SPECIAL SECTION: Message For Our “Friends” In The Middle Kingdom

You knuckle-dragging barbarians are still trying to muck with this site, so I’ll just repeat what I said last time.

Up your shit-kicking barbarian asses. Yes, barbarian! It took a bunch of sailors in Western Asia to invent a real alphabet instead of badly drawn cartoons to write with. So much for your “civilization.”

Yeah, the WORLD noticed you had to borrow the Latin alphabet to make Pinyin. Like with every other idea you had to steal from us “Foreign Devils” since you rammed your heads up your asses five centuries ago, you sure managed to bastardize it badly in the process.

Have you stopped eating bats yet? Are you shit-kickers still sleeping with farm animals?

Or maybe even just had the slightest inkling of treating lives as something you don’t just casually dispose of?

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

And here’s my response to barbarian “asshoes” like you:

OK, with that rant out of my system…

Loop it if you like; I will wait.

Richly deserved.

Justice Must Be Done

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

The Audit

The Audit is definitely heating up. Let’s see if the Opposition manages to squelch it and its consequences. I’ll be honest; I expect it to be ignored by anyone capable of ordering Biden/Harris to step down.

Nevertheless, anything that can be done to make Biden look less legitimate is a worthy thing!

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

Spot (i.e., paper) Prices

Last week:

Gold $1799.70
Silver $22.45
Platinum $947.00
Palladium $1868.00
Rhodium $14,900.00

This week, 3PM Mountain Time, markets have closed for the weekend. Actually it appears they were closed all day Friday for Christmas Eve.

Gold $1810.20
Silver $22.96
Platinum $981.00
Palladium $2036.00
Rhodium $14,975.00

Slow creep upwards.

James Webb Space Telescope Update

Launch is set for TODAY, Christmas Day at 0720 EST.

Which means that as I write this, I don’t know how it went, but perhaps you reading this, do. Of course, there’s always the chance of a last minute delay, that pushes launch time out of the 32 minute window that the spacecraft must launch during.

After launch (assuming a successful one) about a month of nailbiting begins as over three hundred things have to all happen without fail for this bit of high tech origami to unfold properly, because there is no way to fix a spacecraft that is literally a million miles away. The following video shows the sequence.

The next video, which I should have put in last week’s daily (but I did post it in the comments once I found it) also conveys how tense things are going to be at NASA. This mission has sucked all of the oxygen out of the room for nearly 20 years, and to have it fail…well, let’s just hope it doesn’t.

I have no idea if NASA will have a page to visit that will count down all of the events that must happen. But I do have this one for a launch countdown, in case you are either here before 7AM OR the launch slips again:

Launch Countdown Webb/NASA

The Reason There Even Is A Season

Of course I know what day this. That Advent calendar where Hans Gruber is falling to his death is finally complete (but does that calendar have a “thud” sound effect?).

Of course I am committing the cardinal sin of forgetting “the reason for the season.”

Actually I haven’t. I could write something about that, loaded with chapter and verse. But I am sure you wouldn’t like it. So I will leave it to others to do so.

So I thought I’d do something a bit more typical of what you’ve come to expect from my Saturday dailies and talk about why we even have seasons in the first place. (And yes, I am literal-mindedly talking “season” as in “winter” not “season” as in “season’s greetings.”)

I expect most of you know most of what’s in here, so this should be light reading. Actually, you’ll get a twofer, as I’m going to talk about time of day as well (and more of this will be obscure).

[Note: this is written from the point of view of someone in the northern hemisphere. Our friends in Oz will have to adjust what I wrote as they read it.]

The “first order” view of time, surely figured out long before we learned how to bang the rocks together to make fire, of course, is that this big glowing thing (the sun) would come up over the horizon, making everything light, travel across the sky, and drop again on the other side, and after it did so it would become dark. Maybe (or maybe not) there’d be another very noticeable object in the sky (the moon), and maybe not. There would (if the sky wasn’t completely clouded over) also be a lot of stars out. And then, the sky would grow bright in the east, that super bright glowing thing would show up…And the cycle would repeat itself ad infinitum, which is actually the important point.

The bright period and dark period were of very roughly equal length most places.

But thousands of years ago, if not much longer, we noticed some more subtle patterns. This understanding surely predates the invention of writing; we know this because we’ve found plenty of remains of tools to measure these more subtle patterns, left behind by cultures that didn’t write. (E.g., one of many: Stonehenge.)

