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I'm trying to teach my sons the difference between using azimuth-altitude coordinates and ecliptic coordinates. In the course of setting up some demonstrations, using Stellarium, I set my location to N 0° 0' 0.00" E 0° 0' 0.00", the time to GMT, and the date/time to noon on March 20, 2021 (March equinox). I expected that the sun would be directly overhead at this time (altitude 90°), but it's not: the altitude is about 88° 08'. I examined several days before and after, and the altitude never reaches 90°. The highest altitude I could find on March 20, 2021 was at 12:07:25, 89° 57' 31.2".

What's the gap in my thinking here? Why isn't the sun at the zenith at that time?

I'm using Stellarium, but my question is conceptual, not about the software (which I assume to be working correctly).

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    $\begingroup$ Related: en.wikipedia.org/wiki/Subsolar_point $\endgroup$
    – PM 2Ring
    Sep 1 at 14:34
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    $\begingroup$ While N 0° 0' 0.00", the equator, is "natural", the so-called main meridian E 0° 0' 0.00" is an entirely arbitrary human convention, originally based on the location of a particular observatory in England. While the equinox is by definition the instant when the Sun crosse the equator (so zero degrees north), it is extremely unlikely that this should occur at the Greenwich meridian. Instead, it will occur at different longitudes each year (because the length of the day is "incommensurable" with the length of the year). So there exists no "naturally" preferred meridian/line of longitude. $\endgroup$ Sep 3 at 17:19
  • $\begingroup$ If Stellarium uses WGS84, that geoid is derived from a US datum. So it is super accurate in the US, very accurate elsewhere but it is a little off at 0N 0E. If you look at your GPS at Greenwich observatory it is slightly off 0E, Switching to a more localised datum, such as ODN for Greenwich, would reduce the inaccuracy in that locality $\endgroup$
    – teambob
    Sep 4 at 13:04
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It never is exactly, directly overhead on the vernal equinox at the Greenwich meridian. You know that it happens on different days in different years so it must be happening at different times on those days. March 20 in 2021 was the day the Sun's declination changed from south to north. It happened at about 0937 UTC and its greenwich hour angle was about 322 degrees. The Sun was directly over a spot in Kenya.

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    $\begingroup$ In other words: The equinox is not a day. It is an instant. "Noon on the equinox" is (in most time zones) a completely different instant. $\endgroup$
    – Kevin
    Sep 2 at 21:02
  • $\begingroup$ stretch. Great answer, but can you include the coordinates of the "spot in Kenya"? Thanks! $\endgroup$
    – Jim
    Sep 4 at 15:37
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    $\begingroup$ @Jim 37 degrees 36.9 minutes E longitude $\endgroup$
    – stretch
    Sep 6 at 22:40
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In addition to the March 2021 equinox occurring 2.4 hours before 12:00 UTC as stretch explains, you found a maximum altitude at 12:07:25 UTC because apparent solar time was 7.4 minutes behind mean solar time on that date. The equation of time combines the effects of the Earth's obliquity and orbital eccentricity.

If you set the time in Stellarium to 2021-03-20 09:37:09 UTC, the Sun's declination of date is 0.00°. If you then set the location to N 0°, E 37°34'05", the Sun's altitude is 90.00°.

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The time of the equinox, and the Sun being over the 0° meridian are determined by different motions:

  • The Earth spins around its axis. The Sun crosses over the 0° meridian once every solar day, when the earth completes a little bit over one rotation.
  • The Earth orbits around the Sun. The vernal equinox is the specific point in this orbit when Sun crosses the celestial equator into the northern hemisphere.

There is nothing synchronizing these two motions. So at the equinox the Sun is exactly at the zenith at some point on the equator, but it won’t be at 0°E.

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