Of Time, Space, and Other Things
Part I Of Time And Space 4. The Heavenly Zoo
On July 20, 1963 there was a total eclipse of the Sun, visible in parts of Maine, but not quite visible in its total aspect from my house. In order to see the total eclipse I would have had to drive two hundred miles, take a chance on clouds, then drive back two hundred miles, braving the traffic congestion produced by thousands of other New Englanders with the same notion.
I decided not to (as it happened, clouds interfered with seeing, so it was just as well) and caught fugitive glimpses of an eclipse that was only 95 per cent total, from my backyard. However, the difference between a 95 per cent eclipse and a 100 per cent eclipse is the difference between a notion of water and an ocean of water, so I did not feel very overwhelmed by what I saw.
V-/bat makes a total eclipse so remarkable is the sheer astronomical accident that the Moon fits so snugly over the Sun. The Moon is just large enougb. to cover the Sun completely (at times) so that a temporary night falls and the stars spring out. And it is just small enough so that during the Sun's obscuration, the corona, especially the brighter parts near the body of the Sun, is completely visible.
The apparent size of the Sun and Moon depends upon both their actual size and their distance from us. The diameter of the Moon is 2160 miles while that of, the Sun is 864,000 miles. The ratio of the diameter of the Sun to that of the Moon is 864,000/2160 or 400. In other words, if both were at the same distance from us, the Sun would appear to be 400 times as broad as the Moon.
However, the Sun is farther away from us than the Moon is, and therefore appears smaller for its size than the Moon does. At great distances, such as -those which characterize the Moon and the Sun, doubling the distance halves the apparent diameter. Remembering that, consider that the average distance of the Moon from us is 238,000 miles while that of the Sun is 93,000,000 miles. The ratio of the distance of the Sun to that of the Moon is 93,000, 000/238,000 or 390. The Sun's apparent diameter is cut down in proportion.
In other words, the two effects just about cancel. The Sun's greater distance makes up for its greater size and the result is that the Moon and the Sun appear to be equal in size. The apparent angular diameter of the Sun averages 32 minutes of arc, while that of the Moon averages 31 minutes of arc.
These are average values because both Moon and Earth possess elliptical orbits. The Moon is closer to the Earth (and therefore appears larger) at some times than at others, while the Earth is closer to the Sun (which therefore appears larger) at some times than at others. This variation in apparent diameter is only 3 per cent for the Sun and about 5 per cent for the Moon, so that it goes unnoticed by the casual observer.
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).
The Egyptians and, by dint of copying, the Romans and ourselves abandoned the Moon and made each year equal in length, and each with 12 slightly long months'
The "calendar month" averaged 301/2 days long in place of the 291/2. days of the synodic month. This meant the months fell out of line with the phases of the Moon, but mankind survived that.
The progress of the Sun along the ecliptic marked off the calendar, and since the year (one complete circuit) was divided into 12 months it seemed natural to divide the ecliptic into 12 sections. The Sun would travel through one section in one month, through the section to the east of that the next month, through still another section the third month, and so on. After 12 months it would come back to the first section.
Each section of the ecliptic has its own pattern of stars, and to identify one section from another it is the most natural thing in the world to use those patterns. If one section has four stars in a roughly square configuration it might be called "the square"; another section might be the "V-shape," another the "large triangle," and so on.
Unfortunately, most people don't have my neat, geo metrical way of thinking and they tend to see complex figures rather than simple, clean shapes. A group of stars arranged in a V might suggest the head and homs of a bull, for instance. The Babylonians worked up such imaginative patterns for each section of the ecliptic and the Greeks borrowed these giving each a Greek name. The Romans borrowed the iist next, giving them Latin names, and passing them on to us.
The following is the list, with each name in Latin and in English: 'I) Aries, the Ram; 2) Taurus' the Bull; 3) Gemini, the Twins; 4) Cancer, the Crab; 5) Leo, the Lion; 6) Virgo, the Virgin; 7) Libra, the Scales; 8) Scorpio, the Scorpion; 9) Sagittarius, the Archer; 10) Capricomus, the Goat; 11) Aquarius, the Water-Carrier; 12) Pisces, the Fishes.
