Elements of Astronomy
“Can an idea of the laws and phenomena of the celestial motions be conveyed to a pupil who has not completed the regular course in geometry and physics?” So writes Simon Newcomb in his preface to this thin (240 page) book on astronomy published in 1900. The pupil Newcomb had in mind was “the inquiring layman seeking to know something of the heavenly bodies and their relation to the earth, including such subjects of human interest as the changing seasons, the measurement of time, and the varying aspects of the planets.”
Newcomb, of course, answered his question in the affirmative, and this book is his proof. We reproduce here his “Chapter II” in its numbered sections:
The Revolution of the Earth round the Sun
- The Earth as a Planet.
- Annual Motion of the Earth around the Sun.
- How the Sun shines on the Earth at Different Seasons.
- Apparent Motion of the Sun — The Zodiac.
- Seasons in the Two Hemispheres.
- The Solar and Sidereal Years.
- Precession of the Equinoxes.
1. The Earth as a Planet
In the preceding chapter we have explained the various phenomena which arise from the rotation of the earth on its axis. We have to explain another change with which we are all familiar, — that of the seasons. We know that these go through a regular change in a period of about 365 days. During one part of this period, which we call summer, we see the sun rise to the north of east, pass the meridian high up in the heavens, and set to the north of west. At the opposite season the sun rises south of east, culminates low in the south, and sets south of west. In the first case the days are long and the nights short; in the second the days are short and the nights long.
Any one who thinks will see that this annual change of the seasons depends in some way on the sun; that the season is hot or cold, and the days long or short, according to the apparent path of the sun in the heavens. We have now to show that the changes of the seasons arise from the earth making an annual revolution around the sun. Thus the earth has two motions, its rotation on its own axis, and its revolution around the sun. The first produces day and night, the second summer and winter. To conceive the combined effect of these two revolutions is a task which requires some thinking. We have two things to consider, — the actual motion of the earth, and the apparent motion of the sun as we seem to see it.
If we could fly upward in a direction near that of the earth’s axis to a distance of a thousand million miles, and then look back, we should see the earth and a number of other bodies forming, as it were, a little family far distant from all other heavenly bodies. The largest and brightest of those bodies would be the sun. At various distances and directions from the sun we should see eight or more smaller bodies looking like stars. If we watched long enough, we should see that those seeming stars were all in motion around the sun, each one keeping nearly, but not exactly, at the same distance from it during its course. The nearest would complete its circuit in about three months, while the most distant would take more than 160 years. These small starlike bodies are called planets.
The paths in which the planets perform their courses round the sun are called their orbits.
One of these planets is the earth on which we dwell. It is the third in the order of distance from the sun, and, as we have said, it requires a year to complete its circuit around the sun. It would be more exact to say that the time required for it to complete its circuit is what we call a year.
Besides the eight planets which we have described there are a number of smaller bodies going round the sun which we shall describe hereafter. This whole family of bodies is called the solar system. It is so called because the sun is the great central body on which all the others depend, and to which they all do homage, so to speak.
The distance of the earth from the sun has been determined in a number of different ways. According to the latest researches it is very nearly 93,000,000 miles; we scarcely know whether a little greater or a little less. Some idea of this distance may be gained by saying that a railway train running 60 miles an hour, and making no stop, would require more than 160 years to reach the sun. Five generations might be born upon it before the journey was completed.
The most marked difference between the sun and the planets is that the sun shines by its own light, while the planets shine only by the light that falls on them from the sun. Thus, so far as means of seeing are concerned, the sun is like a candle in an otherwise dark room and the planets are like little bodies seen by the light of the candle.
We have said that the bodies of the solar system form a group by themselves. Looking down from the height we have supposed, we should see this very clearly. The stars which stud the heavens would be seen just as we see them from the earth, in every direction. Their distances are so vast compared with the size of the solar system that even the latter, immense though it is, is but a speck in comparison. We may, if we please, call them suns. Most of them are brighter than the sun. They look small and dim because they are so much farther away.
Thus, having expanded our conceptions so that the earth shall be but as a point in the solar system, we must again expand them so as to think of the whole solar system as but a point in comparison with the distance of the stars.
2. Annual Motion of the Earth round the Sun
We must now explain the motion of the earth in its orbit round the sun. This is called its annual motion, because it takes a year to complete one revolution.
We cannot draw a figure which shall represent the earth and its orbit in anything like their true proportions, because the diameter of the orbit is more than 20,000 times that of the earth itself. So we have to draw figures, as before, on two very different scales. Figure 16 shows the orbit of the earth seen nearly edgewise. The plane containing this orbit is called the plane of the ecliptic. On a true scale the earth in this figure would be an invisible dot, so we make it larger, and then represent it on a still larger scale in figure 17.
