Lessons in astronomy including uranography. A brief intoductory course without mathematics

Front matter

Chap. Copyright No.

Shel£.„ti«dL 74-

Sheli„^Z/.

Preface To The Edition Of 1895

Since the fir^t publication of this work the progress of astronomy has been so rapid that in order to keep abreast of the times it has become necessary to give the book a thorough revision. This has been done : numerous minor changes and corrections have been made, some articles have been rewritten, and others added. At the same time the alterations have been so managed that they will cause no serious inconvenience in using the older editions in connection with the new one in class-room work.

It is hoped that, so far as its scope permits, the book now presents a satisfactory summary of the existing state of the science.

August, 1895.

Contents

PAGES

CHAPTER I. — Introduction : Fundamental Notions and Definitions. — The Celestial Sphere and its Circles. — Altitude and Azimuth. — Right Ascension and Declination. — Celestial LatitudeandLongitude . . . . . . . . 1-16

CHAPTER II. — Ukanography : Globes and Star-maps. — Star . Magnitudes. — Names and Designations of Stars. — The Constellations in Detail 17-54

Appendix

PAGES

CHAPTER XIII. — Astronomical Instruments: The Telescope, Simple Refracting, Achromatic, and Reflecting. — The Equatorial. — The Filar Micrometer. — The Transit Instrument. — The Clock and the Chronograph. — The Meridian Circle. — The Sextant 302-320

CHAPTER XIV. (for the most part supplementary to Articles in the Text). — Hour- angle and Time. — Twilight. — Determination of Latitude. — Place of a Ship at Sea. — Finding the Form of the Earth's Orbit. — The Ellipse. — Illustrations of Kepler's l Harmonic • Law. — The Equation of Light, and the Sun's Distance determined by it. — Aberration of Light. — De l'lsle's Method of getting the Sun's Parallax from a Transit of Venus. — The Parabola and the Conic Sections. — Determination of Stellar Parallax .... 321-339

QUESTIONS FOR REVIEW ....... 340

TABLES OF ASTRONOMICAL DATA:

I. Astronomical Constants 347

II. The Principal Elements of the Solar System . . . 348

III. The Satellites of the Solar System 349

IV. The Principal Variable Stars 350

V. The Best Determined Stellar Parallaxes .... 351

VI. The Greek Alphabet and Miscellaneous Symbols . . 352

INDEX 353

STAR-MAPS 367

Chapter I

INTRODUCTION. — FUNDAMENTAL NOTIONS AND DEFINI- TIONS. — THE CELESTIAL SPHERE AND ITS CIRCLES. — ALTITUDE AND AZIMUTH. — RIGHT ASCENSION AND DECLINATION. — CELESTIAL LATITUDE AND LONGITUDE.

1. Astronomy 1 is the science which deals with the heavenly bodies.

As it is the oldest of the sciences, so also it is one of the most perfect, and in certain aspects the noblest, as being the most " unselfish " of them all. And yet, although not bearing so directly upon the material interests of life as the more modern sciences of Physics and Chemistry, it is of high utility. By means of Astronomy the latitudes and longitudes of places upon. the earth's surface are determined, and by such determinations alone is it possible to conduct vessels upon the sea. Moreover, all the operations of surveying upon a large scale, such as the determination of the boundaries of countries, depend more or less upon astronomical observations. The same is true of operations which, like the railway service, require an accurate knowledge and observance of time ;. for the fundamental timekeeper is the diurnal revolution of the heavens, as determined by the astronomer's transit-instrument.

In ancient times the science was supposed to have a still higher utility. It was believed that human affairs of every kind, the welfare of nations, and the life history of individuals alike, were controlled,

1 The term is derived from two Greek words: astron, a star, and nomos, a law.

2 THE HEAVENLY BODIES. [§ 1

or at least prefigured, by the motions of the stars and planets ; so that from the study of the heavens it ought to be possible to predict futurity. This belief is embodied in the pseudo-science of " Astrology," long since shown to be a baseless delusion though it still retains a hold upon the credulous.

