When is the Spring Equinox?

[John O’Neill]

Hi,

I noticed that the BAAH 2019 (p.27) gives the time of the Spring Equinox in 2019 as 22:00. I presume this is UT, per the note on p.112.

The USNO website (https://aa.usno.navy.mil/data/docs/EarthSeasons.php#formb) gives the time as 21:58 UT, as does the RASC Handbook 2019.

I am wondering why the difference?

John

[Dominic Ford]

I was about to say that I could think of few reasons why anybody would need to know the time of the equinox to the nearest minute, before realising a rather entertaining set of circumstances took place last night…

* Wed 20/03/2019, 21:58 UTC, March equinox.
* Thurs 21/03/2019, 01:44 UTC, Full Moon.

The date of the equinox is used in the calculation of the date of Easter. To quote Saint Bede (The Reckoning of Time, 725), “The Sunday following the full Moon which falls on or after the equinox will give the lawful Easter.”

As I understand it, the church mucks up the calculation by defining the equinox to occur at midnight on 21st, and further defining full moon to occur 14 days after new moon.

Perhaps the BAA should start a campaign to “get back to Bede” and celebrate the astronomically-correct date for Easter this weekend.

To answer your actual question…. my impression is that these times are calculated by the US Naval Observatory and printed in the Astronomical Almanac, and that basically any and every source that quotes times for the equinoxes and solstices get them from the AA. So, I think if 21:58 is what the USNO says, basically that’s the time that everyone will quote.

I’m not sure what algorithm the USNO uses. When I have tried to do the calculation myself — which I tried to do in order to put equinox times on my website, In-The-Sky.org, I struggled to get exactly the same tiime as the USNO. For last night’s equinox, I get 21:44 UT. A difference of 14 minutes is larger than I would expect, since I used the NASA DE405 ephemeris to get the position of the Earth and Sun to high accuracy. I suspect I screwed something up — quite possibly there was an inaccuracy in my correction for the precession of the equinoxes (which is necessary to get the Sun’s RA and Dec for the epoch of the equinox, not J2000 coordinates).

[David Basey]

Does anybody know the claimed accuracy of the USNO or Handbook values? I’ve had a quick look and could not see anything.

My point is this, is the two minute difference actually significant? If the USNO figure is accurate to 10 seconds then yes, if accurate to 10 minutes then no. Same with the Handbook value.

To assess the actual difference I have done a rough calculation which may well be wrong – I am not a mathematical astronomer by any means so feel free to fault my approach. What I did was as follows:

1. From the Handbook calculate the rate of change in declination by taking values either side of the equinox.
2. Pro-rata this to arrive a shift in the two minute difference of roughly 0.2 arcsec.
3. Using the polar radius of the Earth, 0.2 arcsec translates into 61 metres.
4. So in the two minute difference the position on the Earth’s surface where the Sun is directly overhead moves northward by just 61 metres.

Are the Earth’s orbit, the planet’s shape and axial tilt sufficiently well defined to give this level of accuracy?

David.

[Dominic Ford]

David,

I have likewise not found any information about how the USNO calculate the values, or how accurate they are, though I have admittedly not looked very hard. I would expect they’re pretty good, though. I’m sure somebody like Jean Meeus would have noticed by now if they were publishing times that were wrong!

I think that if the times are computed using the most accurate data available, one-minute precision should be easily achievable. Both the Earth’s orbit and its rotation are very well characterised. Its rotation is measured by monitoring distant quasars with radio interferometers, which can achieve micro-arcsecond precision. That precision is required by Gaia, for example, which is doing astrometry at micro-arcsecond precision in a coordinate system defined by the Earth’s rotation axis.

The Earth’s orbit is very well characterised from spacecraft tracking work (Nick James’ day job). The idea is to track the position of spacecraft by measuring the time taken for telemetry to reach them from ground stations. In extreme cases (e.g. Rosetta) this has been done to one-metre precision or better. That requires you to know the position of each ground antenna to one-metre precision, which is no mean feat as that’s below the scale of seismic oscillations in the Earth’s crust…

So my guess would be that the Earth’s orbit is known to about one-metre precision, and the position of the celestial poles is known to micro-arcsecond precision. Of course, that’s not to say the USNO used an ephemeris that was that good. I would think it’s very likely they used some publicly-available ephemeris of lower accuracy.

[David Basey]

Dominic,

Thanks for the prompt response. I had no idea that things were tied down that tightly nowadays. Truly remarkable.

[John O’Neill]

Hi,

Thank you for your responses.

Jean Meeus gives a time of the spring equinox in 2019 to be 21:59:34 TD in his Astronomical Tables of the Sun, Moon and Planets, 3rd Edition (p.151). Taking Delta T is be 69 s currently and subtracting this value gives 21:58:25 UT. Rounded to the nearest minute this is 21:58 UT.

John

[MikeRushton]

The explanatory supplement to the Astronomical Almanac (1992 edition page 477 para 9.211Equinoxes and solstices) defines the time of the equinox as that when the sun’s apparent ecliptic longitude is 0, 90, 180, 270 rather than in terms of declination. I suppose from a geocentric point of view these should be equal but I wonder if it may account for the difference.

Mike

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