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From timezone.com's On the Units of Time Part III: The Year February 19, 2001, by Edward Hahn:

Uh, Oh…He’s Going to Ask That Question Again…

So, what, exactly, is a year?


@PM2Ring's comment

FWIW, that's a mean tropical year, which is slightly different to a Vernal Equinox year (~365.242374 days). See https://www.timezone.com/2002/09/25/on-the-units-of-time-part-iii-the-year/

and that includes the following:

(A side note: Some people out there might be wondering why I didn’t use the Tropical Year of 365.24219 days length? In Duncan Steel’s book Marking Time, he points out that both the US Naval Observatory and the Royal Greenwich Observatory make a mistake when saying that, “the tropical year is defined as the mean interval between vernal equinoxes.” This is not astronomically correct – the tropical year is the average time between consecutive occurrences of any date on the calendar. Since the earth on average orbits the sun in the same amount of time regardless of when you start your measurement, shouldn’t they be the same? Well…they aren’t – the vernal equinox year is an average over some number of orbits measured on a single calendar day, while the tropical year averages once more across all the days of the year. The difference is about 16 seconds a year – not much, but even so the people who designed the Gregorian calendar knew enough to aim for the vernal equinox year since they were trying to stabilize the date of Easter, and not the entire year.)

Wikipedia's Tropical year does indeed refer to the Astronomical Almanac Online Glossary (2015) and while the link does not work for me sitting on a bus where I am Wikipedia quotes it:

the period of time for the ecliptic longitude of the Sun to increase 360 degrees. Since the Sun's ecliptic longitude is measured with respect to the equinox, the tropical year comprises a complete cycle of seasons, and its length is approximated in the long term by the civil (Gregorian) calendar. The mean tropical year is approximately 365 days, 5 hours, 48 minutes, 45 seconds.

Question(s):

  1. Is the US Naval Observatory wrong somehow here? Have mistakes been made? Or are there misquotes?
  2. Is it possible to explain in everyday English the geometrical difference between a "Vernal Equinox year" and a tropical year or a mean tropical year?

The basis of an answer may be within the links I've included or it may not be; while "both the US Naval Observatory and the Royal Greenwich Observatory make a mistake" could be true, it's also possible that the blogpost may not have it right, and I can't access the Astronomical Almanac Online Glossary (2015) to resolve the difference.

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  • $\begingroup$ As a courtesy to readers and to head off the "What have you tried?" comments I've tried to quote several sources on the topic. It is possible that the answers are to be found within them, but I have a hunch there is additional background necessary to address the whole 'USNO is wrong' issue. $\endgroup$ – uhoh Mar 21 at 8:07
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    $\begingroup$ I'm sure I'm missing something but "the tropical year is the average time between consecutive occurrences of any date on the calendar" seems incorrect. That would be the calendar year, not the tropical year. $\endgroup$ – user21 Mar 21 at 16:53
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    $\begingroup$ The length of time it takes to get bored at the beach ? :-) Sorry, had to say it. $\endgroup$ – StephenG Mar 21 at 21:12
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    $\begingroup$ FWIW, here's an article by Meuss & Savoie: The history of the tropical year. Sorry, its format is not very friendly for mobile devices. $\endgroup$ – PM 2Ring Mar 22 at 12:48
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    $\begingroup$ Yes, it's that Jean Meeus. :) $\endgroup$ – PM 2Ring Mar 22 at 16:40
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Is the US Naval Observatory wrong somehow here? Have mistakes been made? Or are there misquotes?

That's a matter of opinion. In Duncan Steel’s opinion, yes, they made a mistake. In the US Naval Observatory's opinion (and also that of Her Majesty's Nautical Almanac Office), there is no mistake. The Nautical Almanac defines a tropical year as the time from one mean vernal equinox to the next. Steel is using a more pedantic definition. Increased pedantry does not always equate with increased correctness.

Is it possible to explain in everyday English the geometrical difference between a "Vernal Equinox year" and a tropical year or a mean tropical year?

Right now, Northern Hemisphere spring and summer (Southern Hemisphere autumn and winter) last longer than do Northern Hemisphere autumn and winter (Southern Hemisphere spring and summer). This situation will be reversed in about 13000 years. These changes are due to the Earth's axial precession. That the Earth undergoes axial precession has multiple ramifications, three of which are that:

  1. The length of a tropical year (no matter how one measures it) is less than is the length of a sidereal year.
  2. The times from one March equinox to the next, one June solstice to the next, one September equinox to the next, and one December solstice to the next are not constant.
  3. The times from one March equinox to the next, one June solstice to the next, one September equinox to the next, and one December solstice to the next are not equal to one another.

Elaborating on the third point, the calculated length of one mean December solstice to the next was 365.242740 days (ephemeris days) on 1 Jan 2000 while one mean June solstice to the next was 365.241626 days, or about 1.6 minutes shorter than the duration from one mean December solstice to the next.

So what is a "tropical year"? The US Naval Observatory, which has a much longer history than does Duncan Steel, defines the tropical year as the passage from one March equinox to the next. The US Naval Observatory inherited this definition from Her Majesty's Nautical Almanac Office, which in turn inherited it from the Church of England, which in turn inherited it from the Catholic Church. One of the key drivers of the Gregorian Calendar was getting the date of Easter correct. (Getting the date of Easter correct was very important to many Renaissance minds.)

Duncan Steel defines the tropical year otherwise, as an average value of the times it takes for the Sun's longitude as perceived from the Earth to advance by 360°. That's fine, but to argue that people who use a different definition is not just wrong. It's "wronger than wrong". The fact is that there are multiple definitions of what constitutes a "tropical year", all of which are valid.

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    $\begingroup$ "situation will be reversed in about 13000 years" - I still think apsidal precession makes it more like 10500 years. $\endgroup$ – Mike G Mar 21 at 23:33
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    $\begingroup$ @MikeG - University of Michigan website: "Earth’s rotational axis gyrates, with a period of 26,000 years." Encyclopedia Brittanica: "cyclic wobbling in the orientation of Earth’s axis of rotation with a period of 25,772 years." IAU Resolutions on Astronomical Reference Systems, ...: "... taking about 26,000 years to complete one circuit." $\endgroup$ – David Hammen Mar 22 at 0:02
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    $\begingroup$ ...relative to the sidereal frame. Meanwhile perihelion precesses the other way with a period of ~110k years. $\endgroup$ – Mike G Mar 22 at 0:23

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