Full moon and equinox

Two images of last night's full moon appear below. One was taken a few minutes before the equinox; the other was taken a few seconds after it. Can you tell which is which? (Hint: the moment at which the equinox occurs has no bearing on the appearance of the moon.) At the time these pictures were taken, the sun was on the opposite side of the earth. The moon was about 6 hours shy of full (which occurred officially at 5:18 a.m. EDT this morning), but close enough that it would take a trained eye to tell that it's not quite all the way there. If you look really, really closely at the south polar region, you can see some sharper relief there than elsewhere. And if you compare the two images long enough, you might be able to convince yourself that the second image shows a little bit less relief than the first, but it might just be a trick of the scale (I wasn't able to get the images to the exact same scale in Photoshop) or of the focus (the second one is slightly "softer" than the first one). If that's enough to convince you that the second shot was taken some 15 minutes after the first, bravo! Me, I went by the time stamp in the image metadata. I stayed up late to get these shots, though, because of what was happening on the other side of the earth at the time: the center of the sun's disk was crossing an imaginary plane projected up from the earth's equator. In other words,the equinoctial point was being passed. You might notice that, in the northern hemisphere, the sun will now rise slightly to the south of east, more and more each day. And it will set slightly to the south of west, more and more each day. Until right around December 20 at 11:44 EST, when the center of the sun's disk will reach about 23.5° S, appear to pause for a little while, and then head back north. This will be the solstice, a word which comes to us from the Latin solstitium, which, loosely translated, means "the sun stands still." The sun won't actually be pausing in its motion, of course, because it isn't moving. (At least, its apparent motion across our sky is not at all correlated with the direction of its travel through space.) We are the ones moving, and we will have swung around to the point in our orbit where we perceive the sun as reversing its course. I was motivated to take these pictures because it's fairly unusual that the full moon falls this close to equinox; the odds of that happening are pretty long. After all, the equinox can happen on any of the 29.5 days of lunation, and there are only two equinoxes a year. Throw in the solstices, and that's still only four times a year that the moon has a shot at being full at a particularly exciting moment. I'm sure there's a way to calculate the closest full moon to an equinoctial or solstitial moment, but I don't know how to do it. Anyone out there know how? And, as usual with these full moon posts, here are all the full moons of 2010:

September equinox around the corner

The September equinox is just around the corner. This year it happens at 11:09 PM EDT on September 22. I wrote about the problem of equating "equal day and night" with the date of the equinox last year, and rather than repeat myself, I just link to that article. Suffice to say here that, because our Sun, unlike all the other stars in the universe, is not a point source of light, not many places on Earth experience equal lengths of day and night precisely on the date that the geometric center of the Sun's disk is above the horizon for 12 hours everywhere on earth. Why is our Sun so different from all the other stars in the universe? Simple geometry. (You don't even need trigonometry for this one.) We are close enough to it that we can see it as a disk (but please don't look directly at it without taking the proper precautions!); all the other stars are trillions and trillions of miles away. (By the way, don't buy a telescope that tells you it can show you objects "billions" of miles away; you won't even make it outside our solar system with that thing!)

March equinox

Today, at approximately 1:32 p.m. EDT, the Sun will be on the celestial equator, in the constellation Pisces. It will then be at the position known as the first point of Aries. (Makes sense, right? If you're in Pisces, you pretend to be in Aries. Chalk this one up to the effects of precession.) Here is an illustration from Wikipedia of the orientation of the Earth relative to the Sun's rays on the equinox: This alignment occurs, not because the Earth's axis is any more or less tilted than it ever is (23.5 degrees from the ecliptic plane), but because the Sun's position is at the intersection of the ecliptic and the celestial equator. Starting tonight, the Sun will set slightly north of due west; just how far north it will go depends on your distance from Earth's own equator. It will move 23.5 degrees to the north, when, at the June solstice, it will have reached its ascending node and start descending to the south. Even though the term equinox is derived from the Latin for "equal night," the lengths of day and night are NOT equal on the equinoxes. This is due to two easily observable phenomena:
  1. The Sun is not a point source of light.
  2. Atmospheric refraction changes the apparent position of the Sun relative to your horizon.
For more on this, see my post about the September equinox.

September Equinox

Today, at 5:18 p.m. EDT, the sun will cross the celestial equator in the constellation Virgo. Often called the autumnal equinox, I prefer to name it by month, since neither South Florida, nor the Southern Hemisphere, experiences autumn in September. (I must admit, though, that the phrase autumnal equinox has a much more mellifluous sound, and is much more satisfying to say, than September equinox. Tennyson, though not an astronomer, would probably agree.)
The celestial equator. Image from NASA