In figure 16 the direction of the axis is shown by the inclined line NS.
An important law of the earth’s motion is this: As the earth moves round the sun, the direction of its axis remains almost unchanged.
This direction is not quite perpendicular to the ecliptic, but is inclined to the perpendicular by 23½°, or a little more than one fourth of a right angle. This angle is called the obliquity of the ecliptic, because it is equal to the angle which the plane of the equator makes with the plane of the ecliptic.
4. Apparent Motion of the Sun. — The Zodiac.
Having explained how the earth turns on its axis and revolves round the sun, while, to us who live on it, it seems to remain at rest, we shall now explain how the sun seems to us to move. The apparent motion of the sun is based on these facts: —
- Each fixed star is really in the same direction from us all day and all the year. The stars seem to us to change their direction only because we live on the moving earth.
- The sun is nearly, but not exactly, in the same direction from us all day, from its rising to its setting. But this direction changes during the year in consequence of the earth revolving round it.
Let us study figure 18, which shows the earth’s orbit, ABC, with the sun in the center. Far outside the orbit lie the stars. To make a figure on the right scale, we should have to place the stars several miles away; as we cannot do this, we represent their positions as in the figure.
Now suppose we could fly a few thousand miles above the earth and accompany it in its course round the sun. Then, looking down, we should see the earth turning on its axis, and bringing its oceans and continents into view, one after the other. Looking at the stars, we should see them at rest. They would neither rise nor set, nor even change their direction by any quantity we could perceive.
Next, let us see how it will be with the sun. When the earth is at the point A, we shall see the sun as if it were among the stars at the point a. A month later when the earth has got to the point B, the sun will appear among the stars at b. In another month, with the earth at C, the sun will be seen as if at c, and so on through the year. As the earth goes through its revolution round the sun, the sun appears to move around in a circle among the stars, until the earth gets back to the position A, when the sun will again appear in the position a. Hence: —
The sun appears to us to describe a complete circle around the celestial sphere, among the stars, every year.
The circle thus described by the sun on the celestial sphere is called the ecliptic.
The zodiac is an imaginary belt in the heavens, extending 8° on each side of the ecliptic, and passing all round the celestial sphere as the ecliptic does. The ecliptic is its central line.
If the axis of the earth were perpendicular to the ecliptic, the plane of the earth’s equator would always pass through the sun, and the sun would always be seen in the celestial equator. Because of the obliquity of the ecliptic, already described, the ecliptic is inclined to the equator by an angle of 23½° , cutting it at two points called the Vernal and Autumnal equinoxes, as shown in figure 19.
To make this clear, we show in figure 20 how, if we could see the stars around the sun, and the ecliptic and equator marked on the celestial sphere, we should, day by day, see the sun moving from west toward east, among the stars.
In very ancient times men mapped out the apparent course of the sun round the celestial sphere, as shown in figure 19. They divided it into twelve parts, each 30° length, and named each part after the constellation in which the sun would have been seen had the stars been visible. Theses parts were called signs of the zodiac. The sun enters a sign about the 21st day of each month. The names of the signs and the months when the sun enters each are as follows: —
|Aries, The Ram
|Taurus, The Bull
|Gemini, The Twins
|Cancer, The Crab
|Leo, The Lion
|Virgo, The Virgin
|Libra, The Balance
|Scorpio, The Scorpion
|Sagittarius, The Archer
|Capricornus, The Goat
|Aquarius, The Water Bearer
|Pisces, The Fishes
When the sun is at the Vernal Equinox, it appears in the celestial equator, rises exactly east, and sets exactly west.
In figure 19 we see that during the six months the sun is passing from Aries to Virgo, it appears north of the celestial equator. It is therefore in north declination; it rises north of east and sets north of west. At this time, in the northern hemisphere, the days are longer than the nights. See the apparent diurnal course of the sun as shown in figure 22.
When the sun passes from Gemini into Cancer, it has reached its greatest north declination, and now begins to move south again. This point is called the Summer Solstice.
When the sun reaches Libra, it again crosses the equator toward the south. This point is called the Autumnal Equinox.
During the remaining six months, while the sun is passing from Libra to Pisces, it is in south declination; it rises south of east and sets south of west. In the northern hemisphere the nights are then longer than the days.
When the sun passes from Sagittarius into Capricornus it has reached its greatest south declination and begins to return toward the equator. This point is called the Winter Solstice.
6. The Solar and Sidereal Years.
There are two ways of finding how long it takes the sun to complete its apparent revolution in the heavens, or, in other words, how long it takes the earth to make a complete revolution around it.
