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AFAIK the summer and and winter solstices are based on longest day and longest night doesn't fall on 1st of Jan and July 1st because we consider the day to begin and end when the middle of the sun is over the horizon but when it stars to rise and after if has completely set.

But the spring equinox is, "defined as the time when the plane of Earth's equator passes through the geometric center of the Sun's disk.". (from wikipedia).

So how come it doesn't fall middle of the year, 365/4 = 91 days into the year. 1st April?

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    $\begingroup$ The events in late June and late December are called solstices rather than equinoxes. $\endgroup$ Mar 26, 2022 at 19:43
  • $\begingroup$ @PM2Ring I edited the question to reflect the correct nomenclature. $\endgroup$ Mar 26, 2022 at 19:44
  • $\begingroup$ The seasons are actually based on the Sun's "declination". At its highest declination is the instant of summer in the Northern hemisphere, and the instant of the lowest declination is winter. At zero declination are the spring and fall equinoxes. The idea that these are the longest, shortest, or equal day/night doesn't always hold true. This is due to time zones, leap years, the Earth's motion around the sun throughout the day, and probably other factors. $\endgroup$ Mar 27, 2022 at 1:10
  • $\begingroup$ The solstices are also on the 21st of the respective months $\endgroup$
    – mcalex
    Mar 27, 2022 at 15:57
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    $\begingroup$ Can you explain how the details in that exposition support the Question? "… it doesn't fall in the middle of the year…" most obviously because 1 April, being 365/4 days is far from the middle of the year. Quite separately, it doesn't fall in the middle of the year because neither the Sun nor the Earth has a circular orbit. The equinox is determined by the intersection of ellipses. $\endgroup$ Mar 27, 2022 at 19:05

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The calendar is designed so the 21st of March is set to the spring Equinox, and everything else is calculated from there.

So the reason that the equinox doesn't occur on the first of April is boring. The first of April isn't the 21st of March.

The calendar isn't designed so that the first day of any month is on any solstice, longest day, equinox etc. This has nothing to do with "the sun being fully over the horizon". That is a misconception.

You might ask "Why 21st" And the reason is complex and historical, with various Roman Calendars being used, adapted changed, fixed. It is a historical accident that this day isn't set to the start of the year, nor even the start of a month but on some random day in March. However the day March 21 is important because it is the starting point for calculating Easter. The Calendar is designed to fix "march 21 = equinox" so that Easter can be calculated.

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    $\begingroup$ In worth also to mention that the method of counting 365/4 days from the solstice, is not going to work either, since Earth speed in his path is not uniform. (though at Earth is pretty close to being so) $\endgroup$
    – d_e
    Mar 26, 2022 at 16:02
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    $\begingroup$ The actual date of the spring equinox is March 20, plus or minus a day in the Gregorian calendar rather than March 21. The Roman Catholic church and most Protestant churches use March 21 (Gregorian calendar) as the ecclesiastic equinox. The Eastern Orthodox churches also use March 21 but in the Julian calendar as the ecclesiastic equinox, even though that is now weeks away from the actual equinox. $\endgroup$ Mar 26, 2022 at 16:06
  • $\begingroup$ "However the day March 21 is important because it is the starting point for calculating Easter." that's only important is you care when Easter is, though. Why the calendar has changed since (some) nations stopped caring is just habits and inertia $\endgroup$
    – njzk2
    Mar 27, 2022 at 21:32
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In slight contradiction to the accepted answer, the Gregorian calendar is designed to have the March equinox occur on March 20, plus or minus a day, not March 21. Christian churches use March 21 as the ecclesiastic equinox. The reason for using March 21 simplifies the calculation of the date of Easter. The March equinox advances by about 5 hours from the previous year's March equinox in non leap year years but retreats by about 19 hours from the previous year's March equinox in the case of a leap year.

Regarding the question itself,

AFAIK the summer and and winter solstices are based on longest day and longest night doesn't fall on 1st of Jan and July 1st because we consider the day to begin and end when the middle of the sun is over the horizon but when it stars to rise and after if has completely set.

The solstices occur a bit over a week before the first of January and the first of July. The calendar used by many nations are based on the calendar reformations mandated by Julius Caesar. Like many things political, shifting the start of the year to the first of January was a bit arbitrary.

So how come it doesn't fall middle of the year, 365/4 = 91 days into the year.

The astronomical seasons are not equal in length. The time span between the December solstice and the March equinox (northern hemisphere astronomical winter / southern hemisphere astronomical summer) currently is about 88.99 days and is getting shorter as perihelion advances by about a day every 70 years. The time span between the June solstice and the September equinox (northern hemisphere astronomical summer / southern hemisphere astronomical winter) currently is about 93.66 days and is getting longer as aphelion likewise advances by about a day every 70 years.

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