Milankovitch Cycles: Find the 53,300,000 Year Cycle

[g48dd]

TL;DR Summary

Determine the time period it takes for three different cycles to intersect at the same time.

I wanted to look at Milankovitch cycles and each cycle like a clock and that would mean we have 3 clocks each one moving at a different speed. We have a 100,000 year clock (Eccentricity), a 41,000 year clock (Obliquity), a 26,000 year clock (Procession). I want to start all the clocks at the same time. I am looking for a cycle of when all three clocks are once again at their starting point at the exact same time. I don’t know if there is a name for that cycle. I didn't think this would be that difficult to figure out; I’m not great with math but OK with a spreadsheet given some time. I thought that sense Eccentricity is the longest cycle why not just find where Obliquity and Procession divide into 100,000 years evenly at the same time. I am assuming this would mark the end of one full Milankovitch cycle and the beginning of the next. I used a spreadsheet for this because I have no idea how to write an equation for it. Excel will only work with so many digits, so I had to reduce 100,000 to 10, 41,000 to 4.1, and 26000 to 2.6 and then when I get my final number, I multiply by 10^4. That said the earliest occurrence of both Obliquity and Procession dividing in evenly at the same time was when Eccentricity was on its 5,330th completed cycle. So 5330 x 10^4 would be 53,300,000 years. I have uploaded a screen shot of my Excel spreadsheet and I have collapsed hundreds of rows. Column A 1-1,000,000, Column B 10*A1 carried down, Column C is the result in B1/4.1 and Column D is the result in B1/2.6 and I rounded to 4 decimals. At line 533 they all lined up. I then multiplied 5330 by 10^4 and got 53,300,000 years. So my questions are; would this represent a full Milankovitch cycle? Is there a name for that? Am I even thinking about this correctly and if not, could you suggest some reading or a video. Thank You

 

[jbriggs444]

You could Google "least common multiple".

But without a good reason to believe that the cycle times have rational ratios there is no good reason to expect a least common multiple to exist.

 

[mfb]

53,300,000 years is indeed the least common multiple, but this is a purely mathematical result without physical relevance. It corresponds to over 2000 precession cycles. If that cycle time is not 26,000 but 25,995 or 26,005 years then the pattern will be off by half a cycle in 53 million years. I'm sure these three cycles are not all nice multiples of 1000 years. Even worse, their period might change over such a long timescale.

You get pretty close to a repetition after just 207,000 years, with 2.1 periods of the eccentricity, 5.0 periods of the obliquity and 8.0 periods of the precession.

 

[g48dd]

Thank you, yes I get that actually Procession calculations say between 19,000 to 26,000 years. So obviously by only choosing 26,000 you that works out but Procession isn't always 26k. There are to many variables to actually say a complete cycle is 53,300,000. In truth I am thinking that there is never a time when all three cycles would be back to the same starting point. None of this takes into affect the Sun and how that influences things nor, magnetic fields? I don't know how things happening far, far away affect indirectly... that's why I am here to try and understand what we do know, and what we think might be possible. Thank you for your comment ... oh yes I did go look up Lcm and I worked that out on my own 2x2x5x5x41x13 and that is 53,300,000. so I learned something and that's cool.

 

[mfb]

If you look closely enough then you'll never get an exact repetition of orbital parameters of Earth. You'll get many cases where the parameters are very similar, however.

Precession, by the way. Procession is a bunch of people walking around.

 

[g48dd]

lol glad you pointed that not paying attention, thank you. I became fixed on this three clock thing. I do realize that there are so many things that influence these three paths that I felt there would be no exact return to the same path. That was cool though because it got me starting to think about what else could have an affect on these cycles, can gravitational waves, movement of the Milky Way Galaxy. It just makes want to understand more about how the universe works. Thank you for your comment.

 

[mfb]

Gravitational waves and everything outside the Solar System don't matter, but the Solar System has enough objects to create interesting dynamics.

 

[g48dd]

Thank you tells me where to look.