Astronomy in a nutshell

by Garrett Putman Serviss

5. Dip of the Horizon. Another correction which has to be applied in many observations depends upon the sphericity of the earth. We have described the rational horizon, and pointed out how it differs from the sensible horizon. We have also said that at sea the sensible horizon nearly accords with the rational horizon (see Part I, Sect. 3). But the accord is not complete, owing to what is called the dip of the horizon. In fact, the sea horizon lies below the rational horizon by an amount varying with the elevation of the eye above the surface. Geometry enables us to determine just what the dip of the horizon must be for any given elevation of the eye. A rough and ready rule, which may serve for many purposes, is that the square root of the elevation of the eye in feet equals the dip of the horizon in minutes of arc, or of angular measure. The reader will readily see that the dip of the horizon is a necessary consequence of the rotundity of the earth. It is because of this that, as a ship recedes at sea her hull first disappears below the horizon, and then her lower sails, and finally her top-sails. The use of a telescope does not help the matter, because a telescope only sees straight, and cannot bend the line of sight over the rim of the horizon. Atmospheric refraction, however, enables us to see an object which would be hidden by the horizon if there were no air. In navigation, which, as a science, is an outgrowth of astronomy, these things have to be carefully taken into account.

Fig. 8. Dip of the Horizon.
It is to be remembered that it is the sensible horizon which dips, and not the rational horizon. The sensible horizon of the observer at the elevation A dips below the horizontal plane and he sees round the curved surface as far as a; in other words his skyline is at a. The observer at the elevation B has a sensible horizon still more inclined and he sees as far as b. If the observation were made from an immense height the observer would see practically half round the earth
just as we see half round the globe of the moon.

Polar Streamers of the Sun, Eclipse of 1889

The Solar Corona at the Eclipse of 1871 From drawings.

6. Aberration. A few words must be said about the phenomenon known as aberration of light. This is an apparent displacement of a celestial object due to the motion of the earth in its orbit. It is customary to illustrate it by imagining oneself to be in a shower of rain, whose drops are falling vertically. In such a case, if a person stands fast the rain will descend perpendicularly upon his head, but if he advances rapidly in any direction he will feel the drops striking him in the face, because his own forward motion is compounded with the downward motion of the rain so that the latter seems to be descending slantingly toward him. The same thing happens with the light falling from the stars. As the earth advances in its orbit it seems to meet the light rays, and they appear to come from a direction ahead of the flying earth. The result is that, since we see a star in the direction from which its light seems to come, the star appears in advance of its real position, or of the position in which we would see it if the earth stood fast. The amount by which the position of a star is shifted by aberration depends upon the ratio of the earth's velocity to the velocity of light. In round numbers this ratio is as 1 to 10,000. The motion of the earth being in a slightly eccentric ellipse, the stars describe corresponding, but very tiny, ellipses once every year upon the background of the sky. But the precise shape of the ellipse depends upon the position of the star on the celestial sphere. If it is near one of the poles of the ecliptic, it will describe an annual ellipse which will be almost a circle, its greater diameter being 41″ of arc. If it is near the plane of the ecliptic, it will describe a very eccentric ellipse, but the greater diameter will always be 41″, although the shorter diameter may be immeasurably small. The effects of aberration have to be allowed for in all careful astronomical observation either of the sun or the stars. This is done by reducing the apparent place of the object to the place it would have if it were seen at the centre of its annual ellipse.

7. Time. Without astronomical observations we could have no accurate knowledge of time. The basis of the measurement of time is furnished by the rotation of the earth on its axis. We divide the period which the earth occupies in making one complete turn into twenty-four equal parts, or hours. The ascertainment of this period, called a day, depends upon observations of the stars. Suppose we see a certain star exactly on the meridian at some moment; just twenty-four hours later that star will have gone entirely round the sky, and will again appear on the meridian. The revolving heavens constitute the great clock of clocks, by whose movements all other clocks are regulated. We know that it is not the heavens which revolve, but the earth which rotates, but for convenience we accept the appearance as a substitute for the fact. The rotation of the earth is so regular that no measurable variation has been found in two thousand years. We have reasons for thinking that there must be a very slow and gradual retardation, owing principally to the braking action of the tides, but it is so slight that we cannot detect it with any means at present within our command.

In Part I it was shown how the passage across the meridian of the point in the sky called the vernal equinox serves to indicate the beginning of the astronomical “day,” but the position of the vernal equinox itself has to be determined by observations on the stars. By means of a telescope, so mounted that it can only move up or down, round a horizontal axis, and with the axis pointing exactly east and west so that the up and down movements of the telescope tube follow the line of the meridian, the moment of passage across the meridian of a star at any altitude can be observed. Observations of this nature are continually made at all great government observatories, such as the observatory at Washington or that at Greenwich, and at many others, and by their means clocks and chronometers are corrected, and a standard of time is furnished to the whole world.