Turning the corner

Several years ago, while visiting my friend Kaleem in Houston, I was afforded my first (and, to this day, only) opportunity to step inside a mosque. Our purpose for our visit was that Kaleem wanted to participate in the mosque's evening prayer, and I would get a chance to see his place of worship.

While Kaleem and his fellow mosque-goers prayed, I, the infidel, remained in the mosque's entry hall, examining the various bulletins and postings on the walls and otherwise biding my time. The bulletins were all pretty typical “church” sorts of stuff, with various community notices and the like, until I saw a chart of sunrise and sunset times for the whole year. My interest piqued.

Muslim prayer times are scheduled according to the sun's position, with one of the daily salah prayers taking place at sunrise and another taking place at sunset. Thus, it's handy for a Muslim to have available a chart of sunrise and sunset times so that he can plan his day more easily. I found the chart handy because I noticed a peculiar detail I had never before realized about our earth: the earliest sunset of the year occurs (in the Northern Hemisphere) weeks before the winter solstice, and the latest sunrise occurs weeks after the solstice. I.e., sunrises and sunsets are not symmetrical over the moment of the solstice. Why is this?

Tomorrow, in Phoenix, as in most timezones in the Northern Hemisphere, is this year's winter solstice. You can get into the winter mood and stump many of your friends at the same time by asking when the earliest sunset and latest sunrise occurs in the year. Some will probably not believe you initially when you factually and correctly answer that the earliest sunset occurred in the first week of December and many will probably not believe you when you state that the latest sunrise of the year occurred over eleven months ago (i.e., during the first week of January), but there you have it. But why?

Answering this question takes the asker on a wonderful trip of examining how our world hurls through space. As most people know, most of the length of a day is determined by the axial tilt of the planet away or towards the sun. During summer, one's hemisphere tilts towards the sun, and the days are long. During winter, the hemisphere tilts away from the sun, and the days are short. So far, so good. But why don't sunrises and sunsets match up precisely with day lengths?

The answer is that there are additional factors. Mainly, there's one additional factor that matters at the scales we care about, and that's the distance from the earth to the sun. Causing no end of confusion and frustration to the ancients, the earth does not orbit the sun in a perfect circle but instead follows an elliptical orbit whereby the earth happens to be nearest to the sun during the Northern Hemisphere's winter and farthest from the sun during the Northern Hemisphere's summer. (The earth is nearest and farthest from the sun at its perihelion and aphelion, respectively, with the perihelion occurring in the first week in January and the aphelion occurring in the first week in July—so close to the solstices.)

What matters for timekeeping here on earth is that the earth moves through space fastest (relative to the sun) at its perihelion and slowest at its aphelion, just as a comet zips quickly around the sun at its perigee and dawdles in the cold of space at its apogee, just as a baseball thrown high in the air moves fastest when it is nearest to the ground and slowest at the top of its arc. But while comets have highly elliptical orbits and change speeds drastically, the earth's orbit is much less eccentric, with the result that the difference between the fastest and slowest of the earth's orbital velocities is only about 3%. But what does this have to do with timekeeping?

There's another great question, related to all this, with which to stump your friends: how many times does the earth rotate in a given year? The obvious answer is 365 rotations with 366 on leap year—i.e., the number of days in a year. However, the correct answer is 366 rotations with 367 on leap year; one rotation is “lost” during the earth's revolution around the sun. You can act this out to see for yourself by finding some object, such as a chair or tree, with cleared space all around it to play the part of the sun and you, walking fully around the object, to play the part of the earth. Only, walk such that you always face one direction, say north. After completing one revolution around the sun, you will have rotated exactly zero times, though you will have simulated one day/night cycle because part of the time you will have faced the sun and part of the time you will have faced away from the sun. Thus, the number of rotations a planet undergoes is always one greater or fewer by one than the number of noons or midnights that that planet experiences; in the earth's case, it happens to be one greater.

What this has to do with timekeeping and sunrises and sunsets is that while the earth takes a fixed amount of time to complete one full rotation, it takes a variable amount of time to complete what we observe as a day—except that nowadays we define a day to be 24 hours long. The length of a solar day, the amount of time between the sun being at its highest point in the sky from one day to the next day, varies by up to a few minutes throughout the year, depending on one's latitude. During the Northern Hemisphere's winter solstice, the solar day is a little longer. Thus, both the sunrise and sunset are each offset a little later, as measured by a 24-hour clock, than they would be otherwise, if the earth orbited along a perfect circle. Thus it is that the sunrises and sunsets don't match up precisely with the day lengths.

The practical effect of this is that while tomorrow marks the year's winter solstice (for the Northern Hemisphere) and the shortest day of the year, we have about another two weeks to go before arriving at what I think of as the more significant of the astronomical events—what I call “turning the corner”, the day of the latest sunrise. Only after that day, occurring in the first week of January each year here in Phoenix, do my morning bicycle rides begin lighting up a little brighter each day.