Astronomy for Everybody/Part 1/Chapter 5

It is well known that the earth not only turns on its axis, but makes an annual revolution round the sun. The result of this motion—in fact, the phenomenon by which it is shown—is that the sun appears to make an annual revolution around the celestial sphere among the stars. We have only to imagine ourselves moving round the sun and therefore seeing the latter in different directions, to see that it must appear to us to move among the stars, which are farther than it is. It is true that the motion is not at once evident because the stars are invisible in the daytime. But the fact of the motion will be made very clear if, day after day, we watch some particular fixed star in the west. We shall find that it sets earlier and earlier every day; in other words, it is getting continually nearer and nearer the sun. More exactly, since the real direction of the star is unchanged, the sun appears to be approaching the star.

If we could see the stars in the daytime, all round the sun, the case would be yet clearer. We should see that if the sun and a star rose together in the morning the sun would, during the day, gradually work past the star in an easterly direction. Between the rising and setting it would move nearly its own diameter relative to the star. Next morning we should see that it had gotten quite ​away from the star, being nearly two diameters distant from it. The figure shows how this would go on at the time of the spring equinox, after March twentieth. This motion would continue month after month. At the end

of the year the sun would have made a complete circuit of the heavens relative to the star, and we should see the two once more together.

How the above effect is produced will be seen by Figure 5, which represents the earth's orbit round the sun, with the stars in the vast distance. When the earth is at A, we see the sun in the line AM, as if it were among the stars at M. As we are carried on the earth from A to B, the sun seems to move from M to N, and so on through the year. This apparent motion of the sun in one year around the celestial sphere, was noticed by the ancients, who seem to have taken much trouble to map it out. They ​imagined a line passing around the celestial sphere which the sun always followed in its annual course, and which was called the ecliptic. They noticed that the planets followed nearly but not exactly the same general course as the sun among the stars. A belt extending around on

each side of the ecliptic, and broad enough to contain all the known planets, as well as the sun, was called the zodiac. It was divided into twelve signs, each marked by a constellation. The sun went through each sign in the course of a month and through all twelve signs in a year. Thus arose the familiar signs of the zodiac, which ​bore the same names as the constellations among which they were situated. This is not the case at present, owing to the slow motion of precession soon to be described.

It will be seen that the two great circles we have described spanning the entire celestial sphere are fixed in entirely different ways. The equator is determined by the direction in which the axis of the earth points, and spans the sphere midway between the two celestial poles. The ecliptic is determined by the earth's motion around the sun.

These two circles do not coincide, but intersect each other at two opposite points, at an angle of twenty-three and a half degrees, or nearly one quarter of a right angle. This angle is called the obliquity of the ecliptic. To understand exactly how it arises we must mention a fact about the celestial poles; from what we have said of them it will be seen that they are not determined by anything in the heavens, but by the direction of the earth's axis only; they are nothing but the two opposite points in the heavens which lie exactly in the line of the earth's axis. The celestial equator, being the great circle halfway between the poles, is also fixed by the direction of the earth's axis and by nothing else.

Let us now suppose that the earth's orbit around the sun is horizontal. We may in imagination represent it by the circumference of a round level platform with the sun in its centre. We suppose the earth to move around the circumference of the platform with its cen​tre on the level of the platform; then, if the earth's axis were vertical, its equator would be horizontal and on a level with the platform and therefore would always be directed toward the sun in its centre, as the earth made its annual course around the platform. Then, on the celestial sphere, the ecliptic determined by the course of the sun would be the same circle as the equator. The obliquity of the ecliptic arises from the fact that the earth's orbit is not vertical, as just supposed, but is in-

clined twenty-three and a half degrees. The ecliptic has the same inclination to the plane of the platform; thus the obliquity is the result of the inclination of the earth's axis. An important fact connected with the subject is that, as the earth makes its revolutions around the sun, the direction of its axis remains unchanged in space; hence its north pole is tipped away from the sun or toward it, according to its position in the orbit. This is shown in Figure 6, which represents the platform we have supposed, with the axis tipped toward the right hand. The north pole will always be tipped in this ​direction, whether the earth is east, west, north, or south from the sun.

