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"I have considered the days of old and the years that have past" and "Whilst Phoebus on me shines then view my shade and lines" are the two inscriptions on the sundial at the University of Limerick. If you've never come across it, it can be found near the entrance to the Stables Courtyard. Walk up to the sundial at 3 o'clock on a sunny afternoon and it'll read one-thirty, or maybe some other time. Yet, if you know how to use it, you will find it to be more accurate than your watch.
The reason for this apparent paradox will, I hope provide you with a fascinating insight into the motion of the Earth itself, and will certainly provoke some thought into how we measure time. What is a day? 24 hours you may say, but this only tells us how we divide the day into smaller units - it doesn't provide a definition. There are in fact several types of day; what most people call a 'day' is officially the Mean Solar Day. Unfortunately, the sundial measures the actual Solar Day. We can also have a Sidereal Day.
Consider the following experiment: one night you point a telescope at a bright star and when the star is in the centre of the telescope view, you take a note of the time. For convenience, we'll assume the time is exactly midnight. Now you leave the telescope untouched until the next night when you again observe the same star and note the time at which it returns to the centre of the telescope view.
In this experiment, you have measured the time taken for the Earth to make one complete rotation on its own axis. "24 hours" you may again say, but this is not correct. The star would return to the same apparent position in the sky at 4 minutes to midnight (approx.). What has been measured here is the Sidereal Day (sidereal means 'by the stars')[1].
To get closer to what we normally mean by a day, we need to measure the Solar Day, which really means repeating the above experiment, not with a distant star, but with the Sun (Remember never to look at the Sun through any optical instrument, especially a telescope, which collects light and will cause permanent vision damage if used to view the Sun). Alternatively, we could use a Sundial. There are many different designs for sundials, but they all have some element to cast a shadow (this element is called the "GNOMON", and a flat surface onto which the shadow falls. The flat surface is graduated in hourly divisions. In the case of the University sundial, the Gnomon is a metal rod oriented to be parallel to the Earth's axis. The benefit of this arrangement is that the graduated surface has hourly divisions equally spaced about the central gnomon. For the more traditional sundial which have essentially vertical gnomons, the hourly markings are irregularly spaced.
To use the Sundial to measure the
Solar Day, we simply need to mark
the position of the Sun's shadow at
some convenient time. then note
the time at which the shadow
returns to the same point the next
day. You will appreciate that the
most difficult part of this experiment
is the acquisition of two consecutive
sunny days.
Measuring the Solar Day in this way
still does not yield the figure of 24
hours as you would expect. During
our northern hemisphere winter, the
measurement would yield more
than 24 hours, and during the
summer, slightly less. It would of
course be very inconvenient to
have a day whose length varied
throughout the year. For a start,
students would insist that all exams
be held in the winter! In practice, we
use an average figure. not
surprisingly called the Mean Solar Day."But" you may ask, "surely the Earth rotates on its axis at a steady rate, so how can the Solar day vary?" Here is where the story gets very interesting, and we must delve into the realms of Astronomy. The earth does rotate on its axis at a very precise rate - it is the Earth's motion around the Sun which causes the solar day to vary.
The earth's orbit around the Sun is not circular, but is an ellipse. The departure from a circle is greatly exaggerated in this diagram. The physics of this orbital motion is such that, if the Earth travels from A to B in the same time as the time taken to travel from C to D, then the two shaded areas FAB and FCD are equal. Since the Earth is closer to the Sun while travelling A to B, then angle Sl will be greater than S2. This is very important in our understanding of the sundial. Incidentally, the Earth is closest to the Sun during our (northern hemisphere) winter - at about the time of the winter solstice and in 11,000 years time ... but that's another story. In position X, the Sun is at a certain position in the sky (let's call it overhead for convenience) at noon as viewed from point P. In position Y, point P, due to Earth's rotations, becomes point Pl after 1 Sidereal Day (remember?), but the Solar Day is not complete until the Earth has rotated through the additional angle d, whereupon P becomes P2, and the Sun is again overhead. This additional time, approximately 4 minutes, is the difference between the Sidereal and Solar Days. However, d is not a fixed angle. Remembering figure 1, you will see that d is greater when the Earth is closer to the Sun, and so more time is required for the Earth to rotate through the extra angle d, resulting in a longer-than-average Solar day.Similarly, when the Earth is in the C D region of its orbit, the Solar Day is shorter than average. Notice that I have shown the Earth moving round the Sun in an anti-clockwise sense, and the Earth's rotation on its own axis as also being anti-clockwise. This is what an observer in space would see if he/she (or it) were looking down on the North Pole.
