Today is the vernal equinox for the Northern Hemisphere, when the Sun crosses the equator and heads into the Northern Hemisphere. It heralds the beginning of spring for the North and the beginning of fall for the South.

According to astronomical predictions, the day should be exactly 12 hours long on the equinox regardless of where you are on the planet. The sun should rise at 6 AM local standard time and set at 6 PM local standard time.

If that’s the case, why was sunrise today at 6:46 AM in Boston and sunset at 6:56 PM? That’s 12 hours 10 minutes, not 12 hours. Furthermore, even if when Daylight Savings Time is taken out of the equation, midday is at 11:51 Standard Time and not 12:00. So what’s going on here?

First things first. Boston is in the Eastern time zone (for now: there are rumors that New England is considering switching to Atlantic Standard Time year round, effectively enshrining Eastern Daylight Time permanently). Since the time zone spans multiple degrees of longitude, the local time matches the time zone time for only one location, at or near the center of the time zone. Boston is not at the the center our time zone: it is in fact about 7 minutes earlier than the center. So we need to adjust for that.

That helps a little but not enough. We still have a day that’s longer than 12 hours, and the sun reaches its zenith at midday a couple of minutes early.

Where do those extra minutes come from? It involves something called the equation of time.

It is well known that Earth orbits the Sun. Most diagrams depict the planet’s orbit as a perfect circle with the Sun at the center. Although this is a good approximation, it in fact is not completely correct. The Earth’s orbit actually traces out an orbit which is an ellipse, with some sections closer to the Sun than others. Earth currently reaches perihelion (the point nearest the Sun) in January — yes, in the middle of our winter — and the point furthest from the Sun in July. These dates change slowly over astronomical time scales as the Earth’s orbit precesses (that is, rotates like the hands of a clock when seen from above the plane of the solar system), but as far as we are concerned they are stationary.

When Isaac Newton explored gravitation, he discovered that planets move faster closer to the Sun than they do further away from the Sun. This even includes situations where the planet’s orbit changes, as is the case with Earth. As a result, one can easily show that the Earth moves further along its orbit in January than it does in July. Seen from the perspective of a human on the planet’s surface, the Sun appears to move further east each day during Boston’s winter than it does in the summer.

It is now time to debunk yet another myth: the claim that the Earth rotates on its axis every 24 hours. If one were to determine the amount of time when Sirius is at its highest in the night sky between one day and the next, you will note that it is not exactly 24 hours: it is in fact roughly 23 hours, 56 minutes. Yet all of the evidence we have seems to indicate that a day is 24 hours exactly. How do we reconcile these?

The answer involves the fact that there are two kinds of time: sidereal time (taken with respect to the background stars) and solar time (taken with respect to the Sun). For all eight planets in our Solar System other than Venus (sorry, Pluto), sidereal days are slightly shorter than solar days.

Why is this? There is an easy way to explain this. Picture an analog clock reading 12:00. The hour hand is on top of the minute hand, and both are pointing at the ceiling. In this analogy, the Sun is the hub at the center, the Earth is the minute hand, and Sirius infinitely far away in the direction of the ceiling, straight up.

To complete a rotation with respect to the stars (the sidereal day), the minute hand has to point straight up again, at Sirius. To complete a rotation with respect to the Sun (a solar day, as in between two noons), the two hands have to overlap again so the bottom of the minute hand faces the center of the clock again.

Since the Earth has moved along its orbit (that is, the hour hand moved) during the time it took the Earth to spin on its axis (the minute hand moving), the two events no longer overlap. The minute hand will point straight up at 1:00, ending the sidereal day, but the minute hand will not overlap the hour hand until about 1:05, ending the solar day. So the solar day is longer than the sidereal day. Note that in the case where the planet orbited in the opposite direction from its rotation axis (which is what Venus does), the solar day would be shorter than the sidereal day.

Why this digression about solar and sidereal time? The reason is thus: the difference between the sidereal day and the solar day depends on how much the Earth as moved along its orbit. And as we noted earlier, the Sun appears to move further in January than it does in July. The more it moves east, the longer the solar day is than the sidereal day.