2. The heavenly bodies include, first, the solar system, — that is, the sun and the planets which revolve around it, with their attendant satellites ; second, the comets and the meteors, which also revolve around the sun, but are bodies of a very different nature from the planets, and move in different kinds of orbits ; and, thirdly, the stars and nebulae. The earth on which we live is one of the planets, and the moon is the earth's satellite. The stars which we see are bodies of the same kind as the sun, shining like him with fiery heat, while the planets and the satellites are dark and cool like the earth, and visible to us only by the sunlight they reflect. As for the comets and nebulae, they appear to be mere clouds, composed of heated gas or swarms of little particles of more solid substances, perhaps not very hot, but luminous from some cause or other. The telescope reveals millions of stars invisible to the naked eye, and there are others, possibly thousands of them, that do not shine, but manifest their existence by affecting the motions of their neighbors.

3. As we look off from the earth at night, the stars appear to be all around us, like glittering points fastened to the inside of a huge hollow globe. Really they are at very different disstances, all enormous as compared with any distances with which geography makes us familiar. Even the moon is eighty times as far away as New York from Liverpool, and the sun is nearly four hundred times as distant as the moon, and the nearest of the stars is more than two hundred thousand times as distant as the sun ; as to the remoter stars, some of them are certainly thousands of times as far away as the nearer ones, — so far that light itself is thousands of years in coming

§ 31 THE HEAVENLY BODIES. 3

to us from thein. These are facts which, are certain, not mere guesses or beliefs.

Then, too, as to their motions. Although the heavenly bodies seem to us for the most part to be at rest, except as the earth's rotation makes them appear to rise and set, yet really they are all moving, and with a swiftness of which we can form no conception. A cannon-ball is a snail to the slowest of them. The earth itself in its revolution around the sun is flying eighteen and a half miles in a second, which is more than thirty times as fast as the swiftest rifle bullet. We fail to perceive the motion simply because it is so smooth and so unresisted. The space outside our air contains nothing that can sensibly obstruct either sight or motion.

4. But this knowledge as to the real distance and motions of the heavenly bodies was gained only after long centuries of study. If we go out to look at the stars some moonless night we find them apparently sprinkled over the dome of the sky in groups or constellations, which are still substantially the same as in the days of the earliest astronomers. At first these constellations were figures of animals and other objects, and many celestial globes and maps still bear grotesque pictures representing them. At present, however, a constellation is only a certain region of the sky, limited by imaginary lines which divide it from the neighboring constellations, just as countries are divided in geography. As to the exact boundaries of these constellations, and even their number, there is no precise agreement among astronomers. Forty-eight of them have come down to us from the time of Ptolemy, 1 and even in his day many of them were already ancient.

About twenty more, which have been proposed by more recent astronomers, are now recognized, besides a considerable number which have been abandoned.

1 Ptolemy, the greatest astronomer of antiquity, flourished at Alexandria about 130 a.d.

4 UR ANOGKAPHY. [§ 6

5. TJranography, or Description of the Visible Heavens.—

The study of the constellations, or the apparent arrangement of the stars in the sky, is called Uranography. 1 It is not an essential ■ p&it of Astronomy, but it is an easy and pleasant study; and in becoming familiar with the constellations and their principal stars, the pupil will learn more readily and thoroughly than in any other way the most important facts in relation to the apparent motions of the heavenly bodies, and the principal points and circles of the celestial sphere. For this reason the teacher is urged to take the earliest opportunity to have his pupils trace such of the constellations as happen to be visible in the evening sky when they begin the study of Astronomy.

6. The Celestial Sphere. 2 — The sky appears like a hollow vault, to which the stars seem to be attached, like specks of gilding upon the inner surface of a dome. We cannot judge of the distance of this surface from the eye, further than to perceive that it must be very far away. It is therefore natural and extremely convenient to regard the distance of the sky as everywhere the same and unlimited. The { celestial sphere? as it is called, is conceived of as so enormous that the whole world of stars and planets lies in its centre like a few grains of sand in the middle of the dome of the Capitol. Its diameter is assumed to be immeasurably greater than any actual distance known, and greater than any quantity assignable. In technical language it is taken as mathematically infinite.