The celestial equator. Image from NASA

On this day, the sun rises directly in the west, and sets directly in the east. Tomorrow, the sun will rise and set slightly to the south of west. Yesterday, it rose and set slightly to the north of west. This is NOT the day of the year when day and night are the same length, despite the opinions of many learned people (geographers included!) to the contrary. The reason for this is that sunrise and sunset are defined by the edges of the sun's disk first appearing (at sunrise) and last disappearing (at sunset). No matter where you are on Earth, it takes some amount of time for the sun to rise, although that time varies with the angle of the sun's path and your position relative to the equator. So, say sunrise occurs at 7:09 a.m., as it does in Boca Raton today. That means that the leading edge of the sun's disk can be seen at 7:09 a.m. The center of the sun will be visible a minute or two later, and the full disk won't clear the horizon for another few minutes more. The same process happens in reverse at sunset: it takes a few minutes for the sun to disappear after its leading edge hits the horizon, and the sun hasn't officially set until it can no longer be seen. That is, at 7:17 p.m. (You can look up sunrise and sunset times for your location at the US Naval Observatory's website. Remember to correct for daylight saving time, which will be in force in most locations at this time of year.) Got it? Good. Now add in another wrinkle. In the morning, you see the leading edge of the sun's disk BEFORE it appears over the horizon. And at sunset, you see the trailing edge of the disk AFTER it has already "physically" disappeared behind the curve of the earth (assuming you have an unobstructed view of each horizon). But, because of the refraction of the sun's rays caused by traveling through miles and miles of Earth's atmosphere, the apparent position of the sun and its astronomical position are not in sync. Sunrise and sunset both occur when the sun is "actually" about one sun diameter below the horizon. So, because the sun, unlike the "fixed stars," is not a point source of light, we have two separate effects that add up to the difference between "equal night and day" and the day the sun crosses the celestial equator (the equinox). Here is some non-garbage from Wikipedia about the phenomenon:

Due to Earth's axial tilt, whenever and wherever sunset occurs, sunset is always to the northwest from the March equinox to the September equinox, and to the southwest from the September equinox to the March equinox. Sunsets occur precisely due west on the equinoxes, and the duration of day and night are approximately equal on the equinoxes for all viewers on Earth (precisely 12 hours if measured from the geometric (unrefracted) centre of the sun).

As sunrise and sunset are calculated from the leading and trailing edges of the sun, and not the centre, the duration of "day" is slightly longer than "night". Further, because the light from the sun is bent by the atmospheric refraction, the sun is still visible after it is geometrically below the horizon.

You have to read it carefully to notice it: day and night are NOT equal on the equinox, except by definition. They would be equal if the sun were a point source of light, or if the center of the disc rose before the edges, but it isn't, and it doesn't. Man does not live by definition alone. In Boca Raton, where I live, the day with equal lengths of night and day is September 27 this year, only 5 days after the equinox.

Happy equinox!

The September equinox arrives today at one minute before noon, Eastern Daylight Time. One technical definition of the equinox (from the U.S. Naval Observatory) is that day when the geometric center of the Sun's disk passing through the equator, with that point appearing above the horizon everywhere on Earth for 12 hours. Another definition, one that I like a little bit better, is "the date when the Sun crosses the celestial equator moving southward in the Northern hemisphere." One thing many people (including geographers, who really ought to know better) fail to understand is that the astronomical equinox does not mean that all regions on Earth have exactly 12 hours of daylight and 12 hours of dusk/dark. The reason for this, according to the U.S. Naval Observatory, is twofold: one, the Sun is not a simple point source of illumination: it has discernible width, and it takes a little while for it to rise or set. Now, because sunrise is defined as first contact (the moment the leading edge of the sun appears above the horizon) and similarly, sunset is defined as last contact (the moment the trailing edge of the sun disappears below the horizon), and because the Sun is not a point source of illumination (it has discernible width: a full half-degree across it measures, same as the full moon--the reason we can have total solar eclipses), it takes a measurable amount of time for the entire disk to appear and disappear. Therefore, there are usually about 12 hours and 6 minutes of daylight on the equinox at the equator, and even longer at the poles, where it takes the sun longer to rise and set, because it's rising and setting at an angle. The second reason day length is greater than 12 hours at the astronomical equinox is atmospheric distortion: when the Sun is low on the horizon, Earth's atmosphere bends the light of the sun a little bit. Just enough, in fact, so that the actual moment of astronomical sunrise at any given location is AFTER the Sun is visible from that location. The same thing happens when the sun sets: the sun disappears from view AFTER it has actually set, because the light rays traveling through Earth's atmosphere bend them just enough. Nevertheless, the equinoxes mark the astronomical ends of summer and winter, respectively, and the beginnings of the transitional seasons. But we shouldn't call them vernal and autumnal equinoxes, because, even though there is twice as much of Earth's land mass in the Northern Hemisphere as in the Southern, it's not fair to those who live in the oceanic hemisphere to call their autumnal equinox a vernal one, and vice-versa. There seems to be a much smaller tradition of partying at the equinoxes than there is at the solstices. Midwinter and Midsummer (Shakespeare's fantasy play takes place on the solstice, actually, not the "true" middle of summer, which would be in late July or early August) have a much wilder history than Michaelmas and the Ides of March (Walpurgisnacht doesn't count, because it comes about midway between equinox and solstice). One obvious exception to this, of course, is the hebraic tradition of the high holy days at the end of September. (Unlike some other lunar-based calendars, the Jewish calendar keeps the new year at about the same time of the astronomical year, although it's rarely on the equinox.) And this lack of partying at the equinox only makes sense; it's far better to party on the shortest and longest nights of the year, when there's little else to do. In the spring, people are too busy getting ready for the planting season to think about partying. And in the fall, people are too busy getting the harvest in to have much more than a cursory celebration. Now, after the harvest's in, that's a different story...