Wednesday, March 20, 2013

Equinox, astronomical spring: now

Now, at 12:02 PM (after the noon), Pilsner Winter Time, the astronomical spring is getting started. The axis of Earth's spin is orthogonal to the plane in which the Earth orbits the Sun i.e. both Southern and Northern Hemispheres are equally far from the Sun.

If you ignore the fact that the length of the day and the night may be "easily" measured just once a day, the day and the night are equally long right now.

What I find bizarre is that people keep on repeating wrong dates of the equinoxes and solstices.

If you check the table of the equinoxes, you will see that at least between 2010 and 2020, the Northward (spring) equinox always comes on March 20th. As kids, we would learn that the date was March 21st. Maybe the same is true for you, too.

These days, children – at least in Europe – should learn March 20th as the date when the spring begins. Is that the case?

Where does the discrepancy come from? Let's look at the times (in Greenwich mean [winter] time i.e. Universal Time which is delayed behind the Pilsner Winter Time by 1 hour) of the Spring equinoxes over a decade:
2010: 17:32
2011: 23:21
2012: 05:14
2013: 11:02 (TODAY)
2014: 16:57
2015: 22:45
2016: 04:30
2017: 10:28
2018: 16:15
2019: 21:58
2020: 03:50
The date is always March 20th. What is the rule? You may see that every non-leap year, the precise moment is about 5 hours and 50 minutes, plus minus 5 minutes or so (the Earth just isn't as regular as you may expect – the irregularities come from the disordered impact of the Moon, Jupiter, and others), after the moment we saw in the previous year.

On the leap years, the special moment takes place about 18 hours and 10 minutes, plus minus 5 minutes or so, before the moment we remember from the last year. Needless to say, the increments are roughly +6 hours and –18 hours i.e. +1/4 and –3/4 of the solar day. This agrees with the fact that the spacing between two spring equinoxes is about 365.25 solar days while the civic calendar records either 365 or 366 new dates during that interval. The difference between 365.25 on one side and 365 or 366 on the other side manifests itself as those +6 or –18 hours.

Note that 18 hours and 10 minutes above is exactly one day minus 5 hours and 50 minutes; these numbers aren't independent.

But you may see that even after 4 years, the timing isn't quite periodic. For example, in 2016, the equinox will arrive 44 minutes earlier than in 2012. In 2020, it will be 40 minutes earlier than in 2016. In average, you may see that every 4 years, the equinox comes about 42 minutes earlier than 4 years earlier. In average, this drift gives you 10.5 minutes per year i.e. 1,050 minutes per century. Because the equinox will be at 3:50 am in 2020 and every 4 years, we will remove 42 minutes or so, 24 more years – roughly in 2044 – the date will jump to March 19th instead of March 20th, Greenwich Mean Time.

On the contrary, in 2011, the time was 23:21. So 4 years earlier, in 2007, it was probably 42 minutes later or so, in the morning of March 21st. If you return deeper to the 20th century, you may encounter many years in which the equinox occurred on March 21st.

I said that the drift gives you about 1050 minutes per century. That translates to about 18 hours per century. Why is this second-order discrepancy 18 hours? You may notice that it's 3/4 of a solar day again. And again, it's no accident. This new discrepancy arises because the year isn't quite 365.25 solar days. It's a little bit less than that. 365.24219 or so. We deal with this fact by stealing the leap year status from the years that are multiples of 100 (1700, 1800, 1900, 2100), even though they're multiples of four, but we restore the leap year status to multiples of 400 again (most prominently 2000), even though they're multiples of 100 as well.

This combined rule brings the average year to 365.2425 average solar days which is close enough. The remaining discrepancy accumulates to one day each 3,000 years or so, see my remarks about the leap years from January 1st, 2012.

Fine. So those 1050 minutes or 18 hours per century occur exactly because once per century – more precisely 3/4 times per century – we remove one leap year i.e. one day (February 29th) again. The times must adjust themselves so that the timing is pretty much the same as 400 years ago. And this is exactly achieved by making the equinox 42+ minutes earlier than 4 years earlier, each four years, except for years like 2100 when it's 18 hours (minus 42+ minutes) later than four years earlier. These required 42+ minutes in 4 years exactly explain why the non-leap-to-the-following-leap-year annual shift was 18 hours and 10 minutes rather than just 18 hours. All these corrections are ultimately calculable from the number of solar days per year, 365.24219.

At any rate, if you're teaching this stuff to kids, you should tell them that the spring begins on March 20th, summer solstice occurs on June 21st (although 20th will be increasingly more often), autumn equinox is on September 22nd or 23rd (this will be almost 50-50), and winter mostly starts on December 21st. Those days will be "mostly OK" when these kids become adults.

Oops, I noticed that I wrote a blog entry about the same topic one year ago. Find the five differences. ;-)

1. look,

the catholics say it's the 21st and so do the astrologers, so you must be wrong

3. Oops, right. Thanks!

4. Where is the Higgs in your avatar ? ;-)

5. Thanks for counter-attacking the kitty hater James (I will change the background because the first spring day only lasts for tens of hours) but I must defend him, too.

The high-resolution version of the picture suggests that the Higgs is in the middle:

6. Thanks Lubos, actually my 6 year old daughter loves the new background, so maybe I should just STFU

7. LOL, this was a secret plan, especially for hypothetical foes of mine who have children who will scream Lumo is so cute! ;-)

8. I'm not your foe, I'm just a VERY argumentative pain in the neck.

9. Thanks for the high resolution Lubos :-)Shouldn't the H be beside the purple forces in a square now ?? On the avatar it looks as if it is still hypothetical. Now James I'm the pain in the neck ;-)

10. It's the fucking HIGGS BOSON, it goes in the middle, that's obvious isn't it, it means untold millions of pointless media coverage and big bucks from the morons in big government who don't realise that fundamental physics is the only point of humanity and want instead to try to fund 100 billion 2+2 families who just want to fuck and ride cars when they aren't fucking and maybe get pissed to some shitty rock music "cultural" shit now and again

11. What???? :-)

12. Yes I think that was right the first time 8).

13. I like the new background too, please leave it !
It has no snow and I want to play with this cute kitty :-D

14. I like both cats and dogs, and I don't like the way James talks, but I can't resist calling everyone's attention to the video Cat Lassie (39 seconds).

Lubos, I've addressed this to you, since maybe you've never seen the old TV series "Lassie." Lassie was a collie that belonged to a young boy. She was always rescuing the boy. You can easily guess what "Cat Lassie" is about. :-) But I think it's unfair, since a cat saved my grandmother, and I've heard other stories of cats rescuing people.

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