There is no astronomical reason why Moon and Sun should fit so well. It is the sheerest of coincidence, and only the Earth among all the planets is blessed in this fashion. Indeed, if it is true, as astronomers suspect, that the Moon's distance from the Earth is gradually increasing as a result of tidal friction, then this excellent fit even here on Earth is only true of our own geologic era. The Moon was too large for an ideal total eclipse in the far past and will be too small for any total eclipse at all in the far future.

Of course, there is a price to pay for this excellent fit.

The fact that the Moon and Sun are roughly equal in ap parent diameter means that the conical shadow of the Moon comes to a vanishing point near the Earth's surface.

If the two bodies were exactly equal in apparent size the shadow would come to a pointed end exactly at the One degree equals 60 minutes, so that both Sun and Moon are about half a degree in diameter.

Earth's surface, and the eclipse would be total for only an instant of time. In other words, as the Moon covered the last sliver of Sun (and kept on moving, of course) the first sliver of Sun would begin to appear on the other side.

Under the most favorable conditions, when the Moon is as close as possible (and therefore as apparently large as possible) while the Sun is as far as possible (and there fore as apparently small as possible), the Moon's shadow comes to a point well below the Earth's surface and we pass through a measurable thickness of that shadow. In other words, after the unusually large Moon covers the last sliver of the unusually small Sun, it continues to move for a short interval of time before it ceases to overlap the Sun and allows the first sliver of it to appear at the other side. An eclipse, under the most favorable conditions, can be 71/2 minutes long.

On the other hand, if the Moon is smaller than average in appearance, and the Sun larger, the Moon's shadow will fall short of the Earth's surface altogether. The small Moon will not completely cover the larger Sun, even when both are centered in the sky. Instead, a thin ring of Sun wilt appear all around the Moon. This is an "annular eclipse" (from a Latin word for "ring"). Since the Moon's apparent diameter averages somewhat less than the Sun's, annular eclipses are a bit more likely than total eclipses.

This situation scarcely allows astronomers (and ordinary beauty-loving mortals, too) to get a good look, since not only does a total eclipse of the Sun last for only a few ,minutes, but it can be seen only over that small portion of the Earth's surface which is intersected by the narrow shadow of the Moon.

To make matters worse, we don't even get as many eclipses as we might. An eclipse of the Sun occurs whenever the Moon gets between ourselves and the Sun. But that happens at every new,Moon; in fact the Moon is "new" because it is between us and the Sun so that it is the op posite side (the one we don't see) that is sunlit, and we only get, at best, the sight of a very thin crescent sliver of light at one edge of the Moon. Well, since there are twelve new Moons each year (sometimes thirteen) we ought to see twelve eclipses of the Sun each year, and sometimes thirteen. No?

No! At most we see five eclipses of the Sun each year (all at widely separated portions of the Earth's surface, of course) and sometimes as few as two. What happens the rest of the time? Let's see.

The Earth's orbit about the Sun is all in one plane.

That is, you can draw an absolutely flat sheet through the entire orbit. The Sun itself will be located in this plane as well. (This is no coincidence. The law of gravity makes it necessary.)

If we imagine this plane of the Earth's orbit carried out infinitely to the stars, we, standing on the Earth's surface, will see that plane cutting the celestial sphere into two equal halves. The line of intersection will form a "great circle" about the sky, and this line is called the "ecliptic."

Of course, it is an imaginary line and not visible to the eye. Nevertheless, it can be located if we use the Sun as a marker. Since the plane of the Earth's orbit passes through the Sun, we are sighting along the,plane when we look at the Sun. The Sun's position in the sky always falls upon the line of the ecliptic. Therefore, in order to mark out the ecliptic against the starry background, we need only follow the apparent path of the Sun through the sky. (I am referring now not to the daily path from east to west, which is the reflection of Earth's rotation, but rather the path of the Sun from west to east against the starry background, which is the reflection of the Earth's revolution about the Sun.)

Of course, when the Sun is in the sky the stars are not visible, being blanked out by the scattered sunlight that turns the sky blue. How then can the position of the Sun among the stars be made out?

Well, since the Sun travels among the stars, the half of the sky which is invisible by day and the half which is visible by night shifts a bit from day to day and from night to night. By watching the night skies throughout the year the stars can be mapped throughout the entire circuit of the ecliptic. It then becomes possible to calculate the position of the Sun against the stars on each particular day, since there is always just one position that will account for the exact appearance of tile night sky on any particular night.

