Part 7

The great reflector of the Paris Observatory is a Newtonian reflector. Its mirror of silvered glass is 4 feet in diameter, and its focal length is 23 feet. This telescope is shown in Fig. 29.

21. The Sun's Motion among the Stars.--If we notice the stars at the same hour night after night, we shall find that the constellations are steadily advancing towards the west. New constellations are continually appearing in the east, and old ones disappearing in the west. This continual advancing of the heavens towards the west is due to the fact that the sun's place among the stars is continually moving towards the east. The sun completes the circuit of the heavens in a year, and is therefore moving eastward at the rate of about a degree a day.

This motion of the sun's place among the stars is due to the revolution of the earth around the sun, and not to any real motion of the sun. In Fig. 30 suppose the inner circle to represent the orbit of the earth around the sun, and the outer circle to represent the celestial sphere. When the earth is at E, the sun's place on the celestial sphere is at S'. As the earth moves in the direction EF, the sun's place on the celestial sphere must move in the direction S'T: hence the revolution of the earth around the sun would cause the sun's place among the stars to move around the heavens in the same direction that the earth is moving around the sun.

22. The Ecliptic.--The circle described by the sun in its apparent motion around the heavens is called the ecliptic. The plane of this circle passes through the centre of the earth, and therefore through the centre of the celestial sphere; the earth being so small, compared with the celestial sphere, that it practically makes no difference whether we consider a point on its surface, or one at its centre, as the centre of the celestial sphere. The ecliptic is, therefore, a great circle.

The earth's orbit lies in the plane of the ecliptic; but it extends only an inappreciable distance from the sun towards the celestial sphere.

23. The Obliquity of the Ecliptic.--The ecliptic is inclined to the celestial equator by an angle of about 23-1/2°. This inclination is called the obliquity of the ecliptic. The obliquity of the ecliptic is due to the deviation of the earth's axis from a perpendicular to the plane of its orbit. The axis of a rotating body tends to maintain the same direction; and, as the earth revolves around the sun, its axis points all the time in nearly the same direction. The earth's axis deviates about 23-1/2° from the perpendicular to its orbit; and, as the earth's equator is at right angles to its axis, it will deviate about 23-1/2° from the plane of the ecliptic. The celestial equator has the same direction as the terrestrial equator, since the axis of the heavens has the same direction as the axis of the earth.

Suppose the globe at the centre of the tub (Fig. 31) to represent the sun, and the smaller globes to represent the earth in various positions in its orbit. The surface of the water will then represent the plane of the ecliptic, and the rod projecting from the top of the earth will represent the earth's axis, which is seen to point all the time in the same direction, or to lean the same way. The leaning of the axis from the perpendicular to the surface of the water would cause the earth's equator to be inclined the same amount to the surface of the water, half of the equator being above, and half of it below, the surface. Were the axis of the earth perpendicular to the surface of the water, the earth's equator would coincide with the surface, as is evident from Fig. 32.

24. The Equinoxes and Solstices.--The ecliptic and celestial equator, being great circles, bisect each other. Half of the ecliptic is north, and half of it is south, of the equator. The points at which the two circles cross are called the equinoxes. The one at which the sun crosses the equator from south to north is called the vernal equinox, and the one at which it crosses from north to south the autumnal equinox. The points on the ecliptic midway between the equinoxes are called the solstices. The one north of the equator is called the summer solstice, and the one south of the equator the winter solstice. In Fig. 33, EQ is the celestial equator, EcE'c' the ecliptic, V the vernal equinox, A the autumnal equinox, Ec the winter solstice, and E'c' the summer solstice.

25. The Inclination of the Ecliptic to the Horizon.--Since the celestial equator is perpendicular to the axis of the heavens, it makes the same angle with it on every side: hence, at any place, the equator makes always the same angle with the horizon, whatever part of it is above the horizon. But, as the ecliptic is oblique to the equator, it makes different angles with the celestial axis on different sides; and hence, at any place, the angle which the ecliptic makes with the horizon varies according to the part which is above the horizon. The two extreme angles for a place more than 23-1/2° north of the equator are shown in Figs. 34 and 35.

The least angle is formed when the vernal equinox is on the eastern horizon, the autumnal on the western horizon, and the winter solstice on the meridian, as in Fig. 34. The angle which the ecliptic then makes with the horizon is equal to the elevation of the equinoctial minus 23-1/2°. In the latitude of New York this angle = 49° - 23-1/2° = 25-1/2°.