Since the celestial sphere is thus infinite, any two parallel lines drawn from distant points on the surface of the earth, or even from points as distant as the earth and the sun, will seem to meet at one point on the surface of the sphere. If the two

1 From the Greek, ouranos (heavens), and graphe (description).

2 The study of the celestial sphere and its circles is greatly facilitated by the use -of a globe, or armillary sphere. Without some such -apparatus it is not easy for a young person to get clear ideas upon the subject.

§6]

APPARENT PLACE OF A HEAVENLY BODY.

lines were anywhere a million miles apart, for instance, they will, of course, .still be a million miles apart when they reach the surface of the sphere ; but at an infinite distance even a million miles is a mere nothing, so that the two lines make apparently but a single point 1 where they pierce the sphere.

7. The Apparent Place of a Heavenly Body. — This is simply the point where a line drawn from the observer through the body in question, continued outward, pierces the celestial sphere. It depends solely upon the direction of the body, and is in no way affected by its distance from us. Thus, in Fig. 1, A, B, C, etc., are the apparent places of a, 6, c, etc., the observer being at 0. Objects that are nearly in line with each other, as h, ?, k, will appear close together. The moon, for instance, often looks to us very near a star, which is really of course at ah enormous distance beyond her.

8. Angular Measurement. — It is clear that we cannot properly describe the apparent distance of two points upon the celestial sphere from each other by feet or inches. To say that two stars are about five feet apart, for instance, — and it is not very uncommon to hear such an expression, — means nothing unless we know how far from the eye the five-foot measure is to be held. The proper units for expressing apparent distance in the sky are those of angle, viz. : degrees (°), minutes ( f ), and seconds (") ; the circumference of a circle being divided into 360 degrees, each degree into 60 minutes, and each minute into 60 seconds. Thus, the Great Bear's tail,

Fig. 1.

1 This is the same as the ' vanishing-point ' of perspective.

6 CIRCLES OF THE CELESTIAL SPHERE. [§ 8

or Dipper-handle, is about 16° long, and the long side of the Dipper-bowl is about 10° ; the moon and the sun are each about half a degree, or 30 ', in diameter.

It is very important that the student in Astronomy should become accustomed as soon as possible to estimate celestial measures in this way. A little practice soon makes it easy, though at first one is apt to be embarrassed by the fact that the sky looks to the eye not like a true hemisphere but like a flattened vault, so that the estimates of distances for all objects near the horizon are apt to be too large. The moon, when rising or setting, looks to most persons much larger than when overhead ; and the Dipper-bowl, when underneath the pole, seems to cover a much larger area than when above it.

9. Circles and Principal Points of the Celestial Sphere. —

Just as the surface of the earth in Geography is covered with a net-work of imaginary lines, — meridians and parallels of latitude, — so the sky is supposed to be marked off in a somewhat similar way. Two such sets of points and reference circles are in common use to describe the apparent places of the stars, and a third was used by the ancients and is still employed for some purposes. The first system depends upon the direction of the force of gravity shown by a plumb-line at the point where the observer stands ; the second upon the direction of the axis of the earth, which points very near the so-called Pole-star ; and the third depends upon the position of the orbit in which the earth travels around the sun.

10. The Gravitational or Up-and-Down System. — (a) The

Zenith and Nadir. The point in the sky directly above the observer is called the zenith; the opposite point, under the earth and of course invisible, the nadir. 1

(b) The Horizon (pronounced ho-ii'-zon, not hor'-i-zon).

1 These are Arabic terms. About 1100 a.d. the Arabs were the world's chief astronomers, and have left their mark upon the science in numerous names of stars and astronomical terms.

VERTICAL CIRCLES.

This is a ' great circle ' * around the sky, half-way between the zenith and the nadir, and therefore everywhere 90° from the zenith. The word is derived from a Greek word which means a 'boundary'; i.e., the line where the earth or sea limits the sky. The actual line of division, which on the land is always more or less irregular, is called the visible horizon, to distinguish it from the true horizon defined above. We may also define the horizon as the great circle where a plane which passes through the observer's eye perpendicular to the plumb-line cuts the celestial sphere.

