For those of you who missed it, yesterday marked the June solstice, the first day of summer. Of course, my children disagree about the "first day of summer" part since they know the first day of summer doesn't really happen until after school is out and here in New York City, the last day of school is June 28.

So just what is the June solstice, beside the basic things "everyone" knows: the first day of summer, the day with the longest sunlit period and shortest night (well, for those of us here in the northern hemisphere)? The soltice, and the equinox, are all about geometry....

To picture the geometry, you have to think about two simple objects: a plane and a line. The plane is the easy part since we can use a sheet of paper. Get out your trusty (or perhaps rusty) compass and draw a circle. This represents the Earth's orbit[1] with the Sun at the center. Next is the line formed by the Earth's rotational axis. Now this is a little tricky because the Earth's rotational axis points out of the plane, up off the sheet of paper. Not straight up. But we can easily draw a line in the plane that represents this by just drawing a line that lies underneath the line formed by Earth's axis. Sound complicated? Well...here's an analogy. You've probably seen guy-lines before, those support ropes or cables attached to towers. Those stick up out of the Earth at an angle. If you imagined yourself in a balloon far above the tower and its guy-line supports, and you try to draw what you see, you'll draw the guy-lines as short lines on the paper, pointing out away from the tower, which might appear as a small round or rectangular structure seen from above. That's what we're doing with the Earth's rotational axis, we're drawing it flat on the paper (plane of Earth's orbit) as seen from way far north of Earth's orbit.

Okay, so we have our two objects: a circle representing Earth's orbit lying in a plane, and a line showing the direction of Earth's rotational axis. But wait! You're wondering what direction the line should point in. It actually doesn't matter. Pick any direction and draw you're line. Here's why it doesn't matter. As the Earth revolves around the Sun, that line is going to always point in the same direction. Whatever direction you picked will correspond to *some* point on the Earth's orbit, that is *some* day of the year. I don't know which day, it depends on what direction you picked. But there are four special days. The two soltices, June and December, correspond to when the Sun is in line with the line. The two equinoxes correspond to the days when that line is perpendicular to a line drawn from Earth to the Sun.

The solstice is all about geometry.

[1] Okay, so you know that the orbit is *really* an ellipse. But the ellipse of Earth's orbit is less out-of-round compared to an ideal circle than the thing you're going to draw with your compass.