As you see, seven of the constellations represent ani mals. An eighth, Sagittarius, is usually drawn as a centaur, which may be considered an animal, I suppose. Then, if we remember that human beings are part of the animal kingdom, the only strictly nonanimal constellation is Libra.
The Greeks consequently called this band of constellations o zodiakos kyklos or "the circle of little animals," and this has come down to us as the Zodiac.
In fact, in the sky as a whole, modem astronomers recognize 88 constellations. Of these 30 (most of them constellations of the southern skies' invented by modems) represent inaniinate objects. Of the remaining 58, mostly ancient, 36 represent mammals (including 14 human beings), 9 represent birds,, 6 represent reptiles, 4 represent fish, and 3 represent arthropods. Quite a heavenly zoo!
Odd, though, considering that most of the constellations were invented by an agricultural society, that not one represents a member of the plant kingdom. Or can,that be used to argue that the early star-gazers were herdsmen and not farmers?
The line of the ecliptic is set at an angle of 231/2 ' to the celestial equator (see Chapter 3) since, as is usually stated, the Earth's axis is tipped 23V2'.
At two points, then, the ecliptic crosses the celestial equator and those two crossing points are the "equinoxes" ("equal nights"). When the Sun is at those crossing points, it shines directly over the equator and days and nights are equal (twelve hours each) the world over. Hence, the name.
One of the equinoxes is reached when the Sun, in its path along the ecliptic, moves from the southern celestial hemisphere into the northern. It is rising higher in the sky (to us in the Northern Hemisphere) and spring is on its way. That, therefore, is the "vernal equinox," and it is on March 20.
On that day (at least in ancient Greek times) the Sun entered the constellation of Aries. Since the vernal equinox is a good time to begin the year for any agricultural society, it is customary to begin the list of the constellations of the Zodiac, as I did, with Aries.
The Sun stays about one month 'm each constellation, so it is in Aries from March 20 to April 19, in Taurus from April 20 to May 20, and so on (at least that was the lineup in Greek times).
As the Sun continues to move along the ecliptic after the vernal equinox, it moves farther and farther north of the celestial equator, rising higher and higher in our northern skies. Finally, halfway between the two equinoxes, on June 21, it reaches the point of maximum separation between ecliptic and celestial equator. Momentarily it "stands stiff" in its north-soufh rdotion, then "turns" and begins (it appears to us) to travel south again. This is the time of the "summer solstice," where "solstice" is from the Latin meaning "sun stand-still."
At that time the position of the Sun is a full 231/2' north of the celestial equator and it is entering the con stellation of Cancer. Consequently the line of 231/2' north latitude on Earth, the line over which the Sun is shining on June 20, is the "Tropic of Cancer." ("Tropic" is from a Greek word meaning "to turn.")
On September 23, the Sun has reached the "autumnal equinox" as it enters the constellation of Libra. It then moves south of the celestial equator, reaching the point of maximum southerliness on December 21, when it enters the constellation of Capricorn. This is the "winter solstice," and the line of 231/2 ' south latitude on the Earth is (you guessed it) the "Tropic of Capricorn."
Here is a complication! The Earth's axis "wobbles."
If the line of the axis were extended to the celestial sphere, each pole would draw a slow circle, 47' in diameter, as it moved. The position of the celestial equator depends on the tilt of the axis and so the celestial equator moves bodily against the background of the stars from east to west in a direction parallel to the ecliptic. The position of the equi noxes (the intersection of the moving celestial equator with the unmoving ecliptic) travels westward to meet the Sun.
The equinox completes a circuit about the ecliptic in 25,760 years, which means that in 1 year the vernal equinox moves 360/25,760 or 0.014 degrees. The, Sun, in making its west-to-east circuit, comes to the vernal equinox which is 0.014 degrees west of its position at the last crossing. The Sun must travel that additional 0.014 degrees to make a truly complete circuit with respect to the stars. It takes 20 minutes of motion to cover that additional 0.014 degrees. Because the equinox precedes itself and is reached 20 minutes ahead of schedule each year, this motion of the Earth's axis is called "the pre cession of the equinoxes."