At this point I want to take the liberty of digressing from the sundial to talk about a little bit of Astronomical history in association with planetary orbits. I think you'll find it worthwhile.
We are all fairly familiar with gravity and have some sort of appreciation that it is gravity which keeps the Earth (and all other planets, of course) in orbit around the Sun.
The gravitational force of attraction
between the Earth and the Sun is
precisely that required to maintain
the Earth's near circular orbit
(remember centrifugal force?). We
haven't always understood this, of
course. The astronomer Johannes
Kepler (1571-1630) first stated his
3 laws of planetary motion in the
early 1600's. These laws were
empirical, based on the
observations of Kepler and Tycho
Brahe. Laws 1 and 2 are:
We've already met these laws in this article. Kepler's 3rd law related the mass of the planet to the length of its year (i.e. time to orbit the Sun once) . The formulation of these laws, based entirely on observation of the planets from Earth with simple instruments (about as good as a good pair of binoculars) was a magnificent accomplishment, and represented one of the high points in Astronomy. But the pinnacle was to come with Newton (1642 -1727) generally regarded as the greatest physicist of all time.
Following the apple falling incident, when Newton saw an apple fall to the ground and wondered why the Moon didn't behave in a similar fashion, he set about establishing the mathematical and physical basis for what we now know as Newton's law of gravitation. This was no mean feat. He needed to prove, for example, that as far as the gravitational attraction of the Sun acting on the Earth is concerned, the mass of the Sun acts as if it were all concentrated a a point at its centre. For this proof alone, Newton was required to 'invent' a new form of mathematics which we now call calculus. It took him 20 years to do this. Applying his laws to planetary motions, he was able to prove Kepler's empirical laws. Kepler's laws don't apply just to the Sun and Earth, but with minor modifications, to any object in orbit about any other.
Back to the sundial. We've seen how the Solar Day varies because of the Earth 's elliptical orbit. The magnitude of the variation is up to 30 seconds per day and is cumulative. Thus, suppose you noted that the Sun was overhead at noon exactly (by your watch) on one particular day in the summer. Next day, the Sun would be overhead at 30 seconds before noon (we're at the C-D point in Fig. 1 ) and the following day it would be there 1 minute 'early'. This error between the Mean Solar Day (from the watch) and the Actual Solar Day (from the Sun) is called the Equation of Time. The Equation of Time (EOT) is thus a fundamental correction factor which must be used to correct the Solar Time, as measured by a sundial, to Mean Solar time, as measured by a watch. Table 1 gives figures for the equation of time. On the University sundial, these figures are conveniently given in the form of a graph on the pedestal.
Everything I've said up until now applies to all sundials However, for the UL sundial, there are two other factors to be considered. First, there is the fact that the sundial is not located on the Greenwich meridian, yet it was constructed as a Greenwich sundial This is obviously important since, even if the Sun is overhead on the Greenwich meridian exactly at noon it will not be overhead here (i e. in Limerick) until 34 minutes later, Limerick being some 10º west of Greenwich. Because of this, we must add 34 minutes to any time measurement made with the sundial.
This is a fixed 34 minutes. Secondly, there is Summer Time (ST) to consider. This applies during the summer months when the sundial is more likely to be usable. ST means simply that your watch is registering time as one hour later than it should be.
So let's see an example of the
sundial in real use.
On July 4th I measure the time on
the sundial as 1.30 pm exactly.
Proceed as follows:
There is another unusual effect associated with the Equation of Time. Att the Winter Solstice (Dec. 23rd), the number of daylight hours is minimum because the sun is above the horizon for the shortest time (colloquially named the Shortest Day). After Dec. 23rd, it would be expected that the Sun would rise eariler and set later as the number of daylight hours increases, but this is not so if we measure the times of sunrise and sunset by our watches (i.e. using Mean Solar Time). The Sun in fact continues to rise later in the morning until the end of the year, though it does not set later in the day as expected.
Our old friend EOT is responsible. Remember that during our winter, the Earth is closest to the Sun, so, each day, the angle x (see fig. 2) is greater than the mean, and the Sun lags behind our watches. This is equivalent to saying that the Sun is late in rising (who isn't in winter?), and this lateness is, you will recall, cumulative. 1/2 minute late the first morning, 1 minute late the second morning, and so on. After December 23rd when we would be expecting the Sun to be rising earlier, this EOT effect dominates for about 7 days so that the Sun appears to rise later up until 1st Jan approximately. The total number of daylight hours must increase, since the Sun is higher in the sky, so the Sun is setting later than expected.
Phil Samways is an Analog Devices Research Fellow and lecturer in Electronic and Computer Engineering at UL. His research interest is in image and vision processing. He is a keen astronomer.