All cultures including our own are well aware of several natural cycles revealed in the heavens. For example, the year is defined as the time required for the Earth to orbit or to revolve about the Sun exactly once; about 365.26 days. (Though the ancients believed incorrectly that the Sun travelled around the Earth instead of the Earth around the Sun, they could still estimate the length of the year quite accurately.) Notice that the length of the year does not contain a whole number of days, but includes the fraction 0.26 which is slightly more than 1/4 of a day. What this shows is that the length of the Earth's "day" and "year" are not related in any way whatsoever. Such randomness is very common in astronomy, though some people are forever trying to find a hidden significance in such numbers.
The month reflects another natural period for the Earth; it is roughly the time for the Moon to cycle through its phases exactly once; just over 29.5 days. The Moon takes about 7 days to go through one-quarter of its cycle from which our week is derived.
The "day" is much trickier to define even though you might think it should be rather simple. Suppose we defined the day as the time required for the Earth to rotate exactly once on its axis. While this sounds reasonable, this is not what we mean by "day" in everyday life! That's where the problem lies.
Before resolving this puzzle, we must become acquainted with a few astronomical terms. Don't worry, these aren't difficult. As you know, the Earth is round (or at least, a sphere) and rotates on its axis which connects the North and South Poles. Now imagine that you're outside at night observing the heavens. Astronomers refer to the point on the sky directly above your head as the Zenith (an Arabic word). Everyone's Zenith is unique. The point on the sky which is directly above the Earth's North Pole is called the North Celestial Pole. Equivalently, the South Celestial Pole is the point directly above the South Pole. These terms are illustrated in the following diagram.
Transparency master [Figure 1]
Now imagine drawing a giant circle on the sky which passes through the Celestial Poles and your Zenith. This is called the Celestial Meridian. What does it signify? It effectively divides your sky exactly in half, separating the eastern half from the western half.
If you are a careful observer of the heavens, you'll know that stars, planets, as well as the Sun and Moon appear to move in a similar fashion across the sky; they appear to rise in the east, get higher in the sky until they reach their maximum altitude on the Celestial Meridian at which point they sink lower and lower, only to eventually set in the west. The fascinating thing is that stars take less time to make two successive crossings of the Celestial Meridian than does the Sun! This is the source of our earlier "problem."
The time between successive crossings by any star of any observer's Celestial Meridian is called a "sidereal day" or literally "star day" (where "sidus" means "star" in Latin). The period between successive crossings of the Sun on any observer's Celestial Meridian is called a "solar day." It is solar time which we refer to in our daily conversations and whose length we measure on our clocks and watches. One solar day contains exactly 24 (solar) hours. One sidereal day, however, is equal to about 23 hours 56 minutes and 4 seconds as measured in solar time. Why is the sidereal day approximately 4 minutes shorter than the solar day (or equivalently, why is the solar day 4 minutes longer than the sidereal), and what effect does this difference have?
The following figure illustrates this effect nicely.
Transparency master [Figure 2]
The Earth is shown here at two places on its orbit separated by exactly one sidereal day (somewhat exaggerated for clarity). The direction of rotation on its axis and of revolution in its orbit about the Sun are marked by arrows. The direction of the Celestial Meridian is indicated by a dashed line in each case. Notice that although the stars have exactly returned to the Celestial Meridian one sidereal day later, it takes the Earth a little longer -- about 4 minutes longer -- before the Sun next crosses the same Meridian in the second position. This is why the Solar day is about 4 minutes longer than the Sidereal.
(For those who are good in geometry, it isn't hard to understand where the 4 minutes comes from. As seen from the Sun, the Earth moves about 1 degree in its orbit each day since it takes the Earth just over 365 days to travel through 360 degrees. You can show that the Earth must rotate through 1 extra degree on its axis to account for the 1 degree it has moved in its orbit in the case of the Solar day. So, if the Earth rotates through 360 degrees on its axis in 24 hours, then it takes 24/360 hours or 4 minutes to rotate through one degree!)