11. Vertical Circles and the Meridian; Altitude, and Azimuth. — Circles drawn from the zenith to the nadir cut the horizon at right angles, and are known as vertical circles. Each star has at any moment its own vertical circle.

z

Fig. 2. — The Horizon and Vertical Circles. O, the place of the Observer.

OZ, the Observer's Vertical.

Z, the Zenith ; P, the Pole.

SWiVE, the Horizon.

SZPN y the Meridian.

EZW, the Prime Vertical.

M y some Star.

ZMH, arc of the Star's Vertical Circle.

TMR, the Star's Almucantar.

Angle TZM, or arc Sff, Star's Azimuth.

Arc HM, Star's Altitude.

Arc ZM t Star's Zenith Distance.

That particular vertical circle which passes north and south is known as the celestial meridian ; while the vertical circle at right angles to this is called the prime vertical. Small circles

1 ' Great Circles \ are those which divide the sphere into two equal parts.

8 DIURNAL ROTATION. C§ H

drawn parallel to the horizon are known as parallels of altitude, or almucantars. Fig. 2 illustrates these circles.

By their help we can easily define the apparent position of a heavenly body.

Its Altitude is its apparent elevation above the horizon ; that is, the number of degrees between it and the horizon, measured on a vertical circle. Thus, in Fig. 2, the vertical circle ZMH passes through the point M. The arc MH, measured in degrees, is the altitude of M, and the arc ZM is called its zenith distance.

The Azimuth of a heavenly body is the same as its 'bearing' in Surveying, but measured from the true meridian and not from the magnetic. 1 It is the arc of the horizon, measured in degrees, intercepted between the south point and the foot of the vertical circle which passes through the object.

There are various ways of reckoning azimuth. Many writers express it in the same way as the ' bearing , in Surveying, i.e., so many degrees east or west of north or south. In the figure, the azimuth of M thus expressed is about 8, 50° E. The more usual way at present, however, is to reckon clear around from the south, through the west, to the point of beginning. Expressed in this way the azimuth of M would be about 310°, — i.e., the arc S WNEH.

Altitude and azimuth, however, are inconvenient for many purposes, because they continually change for a celestial object as it moves across the sky.

12. The Apparent Diurnal Rotation of the Heavens. — If we

go out on some clear evening in the early autumn, say about the 22d of September, and face the north, we shall find the appearance of that part of the heavens directly before us substantially as shown' in Fig. 3. In the north is the constellation of

1 The reader is reminded that the magnetic needle does not point exactly north. Its direction varies widely at different parts of the earth, an I, moreover, is continually changing to some extent.

§12]

DIURNAL ROTATION.

the Great Bear (Ursa Major), characterized by the conspicuous group of seven stars known as the " Great Dipper." It now lies with its handle sloping upward to the west. The two easternmost stars of the four which form its bowl are called d^ xjx

V snuon

A^

*

*V

**

P dP.

x?

**

**.

C/P

$F

C^

*M

J* vtn

Fig. 3. — The Northern Circumpolar Constellations.

the " Pointers/' because they point to the Pole-star, which is a solitary star not quite half-way from the horizon to the zenith (in the latitude of New York), and about as bright as the brighter of the two Pointers.

High up on the opposite side of the Pole-star from the Great Dipper, and at nearly the same distance, is an irregular

10 DIURNAL ROTATION. [§ 12

zigzag of five stars, each about as bright as the Pole-star itself. This is the constellation of Cassiopeia.

If now we watch these stars for only a few hours, Ave shall find that while all the forms remain unaltered, their places in the sky are slowly changing. The Great Dipper slides downward towards the north, so that by eleven o'clock (on Sept. 22) the Pointers are directly under the Pole-star. Cassiopeia still keeps opposite, however, rising towards the zenith; and if we continue the watch through the whole night, we shall find that all the stars appear to be moving in circles around a point near the Pole-star, revolving in the opposite direction to the hands of a watch (as we look towards the north) with a steady motion which takes them completely around once a day, or, to be more exact, once in 23 h 56 m 4.1 s of ordinary time. They behave just as if they were attached to the inner surface of a huge revolving sphere.