To see the effect of the inclination upon the ecliptic suppose that, at noon on some twenty-first day of March, the earth should suddenly stop turning on its axis, but continue its course around the sun. What we should then see during the next three months is represented in Figure 7, in which we are supposed to be looking at the southern sky. We see the sun on the meridian, where it will at first seem to remain immovable. The figure shows the

celestial equator passing through the east and west points of the horizon as already described and also the ecliptic, intersecting it at the equinox. Watching the result for a time equal to three of our months we should see the sun slowly make its way along the ecliptic to the point marked "summer solstice," its farthest northern point, which it would reach about June twentieth.

Figure 8 enables us to follow its course for three months longer. After passing the summer solstice, its ​course gradually carries it once more to the equator, which it again crosses about September twentieth. Its course during the rest of the year is the counterpart of that during the first six months. It is farthest south of the equator on December twentieth, and again crosses it on March twentieth.

We see that there are four cardinal points in this apparent annual course of the sun. (1) Where we have commenced our watch is the vernal equinox. (2) The point where the sun, having reached its northern limit, begins to again approach the equator. This is called the summer solstice. (3) Opposite the vernal equinox is the

autumnal equinox, which the sun passes about September twentieth. (4) Opposite the summer solstice is the point where the sun is farthest south. This is called the winter solstice.

The hour circles which pass from one celestial pole to the other through these points at right angles to the equator are called colures. That which passes through ​the vernal equinox is the first meridian, from which right ascensions are counted as already described. The two at right angles to it are called the solstitial colures.

Let us now show the relation of the constellations to the seasons and the time of day. Suppose that to-day the sun and a star passed the meridian at the same moment; to-morrow the sun will be nearly a degree to the east of the star, which shows that the star will pass the meridian nearly four minutes sooner than the sun will. This will continue day after day throughout the entire year when the two will again pass the meridian at about the same moment. Thus the star will have passed once oftener than the sun. That is to say: In the course of a year while the sun has passed the meridian three hundred and sixty-five times, a star has passed it three hundred and sixty-six times. Of course if we take a star in the south it will have risen and set the same number of times.

Astronomers keep the reckoning of this different rising and setting of the stars by using a sidereal day, or star day, equal to the interval between two passages of a star, or of the vernal equinox, across the meridian. They divide this day into twenty-four sidereal hours, and these into minutes and seconds according to the usual plan. They also use sidereal clocks which gain about three minutes and fifty-six seconds per day on the ordinary clocks, and thus show sidereal time. Sidereal noon is the moment at which the vernal equinox crosses the meridian of the place. The clock is then set at 0 hours, 0 minutes, and 0 seconds. Thus set and regulated, the sidereal ​clock keeps time with the apparent rotation of the celestial sphere, so that the astronomer has only to look at his clock to see, by day or by night, what stars are on the meridian and what the positions of the constellations are.

If the earth's axis were perpendicular to the plane of the ecliptic, the latter would coincide with the equator, and we should have no difference of seasons the year round. The sun would always rise in the exact east and set in the exact west. There would be only a very slight change in the temperature arising from the fact that the earth is a little nearer the sun in January than in July. Owing to the obliquity of the ecliptic it follows that, while the sun is north of the equator, which is the case from March to September, the sun shines upon the northern hemisphere during a greater time of each day and at a greater angle, than on the southern hemisphere. In the southern hemisphere the opposite is the case. The sun shines longer from September till March than it does on the northern hemisphere. Thus we have winter in the northern hemisphere when it is summer in the southern, and vice versa.

Before going farther let us recapitulate the phenomena we have described from the two points of view: one that of the real motions of the earth; the other that of the apparent motions of the heavens, to which the real motions give rise.

​The real diurnal motion is the turning of the earth on its axis.

The apparent diurnal motion is that which the stars appear to have in consequence of the earth's rotation.

The real annual motion is that of the earth round the sun.

The apparent annual motion is that of the sun around the celestial sphere among the stars.

By the real diurnal motion the plane of our horizon is carried past the sun or a star.

We then say that the sun or star rises or sets, as the case may be.

About March twenty-first of every year the plane of the earth's equator passes from the north to the south of the sun, and about September twenty-first it repasses toward the north.

We then say that the sun crosses to the north of the equator in March, and to the south in September.

In June of every year the plane of the earth's equator is at the greatest distance south of the sun, and in December at the greatest distance north.

We say in the first case that the sun is at the northern solstice, and in the second that it is at the southern solstice.

The earth's axis is tipped twenty-three and a half degrees from the perpendicular to the earth's orbit.

The apparent result is that the ecliptic is inclined twenty-three and a half degrees to the celestial equator.

