The elements of astronomy; a textbook

Front matter

Glass _Qjj4 Boole * y 8

COPYRIGHT DEPOSIT;

o y

Preface

The present volume is a new work, and not a mere abridgment of the author's K General Astronomy." Much of the material of the larger book has naturally been incorporated into this, and many of its illustrations are used ; but everything has been worked over with reference to the wants of institutions which demand a more elementary and less extended course than that presented in the " General Astronomy."

It has not always been easy to decide just how far to go in cutting down and simplifying. On the one hand the students who are expected to use the present book are not children, but have presumably mastered the elementary subjects which properly precede the study of Astronomy, and it is an important part of their remaining education to make them familiar with astronomical terms and methods ; on the other hand it is very easy to assume too much, and to make the book difficult and incomprehensible by the use of too many unfamiliar terms, and the unprepared presentation of new ideas and demonstrations — and the danger is greater in a brief course than in a longer one.

While therefore the writer has tried to treat every subject simply and clearly, he has not discarded the use of technical terms in proper places, and he has always sought

IV PREFACE.

to stimulate thought, to discourage one-sided and narrow ways of looking at things, and to awaken the desire for further acquisition.

The book presupposes students anxious to learn, and an instructor who understands the subject in hand, and the art of teaching.

Special attention has been paid to making all statements correct and accurate as far as they go. Many of them are necessarily incomplete, on account of the elementary character of the work ; but it is hoped that this incompleteness has never been allowed to degenerate into untruth, and that the pupil will not afterwards have to unlearn anything that the book has taught him.

In the text no mathematics higher than elementary algebra and geometry is introduced ; in the foot notes and in the appendix an occasional trigonometric formula appears.

Certain subjects, which, while they certainly ought to be found within the covers of every text-book of Astronomy, are perhaps not essential to an elementary course, have been relegated to an appendix. Where time allows, the instructor will find it advisable to include some of them at least in the student's work.

A brief Uranography is also presented, covering the constellations visible in the United States, with maps on a scale sufficient for the easy identification of all the principal stars. It includes also a list of such telescopic objects in each constellation as are easily found and lie within the power of a small telescope.

The author is under special obligations to Messrs. Kelley of Haverhill, Lambert of Fall River, and Par-

PREFACE. V

menter of Cambridgeport, for valuable suggestions and assistance in preparing the work, and to his assistant, Mr. Heed, for help in the proof-reading: also to Warner & Swasey for the cut of the Lick telescope which forms the frontispiece.

Preface To The Revised Edition Of 1897

The progress of Astronomy since the first publication of this work has been such as to require a thorough revision and partial rewriting of the book in order to make it fairly representative of the existing state of the science. Numerous changes and corrections have been made, with some considerable "additions ; but the necessary alterations have been so managed that it is believed that no serious inconvenience will arise in using the old and new editions together.

A " Synopsis for Review and Examination " has been added, which, it is hoped, will be found useful by both teachers and

P u P ils - C. A. Young.

Preface To Issue Of 1918

While the greater part of the text remains as it was written by its author, such changes have been made in this issue as are necessary to bring it down to date.

Mount Holyoke College Anne Sewell Young

September, 1918

Contents

PAGES

INTRODUCTION . . . 1-4

CHAPTER I. — Fundamental Notions and Definitions: the " Doctrine of the Sphere " 5-28

CHAPTER II. — Fundamental Problems of Practical Astronomy : the Determination of Latitude, of Time, of Longitude, of the Place of a Ship at Sea, and of the Position of a Heavenly Body 29-44

CHAPTER III. — The Earth: its Form, Rotation, and Dimensions ; Mass, Weight, and Gravitation in General ; the Earth's Mass and Density 45-66

CHAPTER IV. — The Orbital Motion of the Earth and its Consequences : Precession ; Aberration ; the Equation of Time : the Seasons and the Calendar 67-87

CHAPTER Y.— The Moon: her Orbital Motion; her Distance, Dimensions, Mass, and Density; Rotation and Librations ; Phases; her Light and Heat and Physical Condition; Telescopic Aspect and Surface Features . . . . . 88-113

CHAPTER VI. — The Sun : its Distance, Dimensions, Mass, and

Density ; its Rotation and Equatorial Acceleration ; Methods

of Studying its Surface ; Sun Spots, their Nature, Dimensions,

Development, and Motions ; their Distribution and Perio-

- dicity ; Sun-Spot Theories ...... 114-132

Vlll CONTENTS.

