Astronomy for Everybody/Part 1/Chapter 4

In this chapter I have to use and explain some technical terms. The ideas conveyed by them are necessary to a complete understanding of the celestial motions, and of the positions of the stars at any hour when we may wish to observe them. To the reader who only desires a general idea of celestial phenomena, this chapter will not be necessary. I must invite one who wants a knowledge more thorough than this to make a close study of the celestial sphere as it was described in our second chapter. Turning back to our first figure, we see ourselves concerned with the relation of two spheres. One of these is the real globe of the earth, on the surface of which we dwell, and which is continually carrying us around by its daily rotation. The other is the apparent sphere of the heavens, which surrounds our globe on all sides at an enormous distance, and which, although it has no reality, we are obliged to imagine in order to know where to look for the heavenly bodies. Notice that we see this sphere from its centre, so that everything we see upon it appears upon its inside surface, while we see the surface of the earth from the outside.

There is a correspondence between points and circles on these two spheres. We have already shown how the axis of the earth, which marks our north and south poles, ​being continued in both directions through space, marks the north and south poles of the celestial sphere.

We know that the earth's equator passes around it at an equal distance from the two poles. In the same way we have an equator on the celestial sphere which passes around it at a distance of ninety degrees from either celestial pole. If it could be painted on the sky we should always see it, by day or night, in one fixed position. We can imagine exactly how it would look. It intersects the horizon in the east and west points, and is in fact the line which the sun seems to mark out in the sky by its diurnal course during the twelve hours that it is above the horizon, in March or September. In our northernmost States, it passes about halfway between the zenith and the south horizon, but passes nearer the zenith the farther south we are.

As we have circles of latitude parallel to the equator passing around the earth both north and south of the equator, so we have on the celestial sphere circles parallel to the celestial equator, and therefore having one or the other of the celestial poles as a centre. As the parallels of latitude on the earth grow smaller and smaller toward the pole, so do these celestial circles grow smaller toward the celestial poles.

We know that longitude on the earth is measured by the position of a meridian passing from the north to the south pole through the place whose position is to be defined. The angle which this meridian makes with that through the Greenwich Observatory is the longitude of the place.

​We have the same system in the heavens. Circles are imagined to pass from one celestial pole to the other in every direction, but all intersecting the equator at right

angles, as shown in Figure 3. These are called hour circles. One of them is called the first hour circle, and is so marked in the figure. It passes through the vernal ​equinox, a point to be defined in the next chapter. This takes a place in the sky corresponding to Greenwich on the earth's surface.

The position of a star on the celestial sphere is defined in the same way that the position of a city on the earth is defined, by its latitude and longitude. But different terms are used. In astronomy, the measure which corresponds to longitude is called right ascension; that which corresponds to latitude is called declination. We thus have the following definitions, which I must ask the reader to remember carefully.

The declination of a star is its apparent distance from the celestial equator north or south. In the figure the star is in declination twenty-five degrees north.

The right ascension of a star is the angle which the hour circle passing through it makes with the first hour circle which passes through the vernal equinox. In the figure the star is in three hours right ascension.

The right ascension of a star is, in astronomical usage, generally expresssed as so many hours, minutes, and seconds, in the way shown on Figure 3. But it may equally well be expressed in degrees as we express the longitude of places on the earth. The right ascension expressed in hours may be changed into degrees by the simple process of multiplication by 15. This is because the earth resolves 15° in an hour. Figure 3 also shows us that, while the degrees of latitude are nearly of the same length all over the earth, those of longitude continually diminish, slowly at first and more rapidly afterwards, from the equator toward the poles. At the ​equator the degree of longitude is about 69½ statute miles, but at the latitude of 45° it is only about 42 miles. At 60° it is less than 35 miles, at the pole it comes down to nothing, because there the meridians meet.

We may see that the speed of the rotation of the earth follows the same law of diminution. At the equator, 15° is about 1,000 miles. We may therefore see that, in that part of the earth, the latter revolves at the rate of 1,000 miles an hour. This is about 1,500 feet per second. But in latitude 45° the speed is diminished to little more than 1,000 feet per second. At 60°, north, it is only half that at the equator; at the poles it goes down to nothing.

In applying this system the only trouble arises from the earth's rotation. As long as we do not travel, we remain on the same circle of longitude on the earth. But by the rotation of the earth, the right ascension of any point in the sky which seems to us fixed, is continually changing. The only difference between the celestial meridian and an hour circle is that the former travels round with the earth, while the latter is fixed on the celestial sphere.

There is a strict resemblance in almost every point between the earth and the celestial sphere. As the former revolves on its axis from west to east, the latter seems to revolve from east to west. If we imagine the earth centred inside the celestial sphere with a common axis passing through them, as shown in the figure, we shall have a clear idea of the relations we wish to set forth.

If the sun, like the stars, seemed fixed on the celestial ​sphere from year to year, the problem of finding a star when we knew its right ascension and declination would be easier than it actually is. Owing to the annual revolution of the earth round the sun there is a continual change in the apparent position of the sphere at a given hour of the night. We must next point out the effect of this revolution.