The sun doesn’t rise and set in exactly the same spot every day. It rises in a general easterly location, but sometimes its a bit north of east, and sometimes it’s a bit south of east; it’s a slow progression from the most northerly sunrise, further and further south each day, until we reach the most southerly sunrise, then the process reverses itself, the sun rising further north each day.

This correlated with the stars that were visible at night. For instance, when the sun is close to rising as far south as sunrise gets, right after sunset the constellation of Orion is visible in the east; it travels across the sky overnight and sets before sunrise. But when the sun is most of the way to its most northerly sunrise (and sunset), Orion is already setting just after sunset; a few dozen days later on, you can’t see Orion at all.

[The above is true for southern hemisphere people as well.]

All of this also correlates with the seasons, at least for places like Europe. When the sun is rising further south, the weather tends to be colder, though the coldest time might be a bit after the sun has started rising further and further north. Nevertheless, it was pretty obvious: The further south the sunrise and sunset, the colder it gets, and it gets cold enough that food is impossible to grow and difficult to find.

Fortunately we did know that the sun wouldn’t just keep drifting further south, that there was a limit to how far south it would get, and we’d celebrate when it got furthest south, because there was the promise that the weather would get better. And so we have all those tools to be able to mark the day the sun would start to return; Stonehenge being probably the most famous of them. We now call that day the “Winter Solstice” and on our present calendar it falls on or about December 21.

[Folks in the southern hemisphere will want to swap things around; for them it gets colder when the sun is furthest north.]

There were a couple of other aspects of this, too. When the sun was further north, the day was very noticeably longer, and also when the sun was further north, it was higher at noon, nearly overhead in fact (in Southern Europe at least), but much closer to the horizon when it rose further south.

This is actually a consequence of the fact that the path of the sun across the sky forms the same angle regardless of where it rises.

And now, I need a diagram.

As I alluded to before, the furthest south the sun gets is called the winter solstice. But also, the furthest north it gets is the summer solstice (roughly June 21). The in-between cases where it rises precisely to the east and sets precisely to the west, which happen twice as often as either one of the solstices, are called equinoxes (roughly March and September 21).

Where did that word “equinoxes” come from?

So glad you asked!

As you can see from that diagram, the three arcs have different lengths, and that manifests itself as differences in the length of the day. Furthermore, in the far north and south, the differences are greater. Certainly people in Europe and other places that far away from the equator did notice that daytimes are shorter, and night times longer, in winter, whereas for summer it’s the other way around.

It was, in medieval times, customary to divide the daytime into twelfths and to divide nighttime into twelfths as well–this is the origin of our modern hour–but of course these daytime and nighttime hours were rarely the same length. (The advantage of this was that the sun always rose and set at six o’clock, by definition.)

Only at the two equinoxes were day and night–and the day and night hours–the same length; equinox comes from Latin for “equal night.” And we have two of them, there’s a vernal or “spring” equinox, where the sunrise position is in the process of moving north, and the sun rises directly to the east, and the autumnal or “fall” equinox where the sunrise is headed south for the winter.

Going back to that diagram, there’s a line across the sky that starts at the horizon due south, climbs straight up until it’s precisely overhead, than continues on to the horizon due north; this is the meridian. It turns out that this line crosses the arc the sun is taking across the sky, at the arc’s highest point. The two parts of the arc, before and after this point, are of equal length. When the sun is at that point, it’s “noon.” And our abbreviations AM and PM come from “ante meridian” and “post meridian.”

And there is one more concept to be introduced here, and that is the length of time between two winter solstices, or spring equinoxes, or summer solstices, or fall equinoxes, and that is a year. To be more precise, it’s a tropical year. (And yes, there are other similar concepts known today, that mean slightly different things. By the time I explain those, the name tropical year might make a bit more sense.)

Our calendar is set up to cycle in one such period. Since it’s the sun’s variations it’s based on, our calendar termed a solar calendar. Some cultures (most notably Islamic ones) operate off the moon instead of the sun, and others work off a mixture of both. A pure lunar calendar will follow the phases of the moon, and may have a number of these moon-cycles bundled together into a year…but it won’t be the same length as the solar year, because the length of a moon cycle doesn’t divide evenly into a solar year. This is why the Islamic year is only 354 or 355 days long…they flat out didn’t care about the seasons (known as “hot” and “even hotter”) in Arabia.

The Jewish/Hebrew calendar is a combination lunar-solar calendar; its months follow the moon cycles, but will try to track with the seasons, too, by adding entire extra months in some years to make up the difference.

