Astronomy in a nutshell

by Garrett Putman Serviss

Some persons, when this statement is made, inquire: “Why, then, does not the moon take the water entirely away from the earth?” The answer is, that the effect of the tidal force is simply to diminish very slightly the weight of the water, or its tendency towards the earth's centre, but not to destroy, or overmaster, the gravitational control of the earth. The water retains nearly all its weight, for the tidal force of the moon diminishes it less than one part in 8,000,000. Still, this slight diminution is sufficient to cause the water to swell a little above its general level, at the points where it feels the effect of the tidal force. On the other hand, around that part of the earth which is situated half-way between the two tides, or along a diameter at right angles to the direction of the moon, the latter's attraction increases the weight of the water, i. e., its tendency toward the earth's centre (see Fig. 6). Perhaps this can better be understood, if we imagine the earth to be entirely liquid. In that case the difference in the force of the moon's attraction with difference of distance would be manifested in varying degrees throughout the earth's whole frame, and the result would be to draw the watery globe out into an ellipsoidal figure, having its greatest diameter in the line of the moon's attraction, and its smallest diameter at right angles to that line. The proportions of the ellipsoid would be such that the forces would be in equilibrium.

Owing to a variety of causes, such as the rotation of the earth on its axis, which carries the water rapidly round with it; the inertia of the water, preventing it from instantly responding to the tidal force; the irregular shape of the oceans, interrupted on all sides by great areas of land; their varying depth, producing differences of friction, and so on, the tidal waves do not appear directly under, or directly opposite to, the moon, and the calculation of the course and height of the actual tides, at particular points on the earth, becomes one of the most difficult problems in astronomical physics.

We now turn to consider the effects of the sun's tidal force in connection with that of the moon. This introduces further complications. The solar tides are only about two-fifths as high as the lunar tides, but they suffice to produce notable effects when they are either combined with, or act in opposition to, the others. They are combined twice a month—once when the moon is between the earth and the sun, at the time of new moon; and again when the moon is in opposition to the sun, at the time of full moon. In these two positions the attractions of the sun and the moon must, so to speak, act together, with the result that the tides produced by them blend into a single greater wave. This combination produces what are called spring tides, the highest of the month. When, on the other hand, the moon is in a position at right angles to the direction of the sun, which happens at the lunar phases named first and last quarters, the solar and the lunar tides have their crests 90° apart, and, in a sense, act against one another, and then we have the neap tides, which are the lowest of the month.

Without entering into a demonstration, it may here be stated as a fact to be memorised, that the tidal force exerted by any celestial body varies inversely as the cube of the distance. This is the reason why the sun, although it exceeds the moon in mass more than 25,000,000 times, and is situated only about 400 times as far away from the earth, exercises comparatively so slight a tidal force on the water of the ocean. If the tidal force varied as the square of the distance, like the ordinary effects of gravitation, the tides produced by the sun would be more than 150 times as high as those produced by the moon, and would sweep New York, London, and all the seaports of the world to destruction. In that case it might be possible, by delicate observations, to detect a tidal effect produced upon the oceans of the earth by the planet Jupiter.

4. The Atmosphere. The solid globe of the earth is enveloped in a mixture of gases, principally oxygen and nitrogen, which we call the air, or the atmosphere, and upon whose presence our life and most other forms of life depend. The atmosphere is retained by the attraction of the earth, and it rotates together with the earth. If this were not so—if the atmosphere stood fast while the earth continued to spin within it—a terrific wind would constantly blow from the east, having a velocity at the equator of more than a thousand miles an hour.

Exactly how high the atmosphere extends we do not know—it may not have any definite limits—but we do know that its density rapidly diminishes with increase of height above the ground, so that above an elevation of a few miles it becomes so rare that it would not support human life. The phenomena of meteors, set afire by the friction of their swift rush through the upper air, prove, however, that there is a perceptible atmosphere at an elevation of more than a hundred miles.

From an astronomical point of view, the most important effect of the presence of the atmosphere is its power of refracting light. By refraction is meant the property possessed by every transparent medium of bending, under particular circumstances, the rays of light which enter it out of their original course. The science of physics teaches us that if a ray of light passes from any transparent medium into another which is denser, and if the path of this ray is not perpendicular to the surface of the second medium, it will be turned from its original course in such a way as to make it more nearly perpendicular. Thus, if a ray of light passes from air into water at a certain slope to the surface, it will, upon entering the water, be so changed in direction that the slope will become steeper. Only if it falls perpendicularly upon the water will it continue on without change of direction. Conversely a ray passing from a denser into a rarer medium is bent away from a perpendicular to the surface of the first medium, or its slope becomes less. This explains why, if we put a coin in a bowl, with the eye in such a position that it cannot see the coin over the edge, and then fill the bowl with water, the coin seems to be lifted up into sight. Moreover, if any transparent medium increases in density with depth, the amount of refraction will increase as the ray goes deeper, and the direction of the ray will be changed from a straight line into a curve, tending to become more and more perpendicular.

Now all this applies to the atmosphere. If a star is seen in the zenith, its light falls perpendicularly into the atmosphere and its course is not deviated, or in other words there is no refraction. But if the star is somewhere between the zenith and the horizon, its light falls slopingly into the atmosphere, and is subject to refraction, the amount of bending increasing with approach to the horizon. Observation shows that the refraction of the atmosphere, which is zero at the zenith, increases to about half a degree (and sometimes much more, depending upon the state of the air), near the horizon. It follows that a celestial object seen near the horizon will ordinarily appear about half a degree above its true place. Since the apparent diameters of the sun and the moon are about half a degree, when they are rising or setting they can be seen on the horizon before they have really risen above it, or after they have really sunk below it. Tables of refraction at various altitudes have been prepared, and they have to be consulted in all exact observations of the celestial bodies.

Fig. 7. Refraction.
Suppose an observer situated at O on the earth. The sun, at S, has sunk below the level of his horizon, O H, but since the sun sends out rays in all directions there will be some, such as S A B, which will strike the atmosphere at A, and the refraction, tending to make the ray more nearly perpendicular to the surface of the atmosphere, will, instead of allowing it to go on straight over the observer's head to B, bend it down along the dotted line A O, and the observer will see the sun as if it lay in the direction of the dotted line O A S′, which places the sun apparently above the horizon.