CHAPTER VII. — The Spectroscope, the Solar Spectrum, and the Chemical Constitution of the Sun : the Sun-Spot Spectrum ; Doppler's Principle ; the Chromosphere and Prominences ; the Corona ; the Sun's Light ; the Sun's Heat ; Theory of its Maintenance and Speculations regarding the Age of the Sun 133-160

CHAPTER VIII. — Eclipses : Form and Dimensions of Shadows; Eclipses of the Moon ; Solar Eclipses, Total, Annular, and Partial ; Ecliptic Limits, and number of Eclipses in a Year ; Recurrence of Eclipses, and the Saros ; Occultations . 161-174

CHAPTER IX. — Celestial Mechanics : the Laws of Central Force ; Circular Motion ; Kepler's Laws ; Newton's Verification of the Theory of Gravitation ; the Conic Sections ; the Problem of Two Bodies ; the Problem of Three Bodies and Perturbations ; the Tides 175-198

CHAPTER X. —The Planets in General : Bode's Law ; Apparent Motions ; the Elements of a Planet's Orbit ; Determination of Period and Distance ; Planetary Perturbations and Stability of the System ; Determination of the Data relating to the Planets themselves ; their Diameters, Masses, Rotations, etc. ; Herschel's Illustration of the Scale of the System . 199-219

CHAPTER XI. — The Terrestrial and Minor Planets : Intra-

Mercurial Planets, and the Zodiacal Light . . . 220-242

CHAPTER XII. — The Major Planets : Jupiter, its Satellites, the Equation of Light, and the Distance of the Sun ; Saturn, its Rings and Satellites ; Uranus, its Discovery and Satellite System ; Neptune, its Discovery ; its Satellite . . 243-263

CHAPTER XIII. — Comets and Meteors : Comets, their Number, Designation, and Orbits ; their Constituent Parts and Appearance ; their Spectra, Physical Constitution, and Probable Origin ; Aerolites, their Fall and Characteristics ; Shooting Stars and Meteoric Showers ; Connection between Meteors and Comets 264-302

CONTENTS. IX

CHAPTER XIV. — The Stars : their Nature, Number, and Designation ; Star Catalogues and Charts ; their Proper Motions, and the Motion of the Sun in Space ; Stellar Parallax ; Star Magnitudes and Photometry; Variable Stars; Stellar Spectra . . . . . 303-332

CHAPTER XV. —The Stars (continued): Double and Multiple Stars ; Clusters and Nebulae ; the Milky Way, and Distribution of Stars in Space ; the Stellar Universe ; Cosmogony and the Nebular Hypothesis 333-360

Appendix

CHAPTER XVI. — Supplementary to Articles in the Text : Celestial Latitude and Longitude. — Corrections to a Measured Altitude. — The Local Time from a Single Altitude of the Sun. — Determination of Azimuth. — Theory of the Foucault Pendulum. — Measurement of Mass independent of Gravity. — The Equation of Time. — The Spectroscope and the Solar Prominences. — The Equation of Doppler's Principle. — Areal, Linear, and Angular Velocities. — Gravitation proved by Kepler's Harmonic Law. — Newton's Verification of Gravitation by Means of the Moon. — The Conic Sections.

— Elements of a Planet's Orbit. — The Mass of a Planet. — Danger from Comets. — Twilight 361-382

CHAPTER XVII. — Determination of Solar and Stellar Parallax : Historical. — Geometrical Methods of finding the Parallax of the Sun : Oppositions of Mars ; Transits of Venus and Halley's Method ; De l'Isle's Method ; Heliometric and Photographic Methods ; Gravitational Methods.

— Absolute and Differential Methods of determining Stellar Parallax. . . . . 383-395

CHAPTER XVIII. — Astronomical Instruments: The Telescope, Simple Refracting, Achromatic, and Reflecting. — The Equatorial. — The Filar Micrometer and the Heliometer. — The Transit Instrument. — The Clock and the Chronograph. — The Meridian Circle. — The Sextant. — The Pyrheliometer 396-426

CONTENTS.