Because of the precession of the equinoxes, the vernal equinox moves one full constellation of the Zodiac every 2150 years. In the time of the Pyramid builders, the Sun entered Taurus at the time of the vernal equinox. In the time of the Greeks, it entered Aries. In modem times, it enters Pisces. In A.D. 4000 it will enter Aquarius.
The complete circle made by the Sun with respect to the stars takes 365 days, 6 hours, 9 minutes, 10 seconds. This is the "sidereal year." The complete circle from equinox to equinox takes 20 minutes less; 365 days, 5 hours, 48 minutes, 45 seconds. This is the "tropical year," because it also measures the time required for the Sun to move from tropic to tropic and back again.
It is the tropical year and not the sidereal year that governs our seasons, so it is the tropical year we mean when we speak of the year.
The scholars of -ancient times noted that the position of the Sun in the Zodiac had a profound effect on the Earth.
Whenever it was in Leo, for instance, the Sun shone with a lion's strength and it was invariably hot; when it was in Aquarius, the water-carrier usually tipped his um so that there was much snow. Furthermore, eclipses were clearly meant to indicate catastrophe, since catastrophe always followed eclipses. (Catastrophes also always followed lack of eclipses but no one paid attention to that.)
Naturally, scholars sought for other effects and found them in the movement of the five bright star-like objects, Mercury, Venus, Mars, Jupiter, and Saturn. These, like the Sun and Moon, moved against the starry background and all were therefore called "planctes" ("wanderers") by the Greeks. We call them "planets."
The five star-like planets circle the Sun as the Earth does and the planes of their orbits are tipped only slightly to that of the Earth. Thir% means they seem to move in the ecliptic, as the Sun and Moon do, progressing through the constellations of the Zodiac.
Their motions, unlike those of the Sun and the Moon, are quite complicated. Because of the motion of the Earth, the tracks made by the star-like planets form loops now and then. This made it possible for the Greeks to have five centuries of fun working out wrong theories to ac count for those motions.
Still, though the theories might be wrong, they sufficed to work out what the planetary positions were in the past and what they would be in the future. All one had to do was to decide what particular influence was exerted by a particular planet in a particular constellation of the Zodiac; note the positions of all the planets at the time of a person's birth; and everything was set. The decision as to the particular influences presents no problem. You make any decision you care to. The pseudo-science of astrology invents such influences without any visible difficulty. Every astrologer has his own set.
To astrologers, moreover, nothing has happened since the time of the Greeks. The period from March 20 to April 19 is still governed by the "sign of Aries," even though the Sun is in Pisces at that time nowadays, thanks to the precession of the equinoxes. For that reason it is now necessary to distinguish between the "signs of the Zodiac" and the "constellations of the Zodiac." The signs now are what the constellations were two thousand years ago.
I've never heard that this bothered any astrologer in the world.
AU this and more occurred to me some time ago when I was invited to be on a well-known television conversa tion show that was scheduled to deal with the subject of astrology. I was to represent science against the other three members of the panel, all of whom were professional astrologers.
For a moment I felt that I must accept, for surely it was my duty as a rationalist to strike a blow against folly and superstition. Then other thoughts occurred to me.
The three practitioners would undoubtedly be experts at their own particular line of gobbledygook and could easily speak a gallon of nonsense while I was struggling with a half pint of reason.
Furthermore, astrologers are adept at that line of argu ment that all pseudo-scientists consider "evidence." The line would be something like this, "People born under Leo are leaders of men, because the lion is the king of ,beasts, and the proof is that Napoleon was born under the sign of Leo."
Suppose, then, I were to say, "But one-twelfth of living human beings, amounting to 250,000,000 individuals, were born in Taurus. Have you, or has anybody, ever tried to determine whether the proportion of leaders among them is significantly greater than among non-Leos? And how would you test for leadership, objectively, anyway'.?"
Even if I managed to say all this, I would merely be stared at as a lunatic and, very likely, as, a dangerous sub versive. And the general public, which, in this year of 1968, ardently believes in astrology and supports more astrologers in affluence (I strongly suspect) than existed in all previous centuries combined, would arrange lynching parties.
So as I wavered between the desire to fight for the right, and the suspicion that the right would be massacred and sunk without a trace, I decided to turn to astrology for help. Surely, a bit of astrologic analysis would tell me what was in store for me in any such confrontation.