This is similar to the way the ancient (pre Julius Caesar) Roman calendar worked, too: months followed the moon strictly, but the priesthood would determine when extra months needed to be added to keep things roughly in sync with the seasons. A year without an extra month was 355 days long; a year with the extra month was 378 days long. This was eventually abused by priests who’d add extra months if the consul in power that year was someone they liked. Eventually it turned into a big mess that Julius Caesar would have to take drastic action to fix. More on that later, perhaps.

Between all of this about the sun’s curious behavior and the way the stars behave over the course of the year, people eventually came up with a mental model of what’s going on behind the scenes. Aspects of this model are still in use in astronomy.

It’s known as the celestial sphere and comes in two slightly different forms.

The idea is that the sphere is centered either on Earth or on the observer, and it’s arbitrarily far away. The position of every object in the sky is projected onto that sphere.

In particular the stars, which (almost) don’t move, are regarded as fixed in place upon the celestial sphere.

Earth is at the center, and there is a north celestial pole and a south celestial pole, directly over the earth’s north and south poles. There is also a celestial equator, above the earth’s equator.

The earth, of course, rotates counter-clockwise as seen from over the north pole, but in this model we pretend the earth is stationary and the celestial sphere is rotating clockwise as seen from “above” the north celestial pole.

The second version you will see of the celestial sphere is with respect to an observer on Earth’s surface. There are still celestial poles and a celestial equator, but in a diagram like this, usually drawn assuming someone in the northern hemisphere, you’ll see the north celestial pole above the horizon, the south celestial pole below the horizon (if it’s shown at all), and half of the celestial equator at an oblique angle to the ground. And the celestial equator will intersect the plane of the ground precisely east and west of the observer. In fact you can consider each star in the sky as having a “latitude” above or below the celestial equator, just as places on Earth do with respect to the earth’s equator. Astronomers actually do this, but they call it “declination” rather than latitude.

In fact this diagram is a gif, and you can see three points on the celestial sphere moving in circles as the celestial sphere rotates. A point sufficiently far north on the celestial sphere never sets…a real life example of this for people in the US is the Big Dipper, which doesn’t set (it might do so in the far south of the US; I don’t know). Similarly, there are stars that never rise in the US, our friends in Oz get to see them, though. (Alpha Centauri, the nearest visible-to-the-unaided-eye star other than our own sun, is permanently below the horizon where I live, as are Canopus and Fomalhaut, two other very bright stars.) But most stars in the sky rise and set, following arcs very similar to the arc the sun follows in its daily journey across the sky.

It turns out that, for all intents and purposes unless you have a true atomic clock (not just a receiver) the stars move across the sky at an absolutely constant rate. You can set your watch by them…and indeed for quite a long time, we did set our clocks by them.

Pick a bright star, and start your stopwatch when it crosses the meridian. Wait a day for it to cross again, and how much time elapses?

By modern units, do you suppose it’s 24 hours? After all the earth spins once every twenty four hours, right? Well…almost.

In fact, it’s 23 hours, 56 minutes, 4.0905 seconds (approximately). Or equivalently, with respect to the stars, the earth rotates once every 23 hours, 56 minutes, 4.0905 seconds. This is the sidereal day, the amount of time it takes the earth to rotate once, with respect to the stars.

Astronomers actually have special clocks in their observatories that measure sidereal time. When a certain point in the sky crosses the meridian, that’s zero hours (0h), then every 24th of a sidereal day another hour has passed…but these hours are slightly shorter than what your watch measures, of course. But you can tell what stars will be “up” at any given time by knowing the sidereal time. In fact they will occasionally set their sidereal clocks by watching the stars. It’s fairly simple to convert sidereal time to “normal” time and that’s why observatories were once the places that would define what time it was.

Huh. Why the difference? Hold that thought!

How about measuring the sun’s time between crossings of the meridian? OK, that’s both better and worse. No, it’s not 24 hours. In fact, it’s not even a constant amount of time! Sometimes it is longer than 24 hours, sometimes less. But it does average 24 hours over the course of a year.

And that is how the length of the day was originally defined.

So how can the sun take 24 hours–on average but not on any particular day–to go around the earth (in celestial sphere terms), but the stars do it almost four minutes faster?

Remember earlier when I talked about how Orion would be just rising as the sun sets in autumn, but during the winter, it would be higher and higher in the sky at sunset, until around about May when it’s about to set just as the sun sets?

That means the sun is moving closer and closer to Orion over the course of the winter. Which means the sun is not nailed to the celestial sphere like the (other) stars are. In fact, it moves in a full circle around the celestial sphere, and it takes a year to do so.

