I'm doing what I'm doing: because it's helping me learn more about sunrise, set, moonrise, set, moon phase and so on. 

It seems that, taking into account all the above variations, I have a choice: I can either copy/paste a set of phases (like I've done with moonrise and set after looking into how to calculate that), or use my calculation and accept that it's slightly out. I think I'll go for the former - only needs compiling once for the upcoming year and takes a few mins. I think it's worth it to get it right.

Thanks again. I've learned something new - and I quite like that I noticed something odddddd, and the answer made so much sense. It's almost like rediscovering the basics of the solar system from the data!

Edited November 16, 2020 by BrendanC