Earth's precession and the position of the Sun in the sky 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 &quot;shift&quot; 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?
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.