To indicate the position of the stars as it will be at midnight of Sept. 22, the figure must be held so that XII in the margin is at the bottom; at 4 a.m. the stars will have come to the position indicated by bringing XVI to the bottom, and so on. But at eight o'clock on the next night we shall find things in their original position very nearly.

If instead of looking toward the north we now look southward, we shall find that in that part of the sky also the stars appear to move in the same kind of way. All that are not too near the Pole-star rise somewhere in the eastern horizon, ascend obliquely to the meridian, and descend to their setting at points on the western horizon. The next day they rise and set again at precisely the same points, and the motion is always in an arc of a circle, called the star's diurnal circle, the size of which depends upon its distance from the pole. Moreover, all of these arcs are strictly concentric.

The ancients accounted for these fundamental and obvious facts by supposing that the stars are really fastened to the

§ 12] DEFINITION OF THE POLES. 11

celestial sphere, and that this sphere really turns daily in the manner indicated. According to this view there must really be upon the sphere two opposite points which remain at rest, and these are the poles.

13. Definition of the Poles. — The Poles, therefore, may be defined as those two points in the sky where a star would have no diurnal motion. The exact position of either pole may be determined with proper instruments, by finding the centre of the small diurnal circle described by some star near it, as, for instance, by the Pole-star.

The student must be careful not to confound the Pole with the Pole-star. The pole is an imaginary point; the Pole-star is only that one of the conspicuous stars which happens now 1 to be nearest to that point. The Pole-star at present is about 1\° distant from it. If we draw an imaginary line from the Pole-star to the star Mizar (the one at the bend of the Dipper-handle), it will pass almost exactly through the pole itself ; the distance of the pole from the Pole-star being very nearly one-quarter of the distance between the two " Pointers."

This definition of the pole is that which would be given by one familiar with the sky, but ignorant of the earth's rotation, and it is still perfectly correct ; but knowing, as we now do, that this apparent revolution of the celestial sphere is due to the real spinning of the earth on its axis, we may also define the poles as the two points where the earth's axis of rotation, produced indefinitely, would pierce the celestial sphere.

Since the two poles are diametrically opposite in the sky, only one of them is usually visible from any given place. Observers north of the earth's equator see only the north pole, and vice versa for observers in the southern hemisphere.

14. The Celestial Equator, or Equinoctial; Declination. —

The Equator is a great circle of the celestial sphere drawn half-way between the poles, everywhere 90° from each of them,

1 See Article 126.

12 HOUR-CIRCLES. [§ 14

and is the great circle in which the plane of the earth's equator cuts the celestial sphere. It is often called the Equinoctial. Fig. 4 shows how the plane of the earth's equator produced far enough would mark out such a circle in the heavens.

Small circles drawn parallel to the equinoctial, like the parallels of latitude on the earth, are known as 'Parallels of Declinationj the Declination of a star being its distance in degrees north or south of the celestial equator, -f- if north, — if south.

It corresponds precisely with the latitude of a place on the earth's surface ; but it cannot be

Fig. 4. — The Plane of the Earth's Equa- Called Celestial latitude, because

tor produced to cut the Celestial Sphere. ^at term has been preoccupied for an entirely different quantity (Art. 20). A star's parallel of declination is identical with its diurnal circle.

15. Hour-Circles. — The great circles of the celestial sphere which pass through the poles like the meridians on the earth, and are therefore perpendicular to the celestial equator, are called Hour-Circles. Some writers call them celestial meridians, but the term is objectionable since it is sometimes used to indicate an entirely different set of circles. That particular hour-circle which at any moment passes through the zenith of course coincides with the celestial meridian already defined in Art. 11.

16. The Celestial Meridian and the Cardinal Points. — The

best definition of the celestial meridian is, however, the great circle which passes through the zenith and the poles. The points where this meridian cuts the horizon (the circle of level), are the north and south points, and the east and west points of

§16]

THE VERNAL EQUINOX.

the horizon lie half-way between them, the four being known as the " Cardinal Points." The student is especially cautioned against confounding the north point with the north pole. The north point is on the horizon ; the north pole is high up in the sky.