Unfortunately for reasons that I might not get to this week, it doesn’t take a tropical year to do so, it takes a slightly different amount of time, a sidereal year. And you may have noticed a pattern: “Sidereal” means with respect to the stars. The sidereal year is about 20 minutes longer than a tropical year.

So what about this circle on the celestial the sun travels on over the course of the year? It’s called the zodiac, and it’s tilted with respect to the celestial equator, intersecting it at two points. The tilt is about 23 1/2 degrees. When the sun is at one of those intersections, it is of course right on the celestial equator and will rise (or set) directly to the east (or west). When you hear some newscast saying that spring will start at such-and-such a time on March 21st, that’s actually the exact instant the sun crosses the celestial equator.

That crossing point, called the First point of Aries, is where astronmers start measuring celestial “longitude” analogous to longitude on Earth…except they call it “right ascension” and it is measured in hours, not degrees, with 24 hours making up the full circle. In fact, sidereal 0h is when the march equinox location crosses the meridian.

Since the sun takes a full year to travel around the zodiac, on any given day it moves about 1/365th of the zodiac or just under one degree. And at different times of the year, it’s well north or well south of the celestial equator, accounting for those differing-located (and differing length) arcs across the sky that our prehistoric ancestors first noted.

The difference between the sidereal and the (average) solar day of 24 hours is accounted for this way: Noting that the sun crosses the meridian at a particular time, if you wait exactly one sidereal day, the same stars will cross the meridian again [never mind that you can’t see them in broad daylight!]. But the sun will have traveled about a degree to the east in the meantime, and the celestial sphere must rotate (east to west) about one more degree to bring the sun across the meridian again. (A degree is 1/360th of the circle, and with a day being 1440 minutes, it takes about 4 minutes for the celestial sphere to rotate one degree. Actually, it takes exactly four sidereal minutes to do so, but they’re slightly shorter than your wall-clock minutes.)

Part of the reason the time between meridian crossings of the sun varies from 24 hours, is because of the tilt of the ecliptic. Where it crosses the equator, it does so at a slant, so part of the distance traveled is in the north-south direction and the sun therefore moves a bit less in the east-west direction. Which means the celestial sphere has to rotate slightly less to bring the sun across the meridian the next day, making noon-to-noon a bit shorter than average. At the two solstices the sun’s motion along the zodiac is purely along the east-west direction and the right ascension lines are closer together, so the celestial sphere must rotate more to bring the sun across the meridian line, so noon-to-noon duration is a bit longer.

There is a second factor affecting this, which I’m going to ignore for now, I’ll get to it later.

OK, so what are the practical effects of all of this?

First off, ironically the only instrument that actually tracks the sun’s movement is a very primitive one, a sundial. But even here, there’s a subtlety or two you must keep in mind. A sundial always seems to have a triangular or sloped thing to cast the shadow (the “gnomon” from Monday’s daily). Why is that? The sloped side of the triangle is actually parallel to the earth’s axis (or the celestial sphere’s axis), so that there won’t be any weird perspective shifts over the course of the day. You may have noticed me pointing out how steep that one sundial in Canada was in the comments last Monday. That’s why: gnomons will be steeper the further north you go (or further south in the southern hemisphere), and a vertical (plumb) pole in the ground will work perfectly at the north or south pole.

Incidentally, did you ever wonder why we happened to choose the direction we call “clockwise” to be the direction clocks turn? Why not the other direction (which, of course, we’d then call “clockwise” instead of this direction)?

It’s because that’s the direction the sun’s shadow travels on a sun dial. We were making the clocks “backward compatible” in a way by doing that–a shadow to the left of another shadow indicates an earlier time, and hour hands further left also indicated an earlier time.

If modern, watch-making civilization had developed in Australia instead of Europe, chances are good that clocks would run the other direction and maps would have south at the top. If we ever run into aliens who put south at the top of their maps, chances are good their watches will run “backwards.” You wouldn’t think the two arbitrary decisions are related…but they are both more than likely functions of which hemisphere civilization started modern map making and timekeeping.

OK, so we have a sundial which will actually measure the position of the sun in the sky. But we can’t use them for modern timekeeping, even leaving out the fact that they don’t work at night. Because we’d have to deal with the inconsistent length of the sundial day, from one day to the next…remember that bit about the sun crossing the meridian?

