Part 8

33. Aberration.--Aberration is a slight displacement of a star, owing to an apparent change in the direction of the rays of light which proceed from it, caused by the motion of the earth in its orbit. If we walk rapidly in any direction in the rain, when the drops are falling vertically, they will appear to come into our faces from the direction in which we are walking. Our own motion has apparently changed the direction in which the drops are falling.

In Fig. 46 let A be a gun of a battery, from which a shot is fired at a ship, DE, that is passing. Let ABC be the course of the shot. The shot enters the ship's side at B, and passes out at the other side at C; but in the mean time the ship has moved from E to e, and the part B, where the shot entered, has been carried to b. If a person on board the ship could see the ball as it crossed the ship, he would see it cross in the diagonal line bC; and he would at once say that the cannon was in the direction of Cb. If the ship were moving in the opposite direction, he would say that the cannon was just as far the other side of its true position.

Now, we see a star in the direction in which the light coming from the star appears to be moving. When we examine a star with a telescope, we are in the same condition as the person who on shipboard saw the cannon-ball cross the ship. The telescope is carried along by the earth at the rate of eighteen miles a second: hence the light will appear to pass through the tube in a slightly different direction from that in which it is really moving: just as the cannon-ball appears to pass through the ship in a different direction from that in which it is really moving. Thus in Fig. 47, a ray of light coming in the direction SOT would appear to traverse the tube OT of a telescope, moving in the direction of the arrow, as if it were coming in the direction S'O.

As light moves with enormous velocity, it passes through the tube so quickly, that it is apparently changed from its true direction only by a very slight angle: but it is sufficient to displace the star. This apparent change in the direction of light caused by the motion of the earth is called aberration of light.

34. The Planets.--On watching the stars attentively night after night, it will be found, that while the majority of them appear fixed on the surface of the celestial sphere, so as to maintain their relative positions, there are a few that wander about among the stars, alternately advancing towards the east, halting, and retrograding towards the west. These wandering stars are called planets.

Their motions appear quite irregular; but, on the whole, their eastward motion is in excess of their westward, and in a longer or shorter time they all complete the circuit of the heavens. In almost every instance, their paths are found to lie wholly in the belt of the zodiac.

Fig. 48 shows a portion of the apparent path of one of the planets.

II. THE SOLAR SYSTEM.

I. THEORY OF THE SOLAR SYSTEM.

35. Members of the Solar System.--The solar system is composed of the sun, planets, moons, comets, and meteors. Five planets, besides the earth, are readily distinguished by the naked eye, and were known to the ancients: these are Mercury, Venus, Mars, Jupiter, and Saturn. These, with the sun and moon, made up the seven planets of the ancients, from which the seven days of the week were named.

The Ptolemaic System.

36. The Crystalline Spheres.--We have seen that all the heavenly bodies appear to be situated on the surface of the celestial sphere. The ancients assumed that the stars were really fixed on the surface of a crystalline sphere, and that they were carried around the earth daily by the rotation of this sphere. They had, however, learned to distinguish the planets from the stars, and they had come to the conclusion that some of the planets were nearer the earth than others, and that all of them were nearer the earth than the stars are. This led them to imagine that the heavens were composed of a number of crystalline spheres, one above another, each carrying one of the planets, and all revolving around the earth from east to west, but at different rates. This structure of the heavens is shown in section in Fig. 49.

37. Cycles and Epicycles.--The ancients had also noticed that, while all the planets move around the heavens from west to east, their motion is not one of uniform advancement. Mercury and Venus appear to oscillate to and fro across the sun, while Jupiter and Saturn appear to oscillate to and fro across a centre which is moving around the earth, so as to describe a series of loops, as shown in Fig. 50.

The ancients assumed that the planets moved in exact circles, and, in fact, that all motion in the heavens was circular, the circle being the simplest and most perfect curve. To account for the loops described by the planets, they imagined that each planet revolved in a circle around a centre, which, in turn, revolved in a circle around the earth. The circle described by this centre around the earth they called the cycle, and the circle described by the planet around this centre they called the epicycle.

