Leap Days and Stuff

[peter]

This is going to be more of a thinking out loud exercise for me, to try to see where I can get to, and what I think I know about "Leap Days and Stuff". Hope one or two of you guys will join in for the ride and set me right in the places I hit a duff note.

The world goes around the sun and takes approximately (more of that word later) 365 and a quater days to complete one revolution. It's tilted on it's axis in relation to the plane of it's passage around the sun (by about 23 degrees?) and this tilting and how it effects how the rays of sunlight fall on the earth, brings about our seasons. Now, because of this quater day, if we didn't make adjustments to our calander every now and again the seasons would soon become out of synch with the given time of year that we are used to seeing them. If I'm right, the result of not having this adjustment would be that in each sucessive year the seasons would lag behind the dates a little more and a little more. If your birthday was in dummer [typo I just had to leave in] you would gradually see it shift into spring and the winter. This would cause untold problems in the Christmas card industry and so cannot be tolerated.

Ok, why not take the bull by the horns and extend the length of a day so that that 1/4 day is spread out over the 365 days of the year. Time measurement is after all as arbitrary as any other human imposed measurement system on nature. Why not do away with the need for all this leap year stuff by making a new standard length of time for a second, so that what is now 24 hours becomes just short of 24 hours; in that way the quater day could be divy'd up between all the current days of the year and it would be 'job done'. But hang on - if you did that would you not just shift the problem from the years, over to the days. The day is measured by a complete revolution of the earth on it's axis - it's not an arbitrary thing at all. If you add more time into it then surely you are going to finish up with the times of day wandering around in respect to day and night. By adding more time into each day you are going to finish up with each day starting a bit further into the next - soon the new day will start at dawn, then at the suns highest point for the day, then in the evening. It would be chaos - it just wouldn't do.

Ok - so we're stuck with adding days in. Now as the earths revolution around the sun takes approximately365 and a quater days then if we add one extra day every four years this puts it right(ish). But heres where the 'approximately' starts to count. It isn't exactly one quater day - it's approximately and over the years all these approximatlies start to add up. So how do you deal with them. In fact the error is such that over time the seasonal shift is over compensated for by the addition of one day every four years, and this starts to stack up in the opposit direction ie the seasons start to gain and your summer birthday moves into autumn and then winter. This is dealt with by ignoring the leap year rule (that a day is added into each year number that is divisanle by 4) on one occasion each century - and that is in the first [ie the '00'] year. However again this tips the balance in the other direction (ie back into a seasonal lag - allbeit over a much more extended time) and so for the last trick [I'm aware off anyway]. At the turn of a new millenium you ignore the ignoreing the leap year rule at the start of new centuries, and stick another day in anyway. And this I think puts our calander into pretty good shape, keeping the seasons in place wise, for the next ten or twenty thousand years (might even be more than this). There may be yet a further rule taking us even deeper into the future, but if so I'm not aware of this.

Couple of questions i) What is the point in space by which we decide upon a revolution of the sun having been completed. I don't know if suns revolve or not (I'd guess they do) but if so how do you judge when a revolution has been completed - there must be a point, say the crossing of the earths eqitorial plane with the suns or something, by which you can fix the relative positions of sun and earth.

ii) Every day I bundle up the newspapers from the day before and send them back to the depot. I date the returns slip and I'm always amazed how often there seems to be an symetry or a sequence in the date numbers. Here's a few:- 10/11/12, 09/11/13, 11/12/13 [poor examples I'm afraid - some of them are quite beautiful but alas I can't remember them and never write them down]. I'd guess that as the year number rises the occurence would be less, but not necessarily so. As I say it astounds me how often this happens - and I've often wondered if it would be a predictable thing by algorithm, or whether it is just too random an occurence to lend itself to prediction in this manner.

[Hashi Lebwohl]

Add a day every 4 years...but not if the year is evenly divisible by 100...but add the day if the year is evenly divisible by 500...and add another extra day if the year is divisible by 5000. This gives us the more accurate 365.2422 days/year.

So 1900 was not a leap year (divisible by 100) but 2000 was (divisible by 500). The year 5000, if we get there, will need to have two leap days--it will the the first February 30 in recorded history.

This could be avoided by doing away with months--today is 22 July but we should just mark it is 203/2103. the 203rd day of this calendar year. Just stick the extra days on the end and be done with it...but no one is going to do away with months. No, too many of us would still rather honor ancient Roman emperors.

We have more precise observations of the Sun now so we know its rotational period. It is actually quite slow--0.01045 rad/hour. For comparison, the Earth rotates at a rate of 0.2625 rad/hour.

[wayfriend]

What is the point in space by which we decide upon a revolution of the sun having been completed.

Equinoxes and solstices are measureable by astronomers down to the second. It's based on the angle of the sun at the equator. These establish when should be March 20, June 21, etc. The rest is calculated from there.

[sgt.null]

Superman was born on Feb 29th.

I got nothing else.

[peter]

Thanks Hashi you summed up neatly in a short paragraph what I tried to say in a bucket full of waffle - and still got wrong! Also to Wayfriend - this makes sense and I'm guessing the observations and predicted calculated values lie in extremely close agreement these days.

Sarge - I didn't know that and now I do I won't forget it either !

(re q. ii) - 12/12/12 for another example - more elegant this time I think [came to me last night]].