[Can you show that there is exactly one more sidereal day than solar day in the Earth's year; that is, that the year contains 366.26 sidereal days?]
You can now also understand why we have a leap year every four years (or at least nearly every four years). Our calendar obviously can't accommodate fractional days. If we have a year of 365 days, then the extra 0.26 days per year begin to accumulate. In four years, this makes almost exactly one extra day. As a result, our Gregorian Calendar (named after Pope Gregory XIII who initiated much-needed calendar reform in the sixteenth century) adds one extra day, February 29th, to years which are divisible by 4. These are called leap years. Actually, the rule for leap years is more complicated than this. "Century years" -- years divisible by 100 -- must be divisible by 400 in order to be leap years. Otherwise they're not. So, the year 1900 was not a leap year, but the year 2000 will be. It gets even more involved, but let's leave it at that.
It is interesting that while the sidereal and solar days are well defined, they are also not constant in length. The number of seconds in a day is increasing as the Earth ages. Not by much, mind you; about 1/500 of a second per century, though this adds up over millions of years. In other words, the day was shorter in the past, and will be longer in the future. The reason for this has to do with tidal forces exerted by the Moon and Sun on the oceans which gradually slow the Earth's rotation rate.
While the rhythms of astronomical bodies provided clocks which were accurate enough for most societies, they simply aren't precise enough for our highly technical society. This is why scientists have had to find an alternate natural phenomenon on which to base modern time-keeping. The "second" is now our fundamental unit of time and it is defined precisely as the time for a cesium atom to undergo a certain number of vibrations.
You can perform a simple experiment which not only measures (and confirms) the difference between the length of the sidereal and solar day, but determines what effect this has on the appearance of the night-time sky.
[Teachers: while this experiment is not difficult, it takes some preparation to do correctly.
Night after night, a given star will follow the same path across the sky, though appearing in the same location earlier and earlier each night. By accurately measuring the time at which a well identified bright star reaches a certain position in the sky on one evening and repeating the same observation several evenings later, it is possible to determine the length of the sidereal day relative to the solar day.
This project may be carried out at any time during the lunar phase, though darkest conditions will be experienced between third-quarter and new moon. Some ingenuity is called for on the student's part to design an accurate experiment. For example, one might imagine positioning oneself at a south-facing window and timing when the bright star first disappears behind a neighbour's house or chimney (ie., something with a sharp edge). The trick is to orient oneself in the exact same position one week later while making the same measurement. At the very least, the student will have to design a way of positioning his/her head in the same place so that a fair measurement can be made at the later time. One could also imagine setting up a small telescope (with cross-hairs?) in one's room pointed at the sky so that the bright star in question will pass through the field of view. One would, however, have to make sure that the telescope isn't moved in any way during the week, however! No cleaning the room that week!
The watch or clock used to time the occultations should be calibrated against true solar time. Many radio stations issue timing signals periodically during the day. It should be possible for the student to get a result accurate to 10% of the real value over a baseline of one week. The accuracy could be improved by lengthening the baseline, but even more care must be exercised in selecting a star in this case.
Finally, students will appreciate that this difference of 4 minutes per day has the effect of slowly rotating the entire sky such that all (northern) constellations -- the full 360 degrees -- become visible at night at some time during the year. This is why seasonal star charts are necessary; the sky changes from week-to-week and dramatically from month-to-month.
Students should also be aware that on any one day, roughly half the constellations are visible in the night-time sky, while the other half must be present in the day-time sky but are impossible for us to see because of the Sun's tremendous brightness. (During a total solar eclipse, however, these constellations temporarily become visible.) Nonetheless the Sun passes through 12 constellations over the course of the year, about one per month, on its path through the sky which is called the ecliptic. This is shown in figure 3. These 12
Transparency master [figure 3]
constellations are called the Zodiac and are especially important to astrologers, though they have no undue significance for astronomers.
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