38. The Eccentric.--The ancients assumed that the planets moved at a uniform rate in describing the epicycle, and also the centre in describing the cycle. They had, however, discovered that the planets advance eastward more rapidly in some parts of their orbits than in others. To account for this they assumed that the cycles described by the centre, around which the planets revolved, were eccentric; that is to say, that the earth was not at the centre of the cycle, but some distance away from it, as shown in Fig. 51. E is the position of the earth, and C is the centre of the cycle. The lines from E are drawn so as to intercept equal arcs of the cycle. It will be seen at once that the angle between any pair of lines is greatest at P, and least at A; so that, were a planet moving at the same rate at P and A, it would seem to be moving much faster at P. The point P of the planet's cycle was called its perigee, and the point A its apogee.

As the apparent motion of the planets became more accurately known, it was found necessary to make the system of cycles, epicycles, and eccentrics exceedingly complicated to represent that motion.

The Copernican System.

39. Copernicus.--Copernicus simplified the Ptolemaic system greatly by assuming that the earth and all the planets revolved about the sun as a centre. He, however, still maintained that all motion in the heavens was circular, and hence he could not rid his system entirely of cycles and epicycles.

Tycho Brahe's System.

40. Tycho Brahe.--Tycho Brahe was the greatest of the early astronomical observers. He, however, rejected the system of Copernicus, and adopted one of his own, which was much more complicated. He held that all the planets but the earth revolved around the sun, while the sun and moon revolved around the earth. This system is shown in Fig. 52.

Kepler's System.

41. Kepler.--While Tycho Brahe devoted his life to the observation of the planets. Kepler gave his to the study of Tycho's observations, for the purpose of discovering the true laws of planetary motion. He banished the complicated system of cycles, epicycles, and eccentrics forever from the heavens, and discovered the three laws of planetary motion which have rendered his name immortal.

42. The Ellipse.--An ellipse is a closed curve which has two points within it, the sum of whose distances from every point on the curve is the same. These two points are called the foci of the ellipse.

One method of describing an ellipse is shown in Fig. 53. Two tacks, F and F', are stuck into a piece of paper, and to these are fastened the two ends of a string which is longer than the distance between the tacks. A pencil is then placed against the string, and carried around, as shown in the figure. The curve described by the pencil is an ellipse. The two points F and F' are the foci of the ellipse: the sum of the distances of these two points from every point on the curve is equal to the length of the string. When half of the ellipse has been described, the pencil must be held against the other side of the string in the same way, and carried around as before.

The point O, half way between F and F', is called the centre of the ellipse; AA' is the major axis of the ellipse, and CD is the minor axis.

43. The Eccentricity of the Ellipse.--The ratio of the distance between the two foci to the major axis of the ellipse is called the eccentricity of the ellipse. The greater the distance between the two foci, compared with the major axis of the ellipse, the greater is the eccentricity of the ellipse; and the less the distance between the foci, compared with the length of the major axis, the less the eccentricity of the ellipse. The ellipse of Fig. 54 has an eccentricity of 1/8. This ellipse scarcely differs in appearance from a circle. The ellipse of Fig. 55 has an eccentricity of 1/2, and that of Fig. 56 an eccentricity of 7/8.

44. Kepler's First Law.--Kepler first discovered that all the planets move from west to east in ellipses which have the sun as a common focus. This law of planetary motion is known as Kepler's First Law. The planets appear to describe loops, because we view them from a moving point.

The ellipses described by the planets differ in eccentricity; and, though they all have one focus at the sun, their major axes have different directions. The eccentricity of the planetary orbits is comparatively small. The ellipse of Fig. 54 has seven times the eccentricity of the earth's orbit, and twice that of the orbit of any of the larger planets except Mercury; and its eccentricity is more than half of that of the orbit of Mercury. Owing to their small eccentricity, the orbits of the planets are usually represented by circles in astronomical diagrams.