Since I was born on January 2, that placed me under the, sign of Capricornus-the goat.
That did it! Politel but very firmly, I refused to be on the program!
I decided not to (as it happened, clouds interfered with seeing, so it was just as well) and caught fugitive glimpses of an eclipse that was only 95 per cent total, from my backyard. However, the difference between a 95 per cent eclipse and a 100 per cent eclipse is the difference between a notion of water and an ocean of water, so I did not feel very overwhelmed by what I saw.
V-/bat makes a total eclipse so remarkable is the sheer astronomical accident that the Moon fits so snugly over the Sun. The Moon is just large enougb. to cover the Sun completely (at times) so that a temporary night falls and the stars spring out. And it is just small enough so that during the Sun's obscuration, the corona, especially the brighter parts near the body of the Sun, is completely visible.
The apparent size of the Sun and Moon depends upon both their actual size and their distance from us. The diameter of the Moon is 2160 miles while that of, the Sun is 864,000 miles. The ratio of the diameter of the Sun to that of the Moon is 864,000/2160 or 400. In other words, if both were at the same distance from us, the Sun would appear to be 400 times as broad as the Moon.
However, the Sun is farther away from us than the Moon is, and therefore appears smaller for its size than the Moon does. At great distances, such as -those which characterize the Moon and the Sun, doubling the distance halves the apparent diameter. Remembering that, consider that the average distance of the Moon from us is 238,000 miles while that of the Sun is 93,000,000 miles. The ratio of the distance of the Sun to that of the Moon is 93,000, 000/238,000 or 390. The Sun's apparent diameter is cut down in proportion.
In other words, the two effects just about cancel. The Sun's greater distance makes up for its greater size and the result is that the Moon and the Sun appear to be equal in size. The apparent angular diameter of the Sun averages 32 minutes of arc, while that of the Moon averages 31 minutes of arc.
These are average values because both Moon and Earth possess elliptical orbits. The Moon is closer to the Earth (and therefore appears larger) at some times than at others, while the Earth is closer to the Sun (which therefore appears larger) at some times than at others. This variation in apparent diameter is only 3 per cent for the Sun and about 5 per cent for the Moon, so that it goes unnoticed by the casual observer.
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).
The Egyptians and, by dint of copying, the Romans and ourselves abandoned the Moon and made each year equal in length, and each with 12 slightly long months'
The "calendar month" averaged 301/2 days long in place of the 291/2. days of the synodic month. This meant the months fell out of line with the phases of the Moon, but mankind survived that.
The progress of the Sun along the ecliptic marked off the calendar, and since the year (one complete circuit) was divided into 12 months it seemed natural to divide the ecliptic into 12 sections. The Sun would travel through one section in one month, through the section to the east of that the next month, through still another section the third month, and so on. After 12 months it would come back to the first section.
Each section of the ecliptic has its own pattern of stars, and to identify one section from another it is the most natural thing in the world to use those patterns. If one section has four stars in a roughly square configuration it might be called "the square"; another section might be the "V-shape," another the "large triangle," and so on.
Unfortunately, most people don't have my neat, geo metrical way of thinking and they tend to see complex figures rather than simple, clean shapes. A group of stars arranged in a V might suggest the head and homs of a bull, for instance. The Babylonians worked up such imaginative patterns for each section of the ecliptic and the Greeks borrowed these giving each a Greek name. The Romans borrowed the iist next, giving them Latin names, and passing them on to us.
The following is the list, with each name in Latin and in English: 'I) Aries, the Ram; 2) Taurus' the Bull; 3) Gemini, the Twins; 4) Cancer, the Crab; 5) Leo, the Lion; 6) Virgo, the Virgin; 7) Libra, the Scales; 8) Scorpio, the Scorpion; 9) Sagittarius, the Archer; 10) Capricomus, the Goat; 11) Aquarius, the Water-Carrier; 12) Pisces, the Fishes.
As you see, seven of the constellations represent ani mals. An eighth, Sagittarius, is usually drawn as a centaur, which may be considered an animal, I suppose. Then, if we remember that human beings are part of the animal kingdom, the only strictly nonanimal constellation is Libra.
