By a "march-equinox year" I mean the time between successive march/vernal equinoxes. I understand that this is different from the mean tropical year, and I also understand why this would be different from (say) a "june-solstice year".

This discusses long term variations in the march equinox year but I am looking at (much to my own plight) the short-term variations (year by year)

It seems that the mean tropical year is, over the short term of say 200 years, roughly constant (variation of the order of 1 second).

However, the march equinox year can vary sporadically by upto 15 minutes from the previous year as evident from this time-and-date article (note that even though they title the table as 'tropical' year, each row is unambiguously the march-equinox year and not the mean tropical year). I tried to plot these values:

enter image description here

First of all, why does it look a little different between ~1955 and ~1985? Does it have something to do with difference between observed values and predicted values or is it something simple and unrelated like the higher frequency terms form some kind of 'beat pattern' that vanish near ~1970.

Second of all, what causes this variation? For instance I understand that the earth's nutation (which has a period of 18.6 years) has a component in the same, erm, direction (?) as axial precession so that would be one part of this variation but that part has a period too large to explain a year by year variation of 10-15 minutes

I guessed that somehow it must be the combined effect of all the other planets' gravity on earth but if I try to get a sense of the dominant frequencis of this variation via a discrete fourier transform I see the following:

enter image description here

Where the leftmost peak does indeed happen at (or, well, near) the familiar nutation period of 18.6 years. But from the 2 large peaks on the right, it seems the year by year variation is largely caused by 'something' of period ~4 years and ~2.7 years. None of the planets have an orbital period close to that so I don't have an intuition for this.

I am not particularly curious about every single peak in the above graph but for the sake of completeness the other three major peaks in between correspond to time periods of ~11.76 years (Jupiter!), ~8 years and ~5.9 years.

Can anyone help?

Edit: To summarise some relevant discussions in the comments, @PM2Ring pointed out that since the earth orbits the EMB in a very dynamic orbit it has atleast some effect on, for example, when exactly equinox is achieved. This would be similar to how the "perihelion year" (time between successive perihelions) can vary by upto a day from the previous year.

But I had always assumed that since the orbit of the earth around EMB has periods much lesser than 1 year, its effects observed on a yearly 'sampling rate' (i.e. its influence on time of perihelion) should be somewhat pseudo-random. And by extension I assumed that the observed variation of the order of 1 day in a perihelion-year would be pseudo-random.

But it's not! (I think, not completely atleast. Maybe I've been abusing terminology by calling it pseudo-random to begin with. Anyway:)

From here and here I gather the perihelion-year durations from 1900-2100 and plot them as:

enter image description here

Whose discrete fourier transform is:

enter image description here

Where the rightmost peak corresponds to a period of ~2.7 years same as before! From @PM2Ring's suggestion it could have something to do with other small lunar cycles (which is something I'll try and look into when I next get free time), but now I'm not even completely convinced that it's not somehow an artefact of performing DFTs that I might be overlooking.

Either way it's not yet clear why there is a peak for 2.7 years in both cases.

  • $\begingroup$ Here's a plot I did recently using Horizons data. I used TT time, and the geocenter. i.sstatic.net/4CHtg.png $\endgroup$
    – PM 2Ring
    Commented Apr 15 at 9:54
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    $\begingroup$ I expect that a lot of the variation is just because the Earth & Moon orbit their barycentre. And that orbit is fairly dynamic because of the lunar precessions, even discounting the perturbations due to Jupiter & Venus, etc. astronomy.stackexchange.com/a/55112/16685 $\endgroup$
    – PM 2Ring
    Commented Apr 15 at 10:16
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    $\begingroup$ The mean tropical year (taking the mean of the equinox & solstice years) has a bit less variation. i.sstatic.net/65YQb3CB.png The mean year mentioned on Wikipedia is averaged over a span of many years. $\endgroup$
    – PM 2Ring
    Commented Apr 15 at 11:28
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    $\begingroup$ Yeah, I have no idea where that 2.7 y peak is coming from. But there are lots of small-ish lunar cycles, as mentioned in en.wikipedia.org/wiki/Eclipse_cycle Maybe try some of the lunar months (or small multiples) as your sampling rate, to see what patterns they bring up. Especially the synodic, anomalistic, and draconic months. en.wikipedia.org/wiki/Lunar_month $\endgroup$
    – PM 2Ring
    Commented Apr 15 at 12:53
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    $\begingroup$ Time And Date is a great site. But I can't find what exact definition they're using for equinox / solstice. Are they using the geocenter, or a surface site (eg, Greenwich)? Are they using UTC / GMT in their year length calculations, or an ephemeris time (preferably TT)? BTW, there were subtle changes to timekeeping from the mid-1950s to 1972, with the intoduction of atomic time, and UTC with leap seconds (and a few even more subtle tweaks to atomic time after that), but that doesn't explain the "different" section in your graph over that period. $\endgroup$
    – PM 2Ring
    Commented Apr 15 at 13:29

1 Answer 1


Maybe this is only a partial answer, but the post was getting too long as it anyway.

I’ve since realised that there are major pitfalls to my method of trying to interpret peaking frequencies in the discrete Fourier transform. The closest analogy I can think of is aliasing/folding due to the discrete nature of the Fourier transform.

In short, if I see a peak at frequency $0.37 y^{-1}$ (period of 2.7 years) that could have been from an underlying frequency of $(n+0.37) y^{-1}$ or $(n+0.63) y^{-1}$ for any integer $n$. As if on cue, the synodic and sidereal lunar month periods correspond to the frequencies $12.37 y^{-1}$ and $13.37 y^{-1}$ so it’s probably true that “a lot of the variation is just because the Earth & Moon orbit their barycentre” as pointed by PM2Ring.

I still don’t know why I had convinced myself that high frequencies when sampled at a low rate would be pseudo-random. Of course they would not be, it would just appear to be a lower, different frequency. This whole doubt could have been avoided if I did not have this erroneous mental model. I just wasted my own and other people’s time, sorry about that

As for the other peaks, even though I don’t know exactly what they are from, they’re less interesting in light of this. The peak at $0.25 y^{-1}$ could be due to a 4 year process or 4/3 years or 4/5 or 4/7 etc.

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    $\begingroup$ The cause of the peak at $0.25\,\text{y}^{-1}$ is obvious: Every fourth year between 1901 and 2099 is a leap year. $\endgroup$ Commented Apr 16 at 9:36
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    $\begingroup$ @DavidHammen The leap year cycle certainly affects the calendar date of the equinox. But why should it affect the tropical year length (which anonymous is reading from a table on TimeAndDate)? $\endgroup$
    – PM 2Ring
    Commented Apr 16 at 10:06

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