We can come up with something called “Mean Solar Time” which is the average time the sun will cross the meridian. And in fact we did precisely that, for centuries. We even had tables and graphics showing how far off of mean solar time the sun’s crossing of the meridian would be any given day of the year, and it’s even called “the equation of time.” People in a certain town would set their watches by mean solar time, and those watches would be off from their sundials by a predictable amount, according to the graph below.

Now you’ll note I said “in a certain town.”

Yes, it matters where you are. The sun appears to travel across the sky east to west. Therefore it stands to reason that someone further east than you are will see the sun cross the meridian earlier than you do. And when he does the whole averaging to get mean solar time thing that you did, he’s going to end up setting his watch a bit faster than you are. In fact, only if two people are directly north-south of each other, under the same meridian line, would their clocks be synchronized.

Until the advent of the railroad, in fact, every single city had its own, distinct local mean solar time.

This didn’t matter much in stagecoach days; a stagecoach could maybe make a few dozen miles in a day, and people’s watches were inaccurate enough they needed to be reset every few days anyway; while traveling they’d just have to set them in every new town…not much more often than they already had to.

But railroads could cover hundreds of miles in a day, and there you could see easily see significant differences between towns’ mean solar times in one day of travel.

And railroads liked to run on a schedule. That schedule was a royal pain to set up when the time of day was shifting depending on your position on the track. A trip east to west would be shorter (by wall clock times at every stop on the route) than a trip west to east at the same speed. Time measured on the train would be identical, of course, it’s just that the train’s clock would seem faster at the west end of the trip than at the east end.

So what did the railroads do? They invented time zones. This began in Great Britain in 1840, where the Great Western Railway simply synchronized all of their clocks with the Greenwich observatory’s mean solar time, which became “Greenwich Mean Time.” In essence all of Great Britain ended up in one time zone, with most public clocks showing GMT regardless of the local mean solar time, though this didn’t become a legal thing until 1880. In fact, many clocks from this time actually have two minute hands; one could be set to GMT and the other could be set to local time.

Britain was a relatively small country. The US is much larger. What happened here?

Well, we could have set every clock at every railway station to Washington DC time, or (more likely back then) New York City time. But the US is wide and clocks on the west coast would have been reading noon when the sundials were saying 9AM. A few minutes like the UK had was tolerable (we’d never have noticed without watches in the first place), but two or three hours would be a problem.

Railroads at first simply used the time at their headquarters, transmitted by telegraph so other stations could synchronize. That led to the spectacle of some stations that served two railroads having to show two clocks, one for each railroad, so that people could know at what time trains were supposed to arrive and depart.

In 1863 Charles F. Dowd proposed a set of standard times for all railroads to follow but no real action was taken until he consulted railroad officials in 1869. In 1870 he proposed Washington DC as the center of one time zone. In 1873, finally time zones began to be used, but the boundaries between them would tend to be in major railway stations–depending on whether the train went east or west through the station, it’d have to set its clocks forwards or backwards at the station. Finally, something very akin to what we have now was adopted by Congress in 1918.

The four time zones we use in the Lower 48 are based on the mean solar time at 75, 90, 105, and 120 degrees west longitude.

If you live right on those longitudes, and your watch is set correctly, it reads mean solar time, and the equation of time in the chart above is correct.

If you don’t live on those longitudes, then you’re east or west of the longitude your watch is set for, and you have to add or subtract a constant to your watch to know mean solar time for your location. And of course if the never-to-be-sufficiently-damned Daylight Saving Time is in effect, you’re still off by an hour.

Interestingly enough, there’s a reverse to this: If you have an accurate clock and do not reset it, you can determine your longitude by observing the sun to determine the local solar time, looking at your watch, taking the difference, and correcting for the equation of time. For instance if you set your clock to GMT, go sailing off, and at some point notice that the sun says it’s 9:50 am when your watch reads noon, and the equation of time says your watch is fast by ten minutes on that day, you know that at that instant a sundial in London would say it’s 11:50 AM, but where you are the sundial would say 9:50 am–you are two hours behind London, and with each hour being 15 degrees on the globe (360/24 = 15), that means you’re at 30 degrees W longitude.

Without that accurate clock, determining longitude is nearly impossible, and in fact the British government sponsored a substantial prize (10 to 20 thousand pounds) for the first person who could invent a clock that would keep accurate time even on the swaying and heaving deck of a ship (which left out any clock based on a pendulum). The amount of the prize depended on the accuracy of the method. The prize was finally collected in 1773.

Columbus and Vasco da Gamma (to say nothing of Magellan) would likely have given up significant body parts for one of those chronometers.

