Cycles of the Moon.

[Gerard Seacloud]

Dear readers and members: I am trying to find the cycles of the moon, because I am trying to calculate these cycles
to construct a design of a clockwork (standing clock, timepiece etc.) with a moon dial. Thousands heve been made in the run of the centuries, but all of them must be adjusted every so many months. Because our old moon runs her cycles in an irregular way, varying from
29 days, 8 hours to 29 days and 19 hours, and everything between. Now the big question is: Does the moom run it`s irregular cycles in a regular way? I mean, those irregular cycles do they return every so many years or months? For an imaginary
example: Today it runs every 29 days, 12 hours, and 40 minutes, and after -for just example- 9 years the whole cyclus repeats it self. DOES it repeat every so many months or years? I know, it is a long term calculation, but if these ,,mooncycles" repeat themselves every time then I have found a system to design a moon dial which runs on the minute excacly for at least 40-50 years. So: Please will you drop a technical eye on my problem and I`ll be very gratefull ! Greetings, Gerard Seacloud.

[Shabadoo]

I think that information was in the monthly summary page of the "Farmers Almanac",
A U.S publication.
Anyone got one?

[Lady Fraktor]

Is this what you are looking for?
http://astropixels.com/ephemeris/moon/s ... h2001.html

[mikemarotta]

You need the Metonic Cycle:
https://en.wikipedia.org/wiki/Metonic_cycle

As you seem to know, the problem of gearing to bring the lunar and solar cycles into conformance in a device has been solved many time since the complex medieval clock towers. You might want to explore the Antikythera Device which was constructed about 100 BC - 100 AD and also was geared to work with the lunar cycles.

I find the thought of such a task daunting to say the least. I admire your tenacity.

[Gerard Seacloud]

Thanks Lady Fractor and Mike Marotta for the links. Tomorrow i will look it up an ,,study" it.
Greetings, Gerard.

[Gerard Seacloud]

Thanks for the links Lady Fractor and Mike Marotta, tomorrow I will ,,study" them for more info.
Greetings, Gerard.

[Gerard Seacloud]

Dear members: back in town again. It is said that after retirement you have a lot of time. I don`t agree. The week should have 8 days. Well, about the gears: I made a very interesting ,,discovery" so to say: (And do not laugh..... ) Elliptical gearwheels, excentric gearwheels, etc. They have a huge advantage over the normal gearwheels: You can make them running in irregular periods. Periods resembling the periods of a planet or sun or moon. For example: If the moon runs between 380,000
and 420,000 kilometers from the earth, then these gearwheels must have an ,,ovality" between 38 and 42 milimeters, thus running excact the period of the moon. (just an example here) I think that on this beautiful forum are mecanics, who know to construct such gears, provided you have the tools and a good lathe. If there is any interest I will post some simple drawings here. Greetings, Gerard.

[Gerard Seacloud]

good morning and evening dear Stargazers.
Thanks to the hints of Lady Fractor, and Mike Marotta I found some repeating cycles of our moon. The first is indeed the metonic cycle, and the second is half that periode. So the mooncycles are indeed repeating themselves. At first I thought it was about 3 years, then 9.5, and at last 19 years now. The mountain is somewhat higher than I thought.....
The Metonic cycle is very helpfull, and precise on one whole day. But: Long live the internet. I got some lists of mooncycles of over 30 years, so it`s now easy to calculate these cycles on the minute excactly. It will take time of course, and the gears of the moondial are more intricate, but it can be done. I hope to meet one day an other mechanic with the right tools, since I sold everything included my lathe because going to Asia and working and living there for a while. By the way Mike Marotta: The (very simplified) scheme of that Metonic Cycle looks like this:

I do not know how to paste a photo or image from my PC to this message, any help? Because the tools above do not work.

Greets, Gerard.











Greets to all, Gerard.

[OzEclipse]

One of the books in the MATHEMATICAL MORSELS Parts i-V series by Belgian mathematician Jean Meeus will almost certainly deal with this. I don't have the series so I can't tell you which one. I won't post his email address here without permission. Though quite elderly, Jean is still very active on the Solar Eclipse Mailing List.

You first have to open an account with groups.io then subscribe -

https://groups.io/g/SEML

Joe

[Pikaia]

I have all five MATHEMATICAL MORSELS, and #2 deals with the Metonic cycles. What exactly is the question?

[OzEclipse]

I have all five MATHEMATICAL MORSELS, and #2 deals with the Metonic cycles. What exactly is the question?