During June and the other summer months the northern hemisphere of the earth is tipped toward the sun. ​Places in north latitude, as they are carried round by the turning of the earth, are then in sunlight during more than half their course; those in south latitude less.

The result as it appears to us is that the sun is more than half the time above the horizon, and that we have the hot weather of summer, while in the southern hemisphere the days are short, and the season is winter.

During our winter months the case is reversed. The southern hemisphere is then tipped toward the sun, and the northern hemisphere away from it. Consequently, summer and long days are the order in the southern, and the reverse in the northern hemisphere.

We most naturally define the year as the interval of time in which the earth revolves around the sun. From what we have said, there are two ways of ascertaining its length. One is to find the interval between two passages of the sun past the same star. The other is to find the interval between two passages of the sun past the same equinox, that is, across the equator. If the latter were fixed among the stars the two intervals would be equal. But it was found by the ancient astronomers, from observations extending through several centuries, that these two methods did not give the same length of year. It took the sun about eleven minutes longer to make the circuit of the stars than to make the circuit of the equinoxes. This shows that the equinoxes steadily shift their position among the stars from year to year. This shift is called the precession of the equinoxes. It ​does not arise from anything going on in the heavens, but only from a slow change in the direction of the earth's axis from year to year as it moves around the sun.

If we should suppose the platform in Figure 6 to last for six or seven thousand years, and the earth to make its six or seven thousand revolutions around it, we should find that, at the end of this time, the north end of the axis of the earth, instead of being tipped toward our right hand, as shown in the figure, would be tipped directly toward us. At the end of another six or seven thousand years it would be tipped toward our left; at the end of a third such period it would be tipped away from us, and at the end of a fourth, or about twenty-six thousand years in all, it would have gotten back to its original direction. Since the celestial poles are determined by the direction of the earth's axis, this change in the direction of the axis makes them slowly go around a circle in the heavens, having a radius of about twenty-three and a half degrees. At the present time the pole star is a little more than a degree from the pole. But the pole is gradually approaching it and will pass by it in about two hundred years. In twelve thousand years from now the pole will be in the constellation Lyra, about five degrees from the bright star Vega of that constellation. In the time of the ancient Greeks their navigators did not recognize any pole star at all, because what is now such was then ten or twelve degrees from the pole, the latter having been between it and the constellation of the Great Bear. It was the latter which they steered by, and which they called the Cynosure.

​It follows from all this that, since the celestial equator is the circle midway between the two poles, there must be a corresponding shift in its position among the stars. The effect of this shift during the past two thousand years is shown in Figure 9. Since the equinoxes are the points of crossing of the ecliptic and the equator, they also change in consequence of this motion. It is thus that the precession of the equinoxes arises.

The two kinds of year we have described are called equinoctial and sidereal. The equinoctial year, also called the solar year, is the interval between two returns of the sun to the equinox. Its length is—

Since the seasons depend upon the sun's being north or south of the equator, the solar or equinoctial year is that used in the reckoning of time. The ancient astronomers found that its length was about three hundred and sixty-five and one quarter days. As far back as the time of Ptolemy the length of the year was known even more exactly than this, and found to be a few minutes less than three hundred and sixty-five and one quarter days. The Gregorian Calendar, which nearly all civi​lised nations now use, is based upon a close approximation to this length of the year.

The sidereal year is the interval between two passages of the sun past the same star. Its length is three hundred and sixty-five days six hours and nine minutes.

According to the Julian calendar, which was in use in Christendom until 1582, the year was considered to be exactly 365¼ days. This, it will be seen, was 11 minutes 14 seconds more than the true length of the solar year. Consequently, the seasons were slowly changing in the course of centuries. In order to obviate this, and have a year whose average length was as nearly as possible correct, a decree was passed by Pope Gregory XIII by which, in three centuries out of four, a day was dropped from the Julian calendar. According to the latter, the closing year of every century would be a leap year. In the Gregorian calendar 1600 was still to remain a leap year, but 1500, 1700, 1800, and 1900 were all common years.

The Gregorian calendar was adopted immediately by all Catholic countries, and from time to time by Protestant countries also, so that for the past 150 years it has been universal in both. But Russia has held on to the Julian calendar until this day. Consequently in that country the reckoning of time is now 13 days behind that in the other Christian countries. The Russian New Year of 1900 occurred on what we call January 13. In February of that year we only counted 28 days, but Russia counted 29. Hence, in 1901, the Russian New Year was carried still farther forward to our January 14.