Just a second
Published on Jan 29, 2007 at 2:50 pm.
1 Comment.
Filed under time.
Right at the beginning of first semester physics, we discuss the meaning of various units. One of those units is the second. So, just what is a second?
That turns out not to be so easy to answer. We need to stop and think. A second is 1/60 of minute, and a minute is 1/60 of an hour. So, a second is 1/3600 of an hour. Great. How long is an hour? An hour is 1/24 of a day. Back thousands of years ago, the day and night were each divided into 12 hours. But, the nights are longer than the days in the winter, so that meant that hours were longer at night than during the daytime, and likewise, in the summer, the hours were longer in the daytime than at night. Hmm. That’s not such a good way to do things, since it means that every day of the year, hours would be different day and night, and even from adjacent days! So, we now divide up the day into 24 equal hours. The second is therefore 1/86400 of a day.
But, what is a day? There are multiple ways of defining the term “day.” The sidereal day is one complete rotation of the Earth. But, the Earth moves along its orbit as it turns. That means that if it were noon, one complete rotation wouldn’t be noon again. Instead, you’d have to turn just a shade more (a little under one degree more). That takes about 4 minutes longer. Really, we’d like noon to occur when the Sun is high in the sky. If we just let a day be one rotation of the Earth, then noon would slip about 4 minutes per day, until eventually noon were occurring at dawn, then at midnight, and finally at sunset. Wow, wouldn’t that be confusing! So, we will let a day, what we will call a solar day be the time from when the Sun is highest in the sky until it is highest in the sky again. That will be 24 hours, and a second 1/86400 of that. Oh, but there is another problem. You see, Earth’s orbit is slightly elliptical. It isn’t a huge effect, but it is noticeable. For, you see, the Earth speeds up and slows down as it orbits the Sun in its elliptical orbit. That means that sometimes the Earth must turn just a shade more or a little less past one rotation in order to make a solar day. But, since the rotation of the Earth doesn’t change nearly as much as its orbital speed, that means that the length of the solar day changes a bit over the course of the year. That puts us back into the sort of situation that we had before with the hours changing each day, though with not quite as extreme of a change. Still, it is impracticable to have the clocks speed up or slow down a little each day. So, we take an average value for the length of the day over the course of the year, and thus define a mean solar day. The second will be 1/86400 of that. Oh, but there’s yet another problem. You see, the Earth does change its rotational rate ever so slightly. Part of the change is due to a steady slowing of the Earth’s rotation due to tidal interactions with the Moon. Part of this change is due to conservation of angular momentum as tectonic plates move around, or as convection moves material around inside the Earth. So, again the day changes, and thus the second. So, we define the second to be 1/86400 of the average length of the solar day in the year 1900. This was the definition of the second years ago.
However, it isn’t 1900 any more, and it is difficult to determine exactly the average length of the day in the past. So, a new, more accurate and precise method of measuring a second was needed. Thus was born the atomic clock. The atomic clock is based upon the hyperfine structure of Cesium. The hyperfine structure of an atom refers to the slight difference in energy between electrons in the same energy level and orbital due to their different spins. Because electrons have charge, their spin produces a weak magnetic moment. However, the nucleus of an atom also has charge and spin, and thus a magnetic moment. An electron spin in one direction has slightly more energy than the electron spin in the other direction. Should the electron flip its spin from the high energy state to the low energy state, it would give off some radiation. For Cesium-133, the particular hyperfine transition selected has a frequency of 9,192,631,770 Hertz. In fact, that is how we define second. We define the electromagnetic radiation associated with this transaction to have exactly 9,192,631,770 cycles per second. Since every Cesium atom behaves the same way, then this defines a second. This is the atomic clock.
But, as I said, Earth’s rotation isn’t so exact. So, every now and then, a second has to be added to the clock in order for noon to keep happening at the right time. These “leap seconds” are added as one extra second whenever the accumulated error in the clock gets close to being a second off. It should be noted that routinely adding a second does not mean that the Earth is slowing rotation a second or so every few years. Rather, it is the accumulated effect of the definition of a second now being off by a few billionths. After enough seconds have passed, the error adds up to a whole second.
-Astroprof
Jim Reilly on December 10, 2007 at 5:23 am: 1
Ahh - this particular subject has been really a pain. I was trying to educate myself on the celestial sphere and the ‘day’ tropical/solar sidereal, anomalistic, stellar so I can find catalog items. From the USNO to the IERS they all seem to have different values for a day. At least the second seems to be invariant.