The greatest angle is formed when the autumnal equinox is on the eastern horizon, the vernal on the western horizon, and the summer solstice is on the meridian (Fig. 35). The angle between the ecliptic and the horizon is then equal to the elevation of the equinoctial plus 23-1/2°. In the latitude of New York this angle = 49° + 23-1/2° = 72-1/2°.

Of course the equinoxes, the solstices, and all other points on the ecliptic, describe diurnal circles, like every other point in the heavens: hence, in our latitude, these points rise and set every day.

26. Celestial Latitude and Longitude.--Celestial latitude is distance measured north or south from the ecliptic; and celestial longitude is distance measured on the ecliptic eastward from the vernal equinox, or the first point of Aries. Great circles perpendicular to the ecliptic are called celestial meridians. These circles all pass through the poles of the ecliptic, which are some 23-1/2° from the poles of the equinoctial. The latitude of a heavenly body is measured by the arc of a celestial meridian included between the body and the ecliptic. The longitude of a heavenly body is measured by the arc of the ecliptic included between the first point of Aries and the meridian which passes through the body. There are, of course, always two arcs included between the first point of Aries and the meridian,--one on the east, and the other on the west, of the first point of Aries. The one on the east is always taken as the measure of the longitude.

27. The Precession of the Equinoxes.--The equinoctial points have a slow westward motion along the ecliptic. This motion is at the rate of about 50'' a year, and would cause the equinoxes to make a complete circuit of the heavens in a period of about twenty-six thousand years. It is called the precession of the equinoxes. This westward motion of the equinoxes is due to the fact that the axis of the earth has a slow gyratory motion, like the handle of a spinning-top which has begun to wabble a little. This gyratory motion causes the axis of the heavens to describe a cone in about twenty-six thousand years, and the pole of the heavens to describe a circle about the pole of the ecliptic in the same time. The radius of this circle is 23-1/2°.

28. Illustration of Precession.--The precession of the equinoxes may be illustrated by means of the apparatus shown in Fig. 36. The horizontal and stationary ring EC represents the ecliptic; the oblique ring E'Q represents the equator; V and A represent the equinoctial point, and E and C the solstitial points; B represents the pole of the ecliptic, P the pole of the equator, and PO the celestial axis. The ring E'Q is supported on a pivot at O; and the rod BP, which connects B and P, is jointed at each end so as to admit of the movement of P and B.

On carrying P around B, we shall see that E'Q will always preserve the same obliquity to EC, and that the points V and A will move around the circle EC. The same will also be true of the points E and C.

29. Effects of Precession.--One effect of precession, as has already been stated, is the revolution of the pole of the heavens around the pole of the ecliptic in a period of about twenty-six thousand years. The circle described by the pole of the heavens, and the position of the pole at various dates, are shown in Fig. 37, where o indicates the position of the pole at the birth of Christ. The numbers round the circle to the left of o are dates A.D., and those to the right of o are dates B.C. It will be seen that the star at the end of the Little Bear's tail, which is now near the north pole, will be exactly at the pole about the year 2000. It will then recede farther and farther from the pole till the year 15000 A.D., when it will be about forty-seven degrees away from the pole. It will be noticed that one of the stars of the Dragon was the pole star about 2800 years B.C. There are reasons to suppose that this was about the time of the building of the Great Pyramid.

A second effect of precession is the shifting of the signs along the zodiac. The zodiac is a belt of the heavens along the ecliptic, extending eight degrees from it on each side. This belt is occupied by twelve constellations, known as the zodiacal constellations. They are Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, and Pisces. The zodiac is also divided into twelve equal parts of thirty degrees each, called signs. These signs have the same names as the twelve zodiacal constellations, and when they were first named, each sign occupied the same part of the zodiac as the corresponding constellation; that is to say, the sign Aries was in the constellation Aries, and the sign Taurus in the constellation Taurus, etc. Now the signs are always reckoned as beginning at the vernal equinox, which is continually shifting along the ecliptic; so that the signs are continually moving along the zodiac, while the constellations remain stationary: hence it has come about that the first point of Aries (the sign) is no longer in the constellation Aries, but in Pisces.

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.

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.

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.

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.

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.

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.

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.

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.