It's a range of questions in post #1. Basically he wants to know about any lunar orbital cycles and periodicities.

Joe

[Pikaia]

Wiki has articles about the Metonic, Saros, Octaeteris, Callippic and Hipparchic cycles.

https://en.wikipedia.org/wiki/Metonic_cycle

[Gerard Seacloud]

Metonic simplified.jpg (5.91 KiB) Viewed 2650 times

Dear Joe OzEclips and Pikaia : Thanks for the tips. And that Belgian Forum Joe mentioned is close to my town, so I will
contact them, good idea ! . That Metonic cycle is on the day precise, and with help of the mooncycles of the last 30 years I will try
to refine it on the hour, maybe even on the minute. I hope the image of the simplified Metonic cycle appears here now, it was a small battle to get it. From 1 to 5 is a periode of about 9.5 years, and from 5 to 1 again a periode of 9.5 years, etc. etc. thus making 19 years of repeating cycles. And the Antikitheria Divice is proof of a very high civilizisation in old times, these people were scientific giants. We are just standing on their shoulders, as Sir Newton said. The reason I am searching these forums is: There is none example of mechanical clocks, pendules, and timepieces with a correct running moon disk. They must be adjusted every so many months or years by hand. And here is why: To construct a precise running moondisk for at least , let`s
say, 30 years or more we need a big bunch of gear wheels spanning a 19 year periode of time. And I can imagine it gives the
nerves to clock makers. My first calculation came on about 25-30 extra gears. Much work, but patience does the job. Well, so far on this saturday evening (here) and again many thanks for the tips and ideas ! Greetings and all the best, Gerard.

[OzEclipse]

Hi Gerard

Metonic simplified.jpgDear Joe OzEclips and Pikaia : Thanks for the tips. And that Belgian Forum Joe mentioned is close to my town, so I will
contact them, good idea ! . That Metonic cycle is on the day precise, and with help of the mooncycles of the last 30 years I will try
to refine it on the hour, maybe even on the minute. I hope the image of the simplified Metonic cycle appears here now, it was a small battle to get it. From 1 to 5 is a periode of about 9.5 years, and from 5 to 1 again a periode of 9.5 years, etc. etc. thus making 19 years of repeating cycles. And the Antikitheria Divice is proof of a very high civilizisation in old times, these people were scientific giants. We are just standing on their shoulders, as Sir Newton said. The reason I am searching these forums is: There is none example of mechanical clocks, pendules, and timepieces with a correct running moon disk. They must be adjusted every so many months or years by hand. And here is why: To construct a precise running moondisk for at least , let`s
say, 30 years or more we need a big bunch of gear wheels spanning a 19 year periode of time. And I can imagine it gives the
nerves to clock makers. My first calculation came on about 25-30 extra gears. Much work, but patience does the job. Well, so far on this saturday evening (here) and again many thanks for the tips and ideas ! Greetings and all the best, Gerard.

I vaguely recall back in the 1970's or 1980's a moon phase watch being advertised in astronomy magazines. I can't recall details. I did a search and found this link to high end watches but no link to the watches I recall-

https://iknowwatches.com/best-moon-phase-watches/

Good luck with your project.

Joe

[Gerard Seacloud]

Hallo Joe, thanks for the link ! the Casio is electronic (quartz) the Peugeot, Megalith, Maurice Lacroix too. But: There was a very expensive mechanical watch, the ,,H. Moser & Cie Endeavour Moon'', ,, at a very stout accuracy of 1,027 years of service before needing to be adjusted by one day'' (!!!) . (the moon cycle) with a stunning price of $ 45,000 . So: I stand corrected and give honour to whom it deserves. The makers made a ,,moon gear '' constellation on the minute precise. we cannot compare ourselves with those engineers of course, but, one day if I am in a daring mood I will contact them and ask what they tink of the idea of elliptical and excentric gear wheels, because I think these will save a lot of extra gears because they have repeating cycles of themselves.
Well: Thanks againg and all the best! Greets: Gerard.

[OzEclipse]

Hallo Joe, thanks for the link ! the Casio is electronic (quartz) the Peugeot, Megalith, Maurice Lacroix too. But: There was a very expensive mechanical watch, the ,,H. Moser & Cie Endeavour Moon'', ,, at a very stout accuracy of 1,027 years of service before needing to be adjusted by one day'' (!!!) . (the moon cycle) with a stunning price of $ 45,000 . So: I stand corrected and give honour to whom it deserves. The makers made a ,,moon gear '' constellation on the minute precise. we cannot compare ourselves with those engineers of course, but, one day if I am in a daring mood I will contact them and ask what they tink of the idea of elliptical and excentric gear wheels, because I think these will save a lot of extra gears because they have repeating cycles of themselves.
Well: Thanks againg and all the best! Greets: Gerard.