TABLES OF ASTRONOMICAL DATA:

I. Astronomical Constants . .

II. The Principal Elements of the Solar System

III. The Satellites of the Solar System

IV. The Principal Variable Stars

V. The Best Determined Stellar Parallaxes VI. Motion of Stars in the Line of Sight VII. Orbits of Binary Stars ....

The Greek Alphabet and Miscellaneous Symbols

SUGGESTIVE QUESTIONS 435-438

SUPPLEMENTARY INDEX 463,464

URANOGRAPHY AND STAR-MAPS . * . . . 465-508

Introduction

1. The earth, is a huge ball about 8000 miles in diameter, composed of rock and water, and covered with a thin envelope of air and cloud. Whirling as it flies, it rushes through empty space, moving with a speed fully fifty times as great as that of the swiftest cannon-ball. On its surface we are wholly unconscious of the motion, because it is perfectly steady and without jar.

As we look off at night we see in all directions the countless stars, and conspicuous among them, and looking like stars, though very different in their real nature, are scattered a few planets. Here and there appear faintly shining clouds of light, like the so-called Milky Way and the nebulae, and perhaps, now and then, a comet. Most " striking of all, if she happens to be in the heavens at the time, though really the most insignificant of all, is the moon. By day the sun alone is visible, flooding the air with its light and hiding the other heavenly bodies from the unaided eye, but not all of them from the telescope.

2. The Heavenly Bodies. — The bodies thus seen from the earth are known as the "heavenly bodies." For the most part they are globes like the earth, whirling on their axes, and moving swiftly through space, though at such distances from us that their motions can be detected only by careful observation.

They may be classified as follows: First, the solar system proper, composed of the sun, the planets which revolve around

2 INTRODUCTION. [§ 2

it, and the satellites, which attend the planets in their motion around the sun. The moon thus accompanies the earth, which herself belongs among the planets. The distances between •these bodies are enormous as compared with the size of the earth, and the sun which rules them all is a body of almost inconceivable magnitude.

Next, we have the comets and the meteors which, while they acknowledge the sun's dominion, move in orbits of a different shape from those of the planets, and are bodies of a very different character. Finally, we have the stars and nebulas,, at distances from us immensely greater than even those which separate the planets. The stars are suns, bodies comparable with our own sun in size and nature, and, like it, self-luminous, while the planets and their satellites shine only by reflected sunlight. Of the nebulae we know very little, except that they are cloud-like masses of self-luminous matter, and belong to the region of the stars.

3. Subject-Matter of Astronomy. — Astronomy is the science which treats of the heavenly bodies. It investigates (a) their motions and the laws which govern them; (b) their nature, dimensions, and characteristics ; (c) the influence they exert upon each other either by their attraction, their radiation, or in any other way.

Astronomy is the oldest of the natural sciences : nearly the earliest records that we find in the annals of China and upon the inscribed " library bricks " of Assyria and Babylon relate to astronomical subjects, such as eclipses and the positions of the planets. Obviously in the infancy of the race the rising and setting of the sun, the progress of the seasons, and the phases of the moon must have compelled the attention of even the most unobservant.

As Astronomy 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.

§ 4] INTRODUCTION. 3

4. Utility. — Although, not bearing so directly upon the material interests of life as the more modern sciences of Physics and Chemistry, it is really of high utility. It is by means of Astronomy that 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. If we can imagine that some morning men should awake with Astronomy forgotten, all almanacs and astronomical tables destroyed, and sextants and chronometers demolished, commerce would practically cease, and so far as intercourse by navigation is concerned, the world would be set back to the days before Columbus. 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 all operations which, like the railway service, require an accurate knowledge and observance of the time ; for the fundamental time-keeper 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, 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. The pseudo-science of Astrology based upon this belief really supplied the motives that led to most of the astronomical observations of the ancients. Just as modern Chemistry had its origin in Alchemy, so Astrology was the progenitor of Astronomy.

5. Place in Education. — Apart from the utility of Astronomy in the ordinary sense of the word, the study of the science is of the highest value as an intellectual training. No other science so operates to give us on the one hand just views of our real insignificance in the universe of space, matter, and time, or to teach us on the other hand the dignity of the human intellect as the offspring, and measurably the

4 INTRODUCTION. [§ 5

counterpart, of the Divine ; able in a sense to " comprehend n the universe, and know its plan and meaning. The study of the science cultivates nearly every faculty of the mind; the memory, the reasoning power, and the imagination all receive from it special exercise and development. By the precise and mathematical character of many of its discussions it enforces exactness of thought and expression, and corrects that vague indefiniteness which is apt to be the result of pure literary training. On the other hand, by the beauty and grandeur of the subjects it presents, it stimulates the imagination and gratifies the poetic sense. In every way it well deserves the place which has long been assigned to it in education.

