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I'm trying to calculate the exact time closest to the march and september equinoxes that 12h RA and 0h RA lines up with my local meridian.

The march equinox this year was on March 20 ~03:07 UTC. My assumption then was that if I used something like this tool https://stellarium-web.org/ and plugged in march 20 then at midnight for a given location, after you account for the locations distance from the timezone's meridian and any daylight savings issues, the 12h line on the equatorial grid should match up pretty closely to North/South. This was MOSTLY true, but the difference seemed to be off by more than 4 degrees, which is not what I would've expected. To try to validate my assumptions, I tried plugging march 20 2024 at 00:00 UTC at longitude 0 into a sidereal time calculator https://neoprogrammics.com/sidereal-time-calculator/index.phpexpecting with an expectation that it should show a Greenwich Mean Sidereal Time of ~12:00:00 plus or minus less than a minute since it should only be 3 hours before the equinox. The result I got instead was 11h 52m 04.505. I'm very confused by this because I thought sidereal time was essentially defined by the march equinox in that it should "reset" on that day. Since its off by 8 minutes I figured the day that GMST would actually match up with UTC + 12h would then be 2 days after, on march 22. Plugging that In I got 11h 59m 57.616s which is more what I expected.

So what am I missing here, shouldn't March 22 be the vernal equinox instead of March 20? Everything I can find online seems to corroborate my initial assumptions, and I cant find anything that would account for the 8 minute difference I'm seeing.

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    $\begingroup$ GMST isn't zero at the equinox, it will be offset from the longitude of where ever the Sun crosses the equator. $\endgroup$
    – Greg Miller
    Commented Sep 10 at 3:49
  • $\begingroup$ @GregMiller if I understand correctly, you're saying that GMST is not necessarily 00:00 at the exact time of the equinox. And yes, I understand that - my issue is that I thought that on the day of the equinox, the closest midnight to the actual equinox event will be approximately equal to midnight or noon in GMST. e.g for the equinox of 2024 march 20 03:07 UTC, I thought that on march 20 00:00 UTC, GMST would be somewhere in the range of march 20 11:59:00 < GMST < march 20 12:01:00. In reality that appears to be false and its actually march 20 11:52:00. $\endgroup$
    – kyle
    Commented Sep 10 at 5:17
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    $\begingroup$ @kyle Greg is saying that you need to look at the location on the equator where it was solar noon at the instant of equinox. Eg, this year the equinox occured at 2024-Mar-20 03:06:30 UTC, the Sun was directly overhead at longitude 135.229850°E, and the local apparent sidereal time there was very close to zero. $\endgroup$
    – PM 2Ring
    Commented Sep 10 at 5:50
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    $\begingroup$ @kyle Yes, that sounds about right, since the sidereal day is ~4 minutes shorter than the mean solar day. Take a look at the diagram on en.wikipedia.org/wiki/Hour_angle in the section Relation with right ascension. It's not perfect (I think the double-headed arrows are a bit confusing), but I found it helpful. $\endgroup$
    – PM 2Ring
    Commented Sep 10 at 7:08
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    $\begingroup$ At the March equinox, the sun is near RA 0/Dec 0. So, by definition, LST would be near 0h when the Sun is overhead. But the Sun moves throughout the day, by about 1 degree (4 minutes), so it's not going to be exact. If you look up the actual RA of the Sun for the times in question, you might find it's offset accounts for the discrepancy. Otherwise, I'd just have to say there's an issue with how you calculated the local Solar time. $\endgroup$
    – Greg Miller
    Commented Sep 10 at 12:53

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The issue was that I was using local time midnight as the time which I was trying to calculate sidereal time off of, which fails to account for the equation of time in terms of what the local time is when the sun is in complete opposition from the observation point. This website can be used to figure out solar noon which will align more directly with LST.

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