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To my understanding, the Earth's precession causes an approximately 20-minute difference between the sidereal year and the tropical year. Also to my understanding we use the tropical year for our calendar which means we ignore those 20-minutes. These 20-minutes will cause the calendar to "shift" one day every 72 years so if we don't do anything about it in a few centuries winter and summer will switch places. So every century they add an extra day to the calendar to counter this.

This I understand. What I don't understand is that this 20-minute difference means that the Sun's position in the sky will vary by 20 minutes every year. Meaning if the Sun rises at the right ascension of 0 this year, next year it should rise at the right ascension of 20 minutes, and so on. But each year the Sun will actually rise at the same spot in a particular day.

How is this possible? Where do these 20 minutes go?

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    $\begingroup$ You have a fundamental misunderstanding of the tropical year vs sidereal year, and that misunderstanding is driving many of your subquestions. $\endgroup$
    – David Hammen
    Feb 12, 2021 at 16:42

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Yes, the Gregorian calendar is based on a good approximation of the mean tropical year, so the dates of the equinoxes are stabilised.

Geometrically, the equinoxes occur when the Sun's apparent path on the ecliptic crosses the celestial equator. The March equinox point (aka the First Point of Aries) is the 0° point for ecliptic longitude and also the 0 hour point for Right Ascension.

Due to the precession of the equinoxes, the First Point of Aries moves relative to the stars by about 50 arc-seconds per year, which gives rise to the 72 year value you mentioned.

The upshot of this is that a table of RA and declinations of stars must specify the epoch that it uses, so that the given positions can be adjusted to give the actual RA on a given date. A very popular epoch for the last few decades is J2000 which is 12:00:00 noon (Terrestrial Time) on the 1st of January, 2000, which is Julian date 2451545.0 TT. In UTC, that's 11:58:55.816.

There's a brief explanation on Wikipedia of the effects of precession on Right Ascension.

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  • $\begingroup$ I've already read all of those and it hasn't helped. But this part pretty much sums up what I fail to understand. The second paragraph says that the sidereal year is 20 minutes shorter, which means every three years the sidereal year is 1 hour behind. Which as I understand should mean the sun should be 1 hour behind after 3 years and 24 hours behind after 72 years. But in the third paragraph it says after 72 years the sun is only 1 degree behind. $\endgroup$
    – Pouria P
    Feb 12, 2021 at 17:44
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    $\begingroup$ @PouriaP You appear to be confusing 24 hours (time) with 24 hours (angle). Hour angle is simply 1/24 of a revolution. Time (in hours) works nicely as a stand-in for hour angle when it comes to looking at the stars from the surface of the Earth. 24 hours is a small fraction of a year. $\endgroup$
    – David Hammen
    Feb 12, 2021 at 21:50
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    $\begingroup$ (...continued) But I think what he actually meant is that by using the tropical year for our calendar, which is 20 minutes shorter than the sidereal year, we are EFFECTIVELY adding one day to our calendars every 72 years. We do not actually have 366-day-long years every 72 years. Right? So when we use the tropical year we actually don't have to do anything else. The only side effect this has is that every 6000 years "The First Point Of Aries" will point 90 degrees off in the celestial sphere, or ~1 degree every 100 years. Which is corrected by using epochs. So all is good. $\endgroup$
    – Pouria P
    Feb 13, 2021 at 10:19
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    $\begingroup$ @PouriaP That was a painful video to watch. It has a number of things wrong. The sidereal year has absolutely nothing to do with variations in the timing of the equinoxes and solstices. Over the short term, it's where the Moon is in its orbit about the Earth that cause these variations. Over longer terms, it's the relationship between the Earth's axial tilt and the location of perihelion / aphelion. This final concept leads to a third concept of an astronomical year, the anomalistic year. (Continued) $\endgroup$
    – David Hammen
    Feb 13, 2021 at 16:10
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    $\begingroup$ One anomalistic year is the time it takes for the Earth to go from one perihelion passage to the next. The anomalistic year is currently about 25 minutes longer than the tropical year. In 13000 years or so, perihelion passage will occur in July. (It currently occurs in early January.) This change will make Northern Hemisphere summers be shorter but hotter, winters longer and colder. $\endgroup$
    – David Hammen
    Feb 13, 2021 at 16:15
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These 20-minutes will cause the calendar to "shift" one day every 72 years so if we don't do anything about it in a few centuries winter and summer will switch places.

We don't care as much about the Earth's orbit with respect to the stars as we do about keeping the calendar in sync with the seasons. If we did use the sidereal year as the basis for our calendar the seasons would shift. We instead use the tropical year precisely so that 13000 years from now, January will be wintery and July will be summery in the Northern Hemisphere. (The relationship is the reverse for the Southern Hemisphere.)

So every century they add an extra day to the calendar to counter this.

I suspect you are addressing the change from the Julian calendar to the Gregorian calendar. The Julian calendar had a leap year every four years. This would work fine if the tropical year was 365.25 days long. The tropical year is only 365.242 days long. What this means is that a leap year once every four years is a bit too much. The Gregorian correction is to make every year that is divisible by 100 but not by 400 be a non-leap year. This removes a day every rather than adds a day every century. This makes the Gregorian calendar do a better job of staying in sync with the tropical year than the Julian calendar.

What I don't understand is that this 20-minute difference means that the Sun's position in the sky will vary by 20 minutes every year.

I suspect this is a consequence of your initial misunderstanding. However, the stars do change. In 13000 years, Orion will switch from being a wintertime constellation in the Northern Hemisphere to being a summertime constellation in the Northern Hemisphere.

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  • $\begingroup$ I realize now that all we have to do is just use the tropical year. And yes since the sidereal year is actually a bit shorter we're gonna have to actually remove a day once in a century or so not add one. The misunderstanding's root was that I thought every 72 years a day was added to the calendar to account for the difference between the sidereal and tropical year. Which is of course not the case. Thank you your answer helped a lot. $\endgroup$
    – Pouria P
    Feb 13, 2021 at 11:26
  • $\begingroup$ @PouriaP The sidereal year is a bit longer than rather than a bit shorter than the tropical year. $\endgroup$
    – David Hammen
    Feb 13, 2021 at 13:17
  • $\begingroup$ Ah yes I mistyped. $\endgroup$
    – Pouria P
    Feb 13, 2021 at 15:09

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