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!