The 24 hour period we are familiar with assumes that the Sun moves an “average” amount east each day, equivalent to 4 minutes lag. In January, it may move a little more, and in July it may move a little less. What this means, however, is that during January it takes more than 4 minutes to make up the lag between two consecutive noons — when the Sun is in fact overhead. The net result is that if the sun was at its highest point at 12:00 on a certain day in January, it would not reach its highest point a few days later until maybe 12:01 or so because the Sun has moved east more than expected. The Earth has to rotate a little more, 1 minute or so to make up for the excess movement of the Sun and put the Sun at its highest point again.

The net result of all this is that the middle of the day can vary a great deal, by 15 minutes or so either. The variation is such that in late March, our wristwatch based on the “average” solar day of 24 hours is about 2-3 minutes faster than the actual Sun. So actual midday — 11:58 — occurs earlier than what we would have expected.

Note that the equation of time is also responsible for why the earliest sunset and latest sunrise are not on the same date (and vice versa). Why is this? The earliest sunset will occur at the winter solstice, and the length of the day will not be changing much at that point. However, this is near perihelion, so the Sun will move a great deal east in the ensuing 24 hours. This will delay sunrise and sunset for the next day even though the length of the day is shorter. Consequently, you will find the earliest sunset to be after the winter solstice in the Northern Hemisphere and the latest sunrise to be before the solstice.

With the elliptical orbit out of the way, it is time to ponder the last question: why is the day 10 minutes longer than expected? There are two reasons for this.

First, the 12 hour calculations assume that the sun is a point source. Day is defined to be the interval at which any part of the Sun is visible, including a little sliver. The net result is that the day is going to be lengthened by the amount of time it takes for the Sun to appear to traverse its apparent size in the sky, which is about 2 minutes.

That’s fine, but where did the other 8 come from? As it turns out, it comes from the fact that we can actually see the Sun after it has gone below the apparent horizon. The Sun will only disappear after it has fallen several degrees below the horizon. This lengthens the day by a few more minutes.

Why is that? It is due to something called refraction. When light travels through air at sunset, it is reaching you at an angle. In situations like this, it may bend (refract) to follow the deepest parts of the atmosphere between it and you (effectively hugging the surface of the Earth). As a result, sunlight emitted when the Sun is slightly below the horizon is bent back down to the Earth’s surface instead of escaping into space. As a result, the Sun is still visible.

The amount of bending depends on the frequency of the light, and red light tends refract less than blue light (would you believe that photons, the particles carrying light, are about twice as energetic for blue light as for red?). This has several consequences. First, blue light tends to be scattered far away from the Sun during the daytime, resulting in a blue sky and a yellow Sun (fun fact — the yellow is due to the subtraction of the blue light from a star which is in fact white when viewed from space!). The more air between you and the Sun (this can occur at sunset when the light has to travel through more of the lower atmosphere), the more pronounced this effect. The Sun becomes redder and redder, and the rest of the sky becomes deeper and deeper blue.

Refraction has one final effect which is one of the rarest sights man can see: the green flash. Since blue light refracts more than red at sunset, at some point the Sun is too low for the red light to make it to your eye because it can’t bend enough to reach the surface of the Earth. However, the blue can still reach you because it bends more. The net result is that just before the sun disappears, the last piece you see may look bluish or greenish.

So that’s the story of the equinox that isn’t.

The photo above depicts the astronomical clock in Prague, which dates from medieval times. It depicts the location of the Moon and Sun using a complicated series of gears. This photo was taken in October, when the Sun would have traditionally been in the sign of Libra (albeit 2000 years ago: all the zodiac signs are now off by one due to the fact that the Earth’s axis also precesses through one sign every 2000 years or so due to the fact that it is tilted on its axis and behaves like a spinning top in that regard — I won’t get into that here). The Moon’s position is also shown with one of the other hands. The third hand (I believe it overlaps the Sun hand here), points to the actual time of day (9 AM standard / 10 AM at the time as the Czech Republic was using Daylight Savings at that point).