The solstice (in a two-sphere cosmos).

Here in the Northern Hemisphere (of Earth), today marks the Winter Solstice. Most people have some understanding that this means today is the day of minimum sunlight, or the longest night of the year. Fewer people, I think, have a good astronomical sense of why that is the case.

So, in honor of the solstice, let's do some old school astronomy. Really old school.

Let's consider the two-sphere cosmos:


To the ancients, it was perfectly reasonable to assume the earth is stationary. (Indeed, it wasn't until Galileo that there was a really persuasive argument that an Earth-in-motion was consistent with various observations we might make, including the fact that a cannonball dropped from the top of a tower would land pretty much at the base of the tower. But that's another story for another day.)

So, their model of the universe put the Earth (shown here as a little blue sphere) at a fixed location right in the middle of things.

The stars in the night sky, which seem to rise and set if you stay up all night to watch them, were fixed on the interior of a really big spherical shell called the celestial sphere (shown here as the bigger sphere outlined in gray). To help keep track of what's where, there is a celestial equator (the circle defined by the intersection of the celestial sphere and the same plane that defines the Earth's equator) and there's a celestial axis you get by extending the line that connects the Earth's North Pole and South Pole.

The celestial sphere does a full rotation on its axis once every 24 hours (give or take; if you're doing astronomy and/or astrology for a king, you might need to be more accurate and more precise than that).

See that orange sphere with rays coming off of it stuck in the celestial sphere? That's the sun. Owing to the fact that it's stuck in the celestial sphere, when that sphere makes its full rotation every 24 hours, the sun goes along with it. (This gives us sunrise and sunset, about which more in a moment.)

However, in this model of things, the sun does not stay stuck in place in the celestial spheres like the fixed stars do (whence the name "fixed stars"). Rather, it creeps along the circle shown here in orchid (that's what the crayon says), a circle called the ecliptic which falls roughly in the middle of the Zodiac constellations. This circle is tilted from the celestial equator at an angle of about 23 o, and the sun travels around it counterclockwise (if you're looking down from the North celestial pole) at a rate of about 1 o per 24 hours.

We should pause here to note that this circuit of the sun around the ecliptic explains why there are some stars we only see certain times of year. All the stars in the immediate vicinity of the sun are going to be rendered invisible to us on Earth by the sun's light.

Now notice that our picture shows two points where the ecliptic and the celestial equator intersect (marked VE and AE). It also shows two positions where the sun is at its maximum distance from the celestial equator (marked WS and SS). Those intersection points indicate where in the ecliptic the sun is during the Vernal Equinox and the Autumn Equinox, respectively. The point on the ecliptic where the sun is at its furthest (towards the North celestial pole) from the celestial equator is the sun's location at Summer Solstice, while the point on the ecliptic where the sun is at its furthest (towards the South celestial pole) from the celestial equator is the sun's location at Winter Solstice.

This labeling, of course, is very Northern Hemisphere-centric. If you're in the Southern Hemisphere, you should feel free to correct the labels accordingly.


This diagram shows the path the sun takes around the Earth in the 24 hour period that includes the Winter Solstice. But to get some idea of what these celestial movements look like to an observer on Earth, we need to get situated. Let's assume a location of approximately 40 o N latitude.


Here, looking straight up into the sky from where you're standing on Earth gives you the line at 40 o to the celestial equator (marked "straight up" in the picture). The plane perpendicular to that (and tangent to where you're standing) is your horizon. You can see the stuff above your horizon, but not the stuff below your horizon.

The solid orange line shows the part of the sun's path, as the celestial sphere turns, that is visible to you because it's above your horizon. As you can see, there's not very much of it. Most of the sun's trip around the Earth on this day is spent facing the Southern Hemisphere (shown with the dotted orange line). That's because it's now summer in the Southern Hemisphere. You'll also notice that the sun's highest point in the sky in the Northern Hemisphere today is pretty darn low in the sky.

The heavy orchid line, on the other hand, shows the part of the sun's path, as the celestial sphere turns, that is visible to you (because it's above your horizon) on the Summer Solstice. Not only does the sun spend more time on the right side of the horizon (assuming you're not a vampire), but at its highest point in the sky that day, it's almost directly overhead.

None of this is meant to convince you to abandon your heliocentric world view. But you can think of relative motions of the sun and the Earth with this two-sphere system and get a pretty good feel for what to expect from the sunrises and sunsets in different parts of the year.

Of course, Eva has a post with a more detailed discussion of the solstice in much more modern terms.

Happy Solstice, whichever one you're celebrating at the moment!

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It always pleases me to see some old-fashioned astronomy -- it reminds how much science those ancient Greeks developed, practically from scratch. BTW, Greek geocentrism was neither unquestioned nor entirely from ignorance. Aristarchus developed a heliocentric model. That work, unfortunately, is lost. The argument against it was valid, if not sound: Greek astronomers realized that if the earth circled the sun, that would cause a parallax. They failed to detect any parallax, the actual parallax being both below their ability to measure. They took this as evidence that the earth was fixed, rather than that the stars were so distant. They were doing solid science, even where they went wrong.

A few more miscellaneous comments. 1) Nice illustrations. 2) is a neat website to look up local solar path, tied to local time, with charts and plots. 3) My previous comment has an extraneous word: the "both" in "the actual parallax being both below."

Nice post!
It's a shame how much of this elementary school stuff I've forgotten :(

I just want drop a quick note of thanks in for remembering those of us from the USA. It's a nice touch. (I've linked your article from my blog in a belated recognition of the solstice in Aotearoa and mentioned this there.)

(I believe Heraclides also postulated that the earth revolved around the sun.)

Happy later solstice!

Just what I was looking for - I tried and failed the other day to work this out for myself

"It's a shame how much of this elementary school stuff I've forgotten :("

Elementary school? I've never been taught any of this.

By Harman Smith (not verified) on 23 Dec 2009 #permalink

It's also interesting to extend the discussion to what happens in the tropics. At the equator, the equinoces are the longest days of the year, while the solstices tie for shortest.

Russell notes that stellar parallax, or the lack of it, was an argument for a geocentric world, which is true so far as it goes. But the story goes on from there, even without getting out of antiquity.

If you know your Euclid(!) you know that the parallax effect depends in a computable way from the size of the sphere of fixed stars: if the stars are far enough away, the effect will be too small to observe. Hence, the lack of observable parallax is not an argument against a Sun-centered arrangement unless you assume that the Universe just can't be all that big.

In fact Archimedes talks about the point. In the Sand Reckoner he needed a reasonable upper bound for the size of the universe, in order to be sure he was filling the whole thing with sand; and in case Aristarchus was right about helicentrism, he needed a size that would make stellar parallax undetectable. So he worked out such a size according to the best information available, to accommodate this and other arguments. This he did, almost offhand, in the process of solving another problem, which was to show that you can represent any quantity, no matter how large. Never underestimate Archimedes!

That seems to make a lot of people, up to and beyond Tycho Brahw, pretty unreasonable and narrow-minded in not even considering whether the cosmos could be very large. However, they were less unreasonable than you might think, and I did think for a time. If you look at the fixed stars, they seem to have some finite size, some optical diameter, not just being "point sources". Estimate that, accept some limit on the actual size of a star, and you can figure out the maximum distance to the stars, and it's not big enough to make parallax invisible. Of course, the stars are in fact point sources for the eye and for any optical telescope, but what with the atmosphere and our eyes, it took a while to figure that out.

Sorry about the length of all this, but it's amazing how complicated these simple controversies can turn out to be.

By Porlock Junior (not verified) on 27 Dec 2009 #permalink