The Greeks consequently called this band of constellations o zodiakos kyklos or "the circle of little animals," and this has come down to us as the Zodiac.
In fact, in the sky as a whole, modem astronomers recognize 88 constellations. Of these 30 (most of them constellations of the southern skies' invented by modems) represent inaniinate objects. Of the remaining 58, mostly ancient, 36 represent mammals (including 14 human beings), 9 represent birds,, 6 represent reptiles, 4 represent fish, and 3 represent arthropods. Quite a heavenly zoo!
Odd, though, considering that most of the constellations were invented by an agricultural society, that not one represents a member of the plant kingdom. Or can,that be used to argue that the early star-gazers were herdsmen and not farmers?
The line of the ecliptic is set at an angle of 231/2 ' to the celestial equator (see Chapter 3) since, as is usually stated, the Earth's axis is tipped 23V2'.
At two points, then, the ecliptic crosses the celestial equator and those two crossing points are the "equinoxes" ("equal nights"). When the Sun is at those crossing points, it shines directly over the equator and days and nights are equal (twelve hours each) the world over. Hence, the name.
One of the equinoxes is reached when the Sun, in its path along the ecliptic, moves from the southern celestial hemisphere into the northern. It is rising higher in the sky (to us in the Northern Hemisphere) and spring is on its way. That, therefore, is the "vernal equinox," and it is on March 20.
On that day (at least in ancient Greek times) the Sun entered the constellation of Aries. Since the vernal equinox is a good time to begin the year for any agricultural society, it is customary to begin the list of the constellations of the Zodiac, as I did, with Aries.
The Sun stays about one month 'm each constellation, so it is in Aries from March 20 to April 19, in Taurus from April 20 to May 20, and so on (at least that was the lineup in Greek times).
As the Sun continues to move along the ecliptic after the vernal equinox, it moves farther and farther north of the celestial equator, rising higher and higher in our northern skies. Finally, halfway between the two equinoxes, on June 21, it reaches the point of maximum separation between ecliptic and celestial equator. Momentarily it "stands stiff" in its north-soufh rdotion, then "turns" and begins (it appears to us) to travel south again. This is the time of the "summer solstice," where "solstice" is from the Latin meaning "sun stand-still."
At that time the position of the Sun is a full 231/2' north of the celestial equator and it is entering the con stellation of Cancer. Consequently the line of 231/2' north latitude on Earth, the line over which the Sun is shining on June 20, is the "Tropic of Cancer." ("Tropic" is from a Greek word meaning "to turn.")
On September 23, the Sun has reached the "autumnal equinox" as it enters the constellation of Libra. It then moves south of the celestial equator, reaching the point of maximum southerliness on December 21, when it enters the constellation of Capricorn. This is the "winter solstice," and the line of 231/2 ' south latitude on the Earth is (you guessed it) the "Tropic of Capricorn."
Here is a complication! The Earth's axis "wobbles."
If the line of the axis were extended to the celestial sphere, each pole would draw a slow circle, 47' in diameter, as it moved. The position of the celestial equator depends on the tilt of the axis and so the celestial equator moves bodily against the background of the stars from east to west in a direction parallel to the ecliptic. The position of the equi noxes (the intersection of the moving celestial equator with the unmoving ecliptic) travels westward to meet the Sun.
The equinox completes a circuit about the ecliptic in 25,760 years, which means that in 1 year the vernal equinox moves 360/25,760 or 0.014 degrees. The, Sun, in making its west-to-east circuit, comes to the vernal equinox which is 0.014 degrees west of its position at the last crossing. The Sun must travel that additional 0.014 degrees to make a truly complete circuit with respect to the stars. It takes 20 minutes of motion to cover that additional 0.014 degrees. Because the equinox precedes itself and is reached 20 minutes ahead of schedule each year, this motion of the Earth's axis is called "the pre cession of the equinoxes."
Because of the precession of the equinoxes, the vernal equinox moves one full constellation of the Zodiac every 2150 years. In the time of the Pyramid builders, the Sun entered Taurus at the time of the vernal equinox. In the time of the Greeks, it entered Aries. In modem times, it enters Pisces. In A.D. 4000 it will enter Aquarius.