[There are other methods to determine longitude; they all amount to determining an absolute time. One was to observe Jupiter’s moons’ positions, but that depended on Jupiter being visible, and that was essentially seasonal (and subject to cloudy weather). And, one needed to correct for where the earth was relative to Jupiter; it could be further away than average in which case the actual time was later than indicated by Jupiter’s moons because the light took longer to reach you.]

OK, so now it’s time to get back to seasons.

I’ve been talking about the celestial sphere, which is a handy visualization device and is the basis of astronomical (sky-chart) coordinates, but now we need to get back to reality.

The sky doesn’t rotate, the earth does. And the sun doesn’t travel around the earth on the zodiac, the earth travels around the sun in the plane of the zodiac.

The earth spins about its axis, and the axis of the spin is almost stationary. We can, for now, pretend that it is stationary (but–spoiler–the fact that it is not accounts for the twenty or so minute difference between sidereal and tropical years).

The plane of the earth’s orbit about the sun is the zodiac; and as I said before the angle between the zodiac and the celestial equator–i.e., between the zodiac and Earth‘s equator–is about 23.5 degrees. That also means the earth’s axis, rather than being perpendicular to the zodiac, is tilted 23.5 degrees off perpendicular.

At the time of the summer solstice around June 21st, according to the “celestial sphere” visualization, the sun is at the furthest north point on the zodiac. Stepping back and looking at the whole earth/sun system from space, it’s apparent that Earth’s north pole is tipped towards the sun.

There are parts of the far northerly, arctic regions where the sun won’t set at all! [Conversely since the south pole is tipped away from the sun, it won’t see daylight…and large antarctic regions also won’t see the sun around that time.]

A bit further south than the north pole, there are large areas where the sun will ride high in the sky and the daytime will last well over 12 hours. Those areas are getting a lot of sunlight, almost head-on, and that’s why summers are warm. In fact, at 23.5 north latitude, the sun will cross directly overhead, shining absolutely straight down at local noon. Eratosthenes, in Ptolemaic Egypt, records that the sun would shine clear down to the bottom of wells in Syene, to the south of Alexandria (and he used this fact, plus the sun angle in Alexandria that same day, to estimate the size of the earth; he didn’t do too badly).

Waiting three months until the September equinox, the situation looks like this:

Neither hemisphere is favored and the Sun is directly over the equator…and will rise directly to the east that day.

And you can see what will happen; the winter solstice will have the south pole tilted toward the sun, and the north pole tilted away; sunshine will hit the ground at a more oblique angle in the northern hemisphere, and heat the ground less.

Spring will be the mirror image of fall, with neither hemisphere being favored.

Putting it all together, you see the standard diagram, that looks like this:

Note that at all times, the earth’s axis of rotation points in the same direction; the seasons are caused by the differing relation between the direction of the sun (as seen from earth) and that axis.

And that is the reason we even have seasons. The tilt of the earth’s axis is that reason.

Now there’s one more factor I alluded to when I talked about the equation of time. The earth’s orbit about the sun isn’t a circle, it’s very slightly elliptical. Which means at one time of the year, it’s actually closer to the sun than at any other time; six months later, it’s furthest away.

I have to mention this, because many people think the reason it’s hotter in summer is that Earth is closer to the sun then.

Actually, it’s not. It’s actually closest to the sun in January! Yes, it does get a tiny bit more sunlight then, but the effect of the angle of the sun hitting the ground is much, much greater, which is why the northern hemisphere experiences summer when the north pole is tipped a bit towards the sun–even though Earth is further away from the sun at that time.

But this does have an effect on the equation of time. I mentioned that, as seen on the celestial sphere, the sun moves a bit eastward each day, meaning that in order to bring the sun back to “noon” the celestial sphere had to rotate about another four minues / one degree’s worth.

Stepping back, we see what’s actually happening. At noon on one day, you can draw a line from the sun through the earth. Now wait one sidereal day. The earth is oriented exactly the same as it was before–it has rotated once. But over the course of that day, the earth has moved almost one degree along its orbit. In order for the same spot that was facing the sun before, to be facing the sun again, the earth has to rotate one more degree. That accounts for the difference between the sidereal and solar day.

But as I said, the earth is in an elliptical orbit. Even at a constant speed, at the furthest out end of the orbit, the earth will cover slightly less angle of its orbit than it will closer. But in fact the earth moves faster nearer the sun, so this effect is magnified.