Fig. 5. — Equator, Hour-Circles, etc.

0, place of the Observer; Z, his Zenith.

SENW, the Horizon.

POP', line parallel to the axis of the Earth.

P and P' y the two Poles of the Heavens.

EQ WT, the Celestial Equator, or Equinoctial.

X, the Vernal Equinox, or " First of Aries."

PXP', the Equinoctial Colure, or Zero Hour-Circle.

m, some Star.

Ym, the Star's Declination; Pm t its North- Polar Distance.

Angle mPR = arc Q Y, the Star's (eastern) Hour-Angle ; = 24 h minus Star's western Hour- Angle.

Angle XPm = arc XY t Star's Right Ascension.

Sidereal time at the moment = 24 h minus XPQ.

In Fig. 5, P is the north celestial pole, Z is the zenith, and SQZPN is the celestial meridian. P and P are the poles, PmP is the hour-circle of m, and amRb V is its parallel of declination, or diurnal circle. N and 8 are the north and south points respectively. In the figure, m^Tis the declination of m, and mP is called its polar distance.

17. The Vernal Equinox, or First of Aries. — In order to use this system of circles as a means of designating the places

14 RIGHT ASCENSION. [§ 17

of stars in the sky, it is necessary to fix upon some one hour-circle, to be reckoned from in the same way that the meridian of Greenwich is used on the earth's surface. The "Greenwich of the sky " which has thus been fixed upon, is the point where the sun crosses the celestial equator in the spring. The sun and moon and the planets do not behave as if they, like the stars, were firmly fixed upon the celestial sphere, but rather as if they were glow-worms crawling slowly about upon its surface while it carries them in its diurnal rotation. As every one knows, the sun in winter is far to the south of the equator, and in the summer far to the north, apparently completing a yearly circuit of the heavens on a path known as the ecliptic. It crosses the equator, therefore, twice a year, passing from the south side of it to the north about March 20th, and always at the same point (neglecting for the present the effect of what is known as 'precession'). This point is called the ' Vernal Equinox,'' and is made the starting-point. Unfortunately it is not marked by any conspicuous star ; but a line drawn from the Pole-star through Beta Cassiopei'ae (the westernmost or " preceding" star in the zigzag) (see Map I.) and continued 90° from the pole, strikes very near it. In Fig. 5, X represents this point. It is often called the "First of Aries."

18. Right Ascension. — The right ascension of a star is the arc of the celestial equator intercepted between the vernal equinox and the point where the star's hour-circle cuts the equator, and is reckoned always eastward from the equinox and completely around the circle. It may be expressed either in degrees or in hours. 1 A star one degree west of the equinox has a right ascension of 359°, or of 23 h 56 m . Evidently the diurnal motion does not affect the right ascension of a star, but this, like the declination, remains practically unchanged for years. In Fig. 5, if X be the vernal equinox the right ascension of m is the arc XY measured from X eastward.

1 Twenty-four hours = 360°; one hour = 15°.

§ 19] SUMMARY. 15

19. Thus we can define the position of a star either by its altitude and azimuth, which tell how high it is in the sky, and how it " bears," as a sailor would say ; or we may use its right ascension and declination, which do not change from day to day (not perceptibly at least), and so are better adapted to mapping purposes, corresponding as they do precisely to latitude and longitude upon the surface of the earth.

Perhaps the easiest way to think of these celestial circles is the following : Imagine a tall pole standing straight up from the observer, having attached to it at the top (the zenith) two half circles coming down to the level of the observer's eye, one of them running north and south (the meridian), and the other east and west (the prime vertical). The bottoms of these two semicircles are connected by a complete circle, the horizon, at the level of the eye. This framework, immense but fortunately only imaginary and so not burdensome, the observer takes with him wherever he goes, keeping always at its centre, while over it turns the celestial sphere ; more strictly, he and the earth and his framework turn together under the celestial sphere.