Fig. 37.
Fig. 38 shows the position of the vernal equinox 2170 B.C. It was then in Taurus, just south of the Pleiades. It has since moved from Taurus, through Aries, and into Pisces, as shown in Fig. 39.
Fig. 38.
Fig. 39.
Since celestial longitude and right ascension are both measured from the first point of Aries, the longitude and right ascension of the stars are slowly changing from year to year. It will be seen, from Figs. 38 and 39, that the declination is also slowly changing.
30. Nutation.—The gyratory motion of the earth's axis is not perfectly regular and uniform. The earth's axis has a slight tremulous motion, oscillating to and fro through a short distance once in about nineteen years. This tremulous motion of the axis causes the pole of the heavens to describe an undulating curve, as shown in Fig. 40, and gives a slight unevenness to the motion of the equinoxes along the ecliptic. This nodding motion of the axis is called nutation.
Fig. 40.
31. Refraction.—When a ray of light from one of the heavenly bodies enters the earth's atmosphere obliquely, it will be bent towards a perpendicular to the surface of the atmosphere, since it will be entering a denser medium. As the ray traverses the atmosphere, it will be continually passing into denser and denser layers, and will therefore be bent more and more towards the perpendicular. This bending of the ray is shown in Fig. 41. A ray which started from A would enter the eye at C, as if it came from I: hence a star at A would appear to be at I.
Fig. 41.
Atmospheric refraction displaces all the heavenly bodies from the horizon towards the zenith. This is evident from Fig. 42. OD is the horizon, and Z the zenith, of an observer at O. Refraction would make a star at Q appear at P: in other words, it would displace it towards the zenith. A star in the zenith is not displaced by refraction, since the rays which reach the eye from it traverse the atmosphere vertically. The farther a star is from the zenith, the more it is displaced by refraction, since the greater is the obliquity with which the rays from it enter the atmosphere.
Fig. 42.
At the horizon the displacement by refraction is about half a degree; but it varies considerably with the state of the atmosphere. Refraction causes a heavenly body to appear above the horizon longer than it really is above it, since it makes it appear to be on the horizon when it is really half a degree below it.
The increase of refraction towards the horizon often makes the sun, when near the horizon, appear distorted, the lower limb of the sun being raised more than the upper limb. This distortion is shown in Fig. 43. The vertical diameter of the sun appears to be considerably less than the horizontal diameter.
Fig. 43.
32. Parallax.—Parallax is the displacement of an object caused by a change in the point of view from which it is seen. Thus in Fig. 44, the top of the tower S would be seen projected against the sky at a by an observer at A, and at b by an observer at B. In passing from A to B, the top of the tower is displaced from a to b, or by the angle aSb. This angle is called the parallax of S, as seen from B instead of A.
Fig. 44.
The geocentric parallax of a heavenly body is its displacement caused by its being seen from the surface of the earth, instead of from the centre of the earth. In Fig. 45, R is the centre of the earth, and O the point of observation on the surface of the earth. Stars at S, S', and S'', would, from the centre of the earth, appear at Q, Q', and Q''; while from the point O on the surface of the earth, these same stars would appear at P, P' and P'', being displaced from their position, as seen from the centre of the earth, by the angles QSP, Q'S'P', and Q''S''P''. It will be seen that parallax displaces a body from the zenith towards the horizon, and that the parallax of a body is greatest when it is on the horizon. The parallax of a heavenly body when on the horizon is called its horizontal parallax. A body in the zenith is not displaced by parallax, since it would be seen in the same direction from both the centre and the surface of the earth.
Fig. 45.
The parallax of a body at S''' is Q'''S'''P, which is seen to be greater than QSP; that is to say, the parallax of a heavenly body increases with its nearness to the earth. The distance and parallax of a body are so related, that, either being known, the other may be computed.
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.
Fig. 46.
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.
Fig. 47.
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.
Fig. 48 shows a portion of the apparent path of one of the planets.