So it takes slightly less than four extra minutes to put the sun back on the meridian in July (when earth is furthest away from the sun), and more than four extra minutes to do it in January. That accounts for more off the changes in mean solar time that show up in the equation of time; a couple of those humps and valleys on the graph are due to this effect.

Are you starting to get the idea that simple measuring of time is actually a rather complicated subject?

It gets worse. Let’s go back to the calendar.

The length of the tropical year is 365.24217 mean solar days. Or to put that in long form, the length of time it takes to go from spring equinox to spring equinox is 365.24217 times as long as the average interval between sun crossings of the meridian.

Now, if we’re going to set up a calendar (which will want to be in whole days) and expect it to remain in the same relationship with the seasons, that means some years will have to be 365 days long, and some will have to be 366 days long.

I mentioned the drastic reform Julius Caesar made to the Roman calendar. First he had to restore the traditional alignment of the months to the seasons, which had gotten bollixed up by the priests’ arbitrary insertion of extra months. Then he had to change the lengths of the months so there’d be twelve months, no more, no less in a year. Then he had to do something about that fractional 0.24217 days.

The year 46 BCE was known as the year of confusion. Caesar added multiple extra months that year to get the calendar lined back up with January starting as it should, early in winter. Then the next year he introduced the twelve months we know today, at their current lengths. Those totaled 365 days. He decreed that every fourth year, an extra day be added to February. That would make the average calendar year 365.25 days, which is quite close to 365.24217 days.

There were glitches–for a time people were mistakenly holding leap year every three years, and Caesar Augustus had to straighten that out and re-sync. But after 1 CE, every year divisible by 4 was a leap year, 4, 8, 12, etc.

The “Julian Calendar” held sway for over fifteen centuries.

But after fifteen centuries, the difference between 365.25 and 365.24217 had added up. Consider a century of 36,525 days on the Julian calendar, versus 36524.217 days in an actual tropical century. There’s almost 0.8 days difference. Call it .75 (which is what a certain guy named Gregory did), it becomes apparent that in 1600 years, there’d be a twelve day error.

And indeed, because the year was longer than it “should” have been, spring was now starting on March 12th instead of the 21st, in the 1500s.

Pope Gregory changed the leap year rule from “every fourth year” to one where three of those leap years out of every four centuries would be skipped. And he decreed dropping days to get the calendar back to where it was supposed to be. This is the Gregorian calendar, and it’s the one we use today. Under the Gregorian calendar, every year divisible by 4 is a leap year–except for century years (ending in 00). Those are not leap years even though they are divisible by 4. However, if a century year is divisible by 400 it is still a leap year anyway. The upshot is that 1700, 1800 and 1900 were not leap years, but 2000 was, and 2100 will not be.

This made the average length of a calendar year 365.2425 days, which is a lot closer to 365.24217, and we won’t have to figure out what to do about the difference for at least another thousand years. It looks like we need to ditch three or four more leap days every ten thousand years, or perhaps ditch 33 leap days every hundred thousand years. (On the other hand, Gregory could have come a lot closer if he’d gone with a rule where instead of very 400 years, every 500 years the century leap year is not dropped. Perhaps he didn’t have quite the right number of days in a real tropical year; I imagine it’s tricky to measure accurately.)

Gregory made his change in 1564; but by then the Reformation had happened and Protestant Europe wasn’t going to muck with their calendar because some guy in Rome said to do it. It took until the 1700s to bring them on board (it happened in England and her colonies in September of 1752; in order to get things back in sync 11 days were dropped. The day after September 2, 1752 was September 14, 1752, and occasionally we will refer to dates around then as “O.S.” for “Old Style” and “N.S.” for (wait for it…) “New Style.”

Eastern Orthodoxy didn’t catch up until much, much later (in fact some congregations still haven’t switched). Russia still used the Julian calendar in day-to-day business until the Communists forced the change in 1918. (If you think having to deal with time zones is bad, imagine writing to someone who is thirteen days behind you.)

There’s one last issue. It doesn’t affect our daily lives much…unless we’re astronomers.

Remember how I said the earth’s axis is almost stationary?

In fact, it wobbles, like a top. The angle remains about 23.5 degrees, but it moves around in a big circle, like this:

On the left, a top, wobbling as it spins. On the right, Earth doing the same thing.

Only it takes 25,700 years to do it.

In about 12,850 years, it will have gone 180 degrees around that circle. And the north pole of earth will not point towards Polaris any more. It will be pointing very roughly in the direction of Vega. (Vega is the star in the summer triangle that sets first…it’s probably setting about sunset right now.)