If you prepare a celestial sphere-that is, a globe with the stars marked out upon it-you can draw an accurate great circle upon it representing the Sun's path. The time it takes the Sun to make one complete trip about the ecliptic (in appearance) is about 3651/4 days, and it is this which defines the "year."

The Moon travels about the Earth in an ellipse and there is a plane that can be drawn to include its entire orbit, this plane passing through the Earth itself. Wien we look at the Moon we are sighting along this plane, and the Moon marks out the intersection of the plane with the starry background. The stars may be seen even when the Moon is in the sky, so that marking out the Moon's path (also a great circle) is far easier than marking out the Sun's. The time it takes the Moon to make one complete trip about its path, about 271/3 days, defines the "sidereal month" (see Chapter 6).

Now if the plane of the Moon's orbit about the Earth coincided with the plane of the Earth's orbit about the Sun, both Moon and Sun would mark out the same circu lar line against the stars. Imagine them starting from the same position in the sky. The Moon would make a complete circuit of the ecliptic in 28 days, then spend an additional day and a half catching up to the Sun, which had also been moving (though much more slowly) in the interval. Every 29'h days there would be a new Moon and an eclipse of the Sun.

Furthermore, once every 291/2 days, there, would be a full Moon, when the Moon was precisely on the side op posite to that of the Sun so that we would see its entire visible hemisphere lit by the Sun. But at that time the Moon should pass into the Eartb's shadow and there would be a total eclipse of the Moon.

AR this does not happen-every 291/2 days because the plane of the Moon's orbit about the Earth does not coincide with the plane of the Earth's orbit about the Sun. The two planes make an angle of 5'8' (or 308 minutes of arc) '

The two great circles, if marked out on a celestial sphere would be set off from each other at a slight slant. They would cross at two points, diametrically opposed and would be separated by a maximum amount exactly half way between the crossing point. (The crossin2 points are called "nodes," a Latin word meaning "knots")

If you have trouble visualizing this, the best thing is to get a basketball and two rubber bands and try a few ex periments. If you form a great circle of each rubber band (one that divides the globe into two equal halves) and make them non-coincident, you will see that they cross each other.in the manner I have described.

At the points of maximum separation of the Moon's path from the ecliptic, the angular distance between them is 308 minutes of are. This is a distance equal to roughly ten times the apparent diameter of either the Sun or the Moon. This means that if the Moon happens to overtake the Sun at a point of maximum separation, there will be enough space between them to fit in nine circles in a row, each the apparent size of Moon or Sun.

In most cases, then, the Moon, in overtaking the Sun, will pass above it or below it with plenty of room to spare, and there will be no eclipse.

Of course, if the Moon happens to overtake the Sun at a point near one of the two nodes, then the Moon does get into the way of the Sun and an eclipse takes place.

This happens only, as I said, from two to five times a year.

If the motions of the Sun and Moon are adequately analyzed mathematically, then it becomes easy to predict when such meetings will take place in the future, and when they have taken place in the past, and exactly from what parts of the Eaith's surface the eclipse will be visible.

Thus, Herodotus tells us that the Ionian philosopher, Thales, predicted an eclipse that came just in time to stop a battle between the Lydians and the Medians' (With such a sign of divine displeasure, there was no use going on with the war.) The battle took place in Asia Minor some time after 600 B.c., and astronomical calculations show that a total eclipse of the Sun was visible from Asia Minor on May 28, 585 B.c. This star-crossed battle, there fore, is the earliest event in history which can be dated to the'exact day.

The ecliptic served early mankind another purpose besides acting as a site for eclipses. It was an eternal calendar, inscribed in the sky.

The earliest calendars were based on the circuits of the Moon, for as the Moon moves about the sky, it goes through very pronounced phase changes that even the most casual observer can't help but notice. The 291/2 days it takes to go from new Moon to new Moon is the "synodic month" (see Chapter 6).

The trouble with this system is that in the countries civilized enough to have a calendar, there are important periodic phenomena (the flooding of the Nile, for in stance, or the coming of seasonal rains, or seasonal cold) that do not fit in well with the synodic month, There weren't a whole number of months from Nile flood to Nile flood. The average interval was somewhere between twelve and thirteen months.

In Egypt it came to be noticed that the average intervals between the floods coincided with one complete Sun-circuit (the year). The result was that calendars came to consist of years subdivided into months. In Babylonia and, by dint of copying, among the Greeks and Jews, the months were tied firnay to the Moon, so that the year was made up sometimes 'of 12 months and sometimes of 13 months in a complicated pattern that repeated itself every 19 years. This served to keep the years in line with the seasons and the months in line with the phases of the Moon. However, it meant that individual years were of different lengths (see Chapter 1).