Calanders are interesting things to me. I was one of the few people who took [a humerous level of] umbrage at the fact that we celebrated the turn of the Millenium on THE WRONG DAY! The calander system we use for year allocation was started running from the year 1, not the year zero - thus the Millenium should rightfully have been celebrated at 12 midnight on December 31st of the year 2000, not 1999 as we did it. We are the only generation for...well..... 1000 years who gets to celebrate the dawn of a new Millenium - and we get the wromg day! [In fairness I do get the reson for this - the change from a 1 to a 2 on the calander does seem to be the right place to do this....but 'seems' and 'is' aint the same. Perhaps we should have had two 'blow-outs' instead. {Hang on - I think we did }

[sgt.null]

www.famouswhy.com/Born_Today/2/29.html

[Hashi Lebwohl]

Thanks Hashi you summed up neatly in a short paragraph what I tried to say in a bucket full of waffle - and still got wrong!

The calander system we use for year allocation was started running from the year 1, not the year zero - thus the Millenium should rightfully have been celebrated at 12 midnight on December 31st of the year 2000, not 1999 as we did it. We are the only generation for...well..... 1000 years who gets to celebrate the dawn of a new Millenium - and we get the wromg day!

I do what I can.

I don't know about you, but I didn't celebrate the turn of the Millenium until 31 Dec 2000, the correct day.

[peter]

I never needed much to encourage me to celebrate - I have a feeling the two dates in question may have blended pretty seamlessly into one looong celebration! I remember arriving in the French Quater, New Orleans on about the 5th Jan 2000; after that everything is pretty much a blur!

[Hashi Lebwohl]

Even after Katrina, I gather that New Orleans still has that effect on people.

[Vraith]

I just skimmed quickly...got a lot of reading to do cuz my internet was down completely or mostly [as in taking more than 2 minutes to load each and every page] since Monday.

I think you left one thing out. If you "sync" the year length to a precise point so it is always "reset" to exactly one orbit, you will STILL get seasonal shifting due to precession.
So, what is NOW "Midsummer's day" [or solstice, or Midsummer's Night if one prefers the dreaming] in, say, Stratford-Upon-Avon, in 13000-ish years will be taking place in Australia-ish. In Stratford etc. it will be Midwinter's day...Yule in June.
Don't worry, though...in 26000-ish years, it will all be back to normal.

[I think all that is right. I might be being dumb, but I don't feel like checking or rethinking it.]

[peter]

Damn! I thought this *was* precession. Now I'm maybe thinking that precession is that when you have done one exact orbit of the sun the position of the backdrop of stars has shifted a bit - but it can't be that; if it has to do with the seasons it has to be to do with the tilt of the earths axis and the sun alone. [thinks:"shall I go check this out or be lazy and hope one of the guys will spell it out for me. No - better do the decent thing and go do the 'footwork' myself." ].

[I'm Murrin]

The tilt of the earth's axis both rotates and wobbles (i.e., the angle of tilt changes). The rotation is precession, the wobble is nutation.

[peter]

I'd hazard a guess that the rotation of the axis around a central point (the precession if I have it right) is in the same direction as the rotation of the earth around it's axis [anti-clockwise], and furthur, that the rotation of that central point (the wobble/nutation again if I have it right) is probably also anti-clockwise.

One thing I'm getting here is that, contrary to the views of all philosophers and men of religion prior to about Keplar, there appears to be nothing whatsoever de revolutionibus coelestium that is perfect at all! On the contrary the whole set up seems to crank and wobble it's way along in just the same manner as the rest of life.

One more thing [and I may be stepping over the boarder totally into the realms of 'nutjob' here but] - I've heard this thing about (certainly) the magnetic poles of the earth changing at various times over the course of it's history (ie North becoming South and vica versa) and also (more wierdly) about the earth totally flipping on it's axis like a spinning top as it slows down. If such phenomena have any basis in reality (as opposed to just inside the heads of fools and drunkards) surely they would have to be tied up with this precession and nutation. Questions; do they and are they?

[I'm Murrin]

Changes in the magnetic poles are supposedly down to changes at the earth's core, not its rotational mechanics.

[Vraith]

On the contrary the whole set up seems to crank and wobble it's way along in just the same manner as the rest of life.

One more thing [and I may be stepping over the boarder totally into the realms of 'nutjob' here but] - I've heard this thing about (certainly) the magnetic poles of the earth changing at various times over the course of it's history (ie North becoming South and vica versa) and also (more wierdly) about the earth totally flipping on it's axis like a spinning top as it slows down. If such phenomena have any basis in reality (as opposed to just inside the heads of fools and drunkards) surely they would have to be tied up with this precession and nutation. Questions; do they and are they?

Yep, the whole thing is perturbed...
Speaking of which, the mag field is generated by the solid inner core turning and rubbing within the liquid outer core, setting up currents. Over time these currents shift in a semi-turbulent way...which reorients the magnetic poles.

The earth has never flipped physical poles, I don't think...though there have been differences in axial tilt. Eventually, it COULD lose energy, wobble down and die rotationally like that top...but I suspect the Sun would already have blown up and destroyed us before that could happen [unless a truly massive something runs into us and tips us over].
I suspect it could flip extremely slowly/get very wobbly if the continents drifted into extremely unbalance positions [that might actually have been the case when the one supercontinent existed...greater tilt/wobble IIRC]

There was a quasi-SF book...I think in the early 70's...the author thought that plate tectonics was the stupidest theory he'd ever heard of, that the earth kept flipping as polar ice caps reached critical largeness...hysterical thing.]

[sgt.null]

wobble is a beautiful thing. it Is nice to know that nature does not deal in perfection.