Hi Gerard,
There are vintage watches on this site that date back as far as the 1930's, some from the 70's ...and not super expensive either.

https://www.etsy.com/au/market/moonphase_watch

and this calculator

http://www.1728.org/synodic.htm

Unfortunately, the gear ratio required doesn't divide down to a nice easy ratio. If you use gears, you will need to make regular corrections. elliptical gears are probably not going to solve the issue. Maybe a pair of precisely ground friction disks to take care of the odd 708.72 reduction ratio between the hour hand and the lunar synodic month? A 500:1 gearbox off the hour hand and a pair of friction discs with a 1.41744 diametric ratio?

On average, it will indicate the lunar phase. Due to the inclination of the ecliptic, rotation of the earth, any clock needs to be able to be geographically set- that is the lunar phase on a certain date and local time in the Netherlands, is different to the lunar phase at the same local time in Australia.

cheers

Joe

[Gerard Seacloud]

Hallo Joe. The beauty of these forums and discussions is that in the run every now and than new ideas and tips are popping up.
So are your friction wheels. I appreciate that. The advantage is they can be adjusted steplessly, but: A clock runs on the smoothnes of it`s gears and bearings, and these friction wheels must be cross-axial under pressure to avoid them slipping. But again: Every idea is welcome.
And now something else:

https://www.forbes.com/sites/elizabethd ... a3192716f5

And that is a MECHANICAL timepiece with gear wheels. As small as a wrist watch. Unbelieveble. Makes someone feeling humled......

He must have found infinitly (steplessly) adjustable gears in some way.
Joe, thanks again for thinking and the tips, I am going to ,,study" the links you gave me, and take my drawing materials out of the drawer. Greets and have a nice day: Gerard.

[OzEclipse]

Hallo Joe. The beauty of these forums and discussions is that in the run every now and than new ideas and tips are popping up.
So are your friction wheels. I appreciate that. The advantage is they can be adjusted steplessly, but: A clock runs on the smoothnes of it`s gears and bearings, and these friction wheels must be cross-axial under pressure to avoid them slipping. But again: Every idea is welcome.

HI Gerard,

That watch is certainly a beautifully crafted timepiece. HAAAYY...SAANNTTAA!!!

You initially posted that you are building a standing clock not a watch. Consequently, your spring drive mechanism if it is a spring driven clock can be stronger to provide more torque than a watch. A mechanical clock can also be run by an electric motor - eg a stepper motor driven by a quartz oscillator governed drive. Then the rest of the clock can be mechanical. The 1.417 ratio Moon phase friction wheel is at the end of a more than 2.5M:1 mechanical gear reduction from the second hand. These wheels only need to drive themselves and so don't need to be under a lot of axial radial load to do this without slipping.

Good luck with your project.

I hit the road tomorrow so won't be reading TSS for some days.

Please keep us posted.

Joe

[Gerard Seacloud]

Hallo Joe. Have a safe drive out there.
I am not designing a watch (impossible for a mechanic who worked with 500 ton ships diesels) but just designing in a drawing of gears for the right moon cycles for a standing clock or pendulum. So, much bigger than a wristwatch
By the way, when you are back, please give me the link to that 1.417 ratio Moon phase friction wheel . Very interesting.
Okay, we stay in touch, greets, Gerard.

[OzEclipse]

Hallo Joe. Have a safe drive out there.
I am not designing a watch (impossible for a mechanic who worked with 500 ton ships diesels) but just designing in a drawing of gears for the right moon cycles for a standing clock or pendulum. So, much bigger than a wristwatch
By the way, when you are back, please give me the link to that 1.417 ratio Moon phase friction wheel . Very interesting.
Okay, we stay in touch, greets, Gerard.

Hi Gerard,

Still here after two 44 degree celsius days on the road.

I am the link. I calculated it.
29.53 days per lunar synodic month
708.72 hours per lunar synodic month
÷500 = 1.41744

I chose 500 because it is a common easy gearbox ratio to buy and resulted in 1.41744, a diametric ratio easy to machine to high precision. I suggest you research the synodic month length to the highest precision and recalculate the ratio required.

Cheers

Joe