One of these consists in observing the exact time at which the sun reaches the equinoxes. In ancient times astronomical observers were able to do this by noting the days when the sun rose exactly in the east or set exactly in the west. By observing the rising and setting from day to day, they could find not only the day, but almost the hour in which the sun was on the celestial equator. Of course, with our more exact instruments we can get this time with still greater precision.
The period between two returns of the sun to the same equinox is called the solar year or equinoxial year.
The other way of finding the length of the year consists in observing the interval of time between two passages of the sun past the same star in the heavens; for example, the period between two of its passages past one of the stars shown in figure 20.
This method seems to involve the great difficulty that we cannot see when the sun is near the star. But the astronomer has methods of knowing exactly where a star is by day as well as by night, and can determine the moment at which the sun passes it.
The ancient astronomers got the same result by using the moon as an intermediate object to measure from. The moon could be seen before sunset and its distance from the sun determined. Then, when the star appeared after sunset, the distance from the star to the moon was measured. Allowing for the motion of the moon during the interval, the apparent distance between the sun and the star could thus be learned from day to day. In this way it could be found how many days it was between the times at which the sun was at the same distance from any given bright star. This would be the period of apparent revolution of the sun in the celestial sphere, or, as we now know it to be, the period of one revolution of the earth in its orbit. This period is called the sidereal year, because it is fixed by the stars.
Hipparchus, who flourished about 150 B.C., was the first to take exact observations of the length of the year. Ptolemy, who flourished about 300 years later, made similar ones. They found that the length of the year, as determined in these two ways, was not the same, and that the solar year, as determined by the equinoxes, was several minutes shorter than the sidereal year determined by the return of the sun to the same star.
With our exact modern observations we have found the lengths of the years to be:–
Solar year, 365 d. 5h. 48m. 46s.
Sidereal year, 365 d, 6h, 9m. 9s.
Difference, 20 m. 23 s.
This difference shows that the position of the equinoxes among the stars is changing from year to year. Hipparchus and Ptolemy estimated the change to be about one degree in a century. We know it to be greater than this, — nearly one degree in 70 years.
7. Precession of the Equinoxes.
The motion of the equinoxes which causes the difference between the solar and sidereal year is going on all the time. It is called the Precession of the Equinoxes.
The nature of precession is now to be explained. The equinox is the point where the sun crosses the celestial equator. The position of the celestial equator on the celestial sphere is determined by the direction of the earth’s axis, because the celestial equator is 90° from either celestial pole.
The precession of the equinoxes arises from the fact that the direction of the earth’s axis in space is slowly changing.
Next, let us see how the change goes on. Imagine a line passing through the sun perpendicular to the plane of the ecliptic. The point in which this line, when continued to the stars, meets the celestial sphere, is called the Pole of the Ecliptic. It lies in the constellation Draco, the Dragon, but there is no bright star near it.
You will readily see that the angular distance between the pole of the ecliptic and the celestial pole, corresponding to the direction of the earth’s axis, is equal to the obliquity of the ecliptic, 23½°.
Now, the law of precession is that the celestial pole is in motion, and makes a complete revolution round the pole of the ecliptic in about 25,700 years. This motion is very slow to ordinary vision; it would take a century for the naked eye to notice it, even by careful observation. But the exact observations made by astronomers with the meridian circle make it evident month after month and year after year.
Owing to this motion of the celestial pole the celestial equator moves also, continually sliding along the ecliptic, and carrying the equinoxes with it, as shown in figure 23. This is why the equinox moves among the stars. The rate of motion is a little more than 50″ in a year, or nearly 14° in 1000 years.
Motion of the Ecliptic. — If the plane of the ecliptic were absolutely fixed, the obliquity of the ecliptic would be always the same, and the motion of precession would go on forever at the same rate that it now does. But the attraction of the other planets on the earth produces a very slow change in the ecliptic itself, about 1/50 the change of precession. In consequence of this change, the revolution of the celestial pole round the pole of the ecliptic does not take place at an exactly uniform rate, nor will it always be completed in exactly the same time. For the same reason the obliquity of the ecliptic slowly changes. It is at the present time diminishing at the rate of about 46″ in a century.
Results of Precession. — One result of precession is that the celestial pole was not so near the polestar in former times as it is now. In ancient times it was so far away from that star that the latter could not be considered as a polestar at all. It has been continually coming nearer, and is still approaching it. About the year 2110 it will pass by the polestar at a distance of only 24′. Continuing its course, the celestial pole will pass some 5° from the star Alpha Lyre, about 11,000 years from now, and will continue its circuit until it gets back to where it now is in about 25,700 years.
The two equinoxes will make a revolution round the equator in the same period of time, being carried along by the earth’s equator, which is always at right angles to the earth’s axis.