I’ve found it difficult to locate a video that shows this, that isn’t chock full of mystical/astrological woo or other irrelevancies. Many years ago I found a video that would have been perfect…except that the perspective rotated, which made it impossible for someone who didn’t already understand it, to understand the video.

But this one isn’t bad. It’s shown from the perspective of the celestial sphere. The flat grid shown is the plane of the earth’s orbit, i.e., the Zodiac.

What that will mean is that at the spot in the earth’s orbit that is now the summer solstice will then be the location of the winter solstice (and vice versa); the vernal and autumnal equinoxes will also trade places, as seen below, where A shows the current situation, and B shows the situation 12,850 years from now. Note that the orientation of Earth’s orbit does not change, just the locations of the equinoxes and solstices.

In both diagrams, Sagittarius is to the left; at the present time, when the earth is at perihelion, just after winter solstice, the Sun is in Sagittarius. (Not Capricorn, which is the “astrological sign” associated with that date; I’ll explain that below.) The earth’s northern axis is tipped almost perfectly away from the sun. 12,850 years from now, at perihelion, the Sun will still be in Sagittarius, but the date (which is aligned with the seasons) will be July 4th. (Happy Independence Day, if there is still a United States in 14,871 CE.) The earth’s northern axis will be tipped almost perfectly toward the sun at this point, because the axis has precessed since 2021.

The location of the “first point of Aries” (upon which astronomical coordinates depends) will have shifted to the other side of the celestial sphere.

So the first point of Aries moves in the celestial sphere. And since the tropical year depends on the first point of Aries, while the sidereal year is fixed with respect to the stars…that’s why the two lengths are different. The first point of Aries is moving in the direction that makes the tropical year shorter than the sidereal year–the earth hits the first point of Aries in slightly less than one orbit around the sun.

I said before the difference was about 20 minutes. Actually we can come closer than that. Over the course of one full precession of the equinoxes, 25,700 years, the total “slip” has to be a full year. So dividing 25,700/365.25 we get 70.36 years to slip one day; 1/70.36 days is about 1228 seconds. So the difference should be about 20 and a half minutes. This is a back-of-the-envelope calculation, of course, but it turns out the real difference between the sidereal year and the tropical year is 20 minutes, 24.5 seconds, so we were only off by 3.5 seconds. Not bad for the back of the envelope!

Notice I said that the first point of Aries moves, and that astronomical coordinates depend on the first point of Aries. Doesn’t that bollix up astronomical coordinates? Yes it does…and it’s worse. The celestial poles move, which means the celestial equator moves. The only constant is the zodiac in fact, but the point on the zodiac that crosses the celestial equator shifts.

Astronomers have to put an “epoch” date next to their coordinates, because they go out of date every fifty years or so. But since they’re (mostly) stuck on the earth, and have to rotate their telescopes against the earth’s rotation so that the stars don’t drift across their field of view, they really do need to follow the celestial poles. Even though they move.

[As a matter of fact, the “first point of Aries” has, for a long time, actually been in Pisces, and it’s moving into Aquarius (the video shows this). Which is what that insipid early 70s song “Age of Aquarius” was referring to. And this means if your astrological “sign” is Aries…well it really should be Taurus. Or maybe Aquarius. One the one hand astrology looks clueless because of this, on the other hand it’s a lot of astrology weenies who prate about the “Age of Aquarius” in the first place. I’m going to go with “they’re clueless” though.]

One last question you might have is what causes Earth’s axis to precess in the first place. Well, because the earth is rotating, it bulges a bit at the equator; this bulge is of course not pointed at the sun. It’s also not pointed at the moon. So both bodies, especially the moon, tug at that bulge, which is a torque against the earth’s angular momentum. That goes through a cross product to cause an actual motion of the poles at right angles to the tug–it’s a funky “gyroscope thing.”

As I said, measuring time is a complicated business.

And I haven’t even gotten to the truly modern complications…where it turns out the earth’s rotation is slowing down! (This is why we have to add leap seconds every once in a while.) Since the GPS satellites don’t bother with leap seconds, GPS time, which many treat as a de facto standard, differs from “Coordinated Universal Time” (basically a spruced up GMT), which is really the standard, by an increasing amount.

And now, with your head throbbing from all of that, I wish you a Merry Christmas.

Hopefully Santa delivered some nice, dirty sulfur-laden coal to Joe Biden’s stocking.

Fuck Joe Biden

Biden, you don’t even get ONE scoop of ice cream today.

(Please post this somewhere permanent, as it will continue to be true.)

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!