The complete circle made by the Sun with respect to the stars takes 365 days, 6 hours, 9 minutes, 10 seconds. This is the "sidereal year." The complete circle from equinox to equinox takes 20 minutes less; 365 days, 5 hours, 48 minutes, 45 seconds. This is the "tropical year," because it also measures the time required for the Sun to move from tropic to tropic and back again.
It is the tropical year and not the sidereal year that governs our seasons, so it is the tropical year we mean when we speak of the year.
The scholars of -ancient times noted that the position of the Sun in the Zodiac had a profound effect on the Earth.
Whenever it was in Leo, for instance, the Sun shone with a lion's strength and it was invariably hot; when it was in Aquarius, the water-carrier usually tipped his um so that there was much snow. Furthermore, eclipses were clearly meant to indicate catastrophe, since catastrophe always followed eclipses. (Catastrophes also always followed lack of eclipses but no one paid attention to that.)
Naturally, scholars sought for other effects and found them in the movement of the five bright star-like objects, Mercury, Venus, Mars, Jupiter, and Saturn. These, like the Sun and Moon, moved against the starry background and all were therefore called "planctes" ("wanderers") by the Greeks. We call them "planets."
The five star-like planets circle the Sun as the Earth does and the planes of their orbits are tipped only slightly to that of the Earth. Thir% means they seem to move in the ecliptic, as the Sun and Moon do, progressing through the constellations of the Zodiac.
Their motions, unlike those of the Sun and the Moon, are quite complicated. Because of the motion of the Earth, the tracks made by the star-like planets form loops now and then. This made it possible for the Greeks to have five centuries of fun working out wrong theories to ac count for those motions.
Still, though the theories might be wrong, they sufficed to work out what the planetary positions were in the past and what they would be in the future. All one had to do was to decide what particular influence was exerted by a particular planet in a particular constellation of the Zodiac; note the positions of all the planets at the time of a person's birth; and everything was set. The decision as to the particular influences presents no problem. You make any decision you care to. The pseudo-science of astrology invents such influences without any visible difficulty. Every astrologer has his own set.
To astrologers, moreover, nothing has happened since the time of the Greeks. The period from March 20 to April 19 is still governed by the "sign of Aries," even though the Sun is in Pisces at that time nowadays, thanks to the precession of the equinoxes. For that reason it is now necessary to distinguish between the "signs of the Zodiac" and the "constellations of the Zodiac." The signs now are what the constellations were two thousand years ago.
I've never heard that this bothered any astrologer in the world.
AU this and more occurred to me some time ago when I was invited to be on a well-known television conversa tion show that was scheduled to deal with the subject of astrology. I was to represent science against the other three members of the panel, all of whom were professional astrologers.
For a moment I felt that I must accept, for surely it was my duty as a rationalist to strike a blow against folly and superstition. Then other thoughts occurred to me.
The three practitioners would undoubtedly be experts at their own particular line of gobbledygook and could easily speak a gallon of nonsense while I was struggling with a half pint of reason.
Furthermore, astrologers are adept at that line of argu ment that all pseudo-scientists consider "evidence." The line would be something like this, "People born under Leo are leaders of men, because the lion is the king of ,beasts, and the proof is that Napoleon was born under the sign of Leo."
Suppose, then, I were to say, "But one-twelfth of living human beings, amounting to 250,000,000 individuals, were born in Taurus. Have you, or has anybody, ever tried to determine whether the proportion of leaders among them is significantly greater than among non-Leos? And how would you test for leadership, objectively, anyway'.?"
Even if I managed to say all this, I would merely be stared at as a lunatic and, very likely, as, a dangerous sub versive. And the general public, which, in this year of 1968, ardently believes in astrology and supports more astrologers in affluence (I strongly suspect) than existed in all previous centuries combined, would arrange lynching parties.
So as I wavered between the desire to fight for the right, and the suspicion that the right would be massacred and sunk without a trace, I decided to turn to astrology for help. Surely, a bit of astrologic analysis would tell me what was in store for me in any such confrontation.
Since I was born on January 2, that placed me under the, sign of Capricornus-the goat.
That did it! Politel but very firmly, I refused to be on the program!