6. The present volume does not aim to make finished astronomers of high-school pupils. That would require years of application, based upon a thorough mathematical training as a preliminary. Our little book aims only to present such a view of the elements of the science as will give the pupils of our high schools an intelligent understanding of its leading facts, — not a mere parrot-like knowledge of them, but an understanding both of the facts themselves and of the general methods by which we ascertain them. These are easily mastered by a little attention, and that without any greater degree of mathematical knowledge than may confidently be expected of pupils in the latter years of a high-school course. Nothing but the simplest Arithmetic, Algebra, and Geometry will be required to enable one to deal with anything in the book, except that now and then a trigonometric equation may be given in a note or in the Appendix for the benefit of those who understand that branch of mathematics.

The occasional references to " Physics" refer to Gage's " Principles of Physics'' (Goodspeed's revision), and those to "Gen. Ast." relate to the author's " General Astronomy," or college text-book.

§ 7] THE CELESTIAL SPHERE.

CHAPTER I.

FUNDAMENTAL NOTIONS AND DEFINITIONS, AND THE DOCTRINE OF THE SPHERE.

7. The Celestial Sphere. — The sky appears as 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 the concavity from the eye, further than to perceive that it must be very far away, because it lies beyond even the remotest terrestrial objects. It is therefore natural, and it is extremely convenient from a mathematical point of view, to regard the distance of the heavens as unlimited. The celestial sphere, as it is called, is conceived of as so enormous that the whole material universe lies in its centre like a few grains of sand in the middle of the dome of the Capitol. The imaginary radius of the celestial sphere is assumed to be immeasurably greater than any actual distance known, and greater than any quantity assignable, — in technical language, mathematically infinite.

There are other ways of regarding the celestial sphere, which are equally correct and lead to the same general results without requiring the assumption of an infinite radius, but on the whole they are more complicated and less convenient than the one above indicated, which is that usually accepted among astronomers.

8. Vanishing Point. — Since the radius of the celestial sphere is thus infinite, any set of lines which are parallel to each other, if extended indefinitely, will appear to pierce it at a single point. The real distances of the parallel lines from

PLACE OF A HEAVENLY BODY.

each other remain, of course, unchanged however far they may be produced ; so that whatever may be the radius of the sphere, they actually pierce the surface in a group of separate points. But since the radius of the sphere is " infinite," the apparent size of the group of points, as seen from the earth, will be less than any assignable quantity. In other words, to the eye the area occupied by the group on the surface of the sphere will shrink to a mere point, — the " vanishing point " of perspective. Thus the axis of the earth, and all lines parallel to it, pierce the heavens at the celestial pole ; and the plane of the earth's equator, which keeps parallel to itself during her annual circuit around the sun, marks out only one celestial equator in the sky.

9. Place of a Heavenly Body. — This is simply the point where a line, drawn from the observer through the body in question and continued onward, pierces the sphere. It depends solely upon the direction of the body, and is obviously in no way affected by its distance. Thus in Fig. 1, A, B, C, etc., are the apparent places of a, 6, c, the observer being at 0.

Objects that are nearly in line with each other, as h, i, 7c, will appear close together in the sky, however great their real distance from each other may be.

The moon, for instance, often looks to us " very near " a star,

which is really of course at an immeasurable distance beyond her.

10. Angular Measurement. — It is clear that we cannot properly measure the apparent distance of two heavenly bodies from each other in the sky by feet or inches. To say that two

Fig. 1.

§ 10] ANGULAR MEASUREMENT. 7

stars are about five feet apart, for instance (and it is not very uncommon to hear such, an expression), means nothing unless you tell how far from the eye the five-foot measure is to be held. If 20 feet away, it means one thing, and corresponds, nearly, to the apparent length of the "Dipper-handle" in the sky (see Art. 23) ; if 100 feet away, it corresponds to an apparent distance only about one-fifth as great, or to one of the shorter sides of the " Dipper-bowl " (see Art. 23) ; but if the five-foot measure were a mile away, its length would correspond to an apparent distance about one-tenth the apparent diameter of the moon. The proper units for expressing apparent distances in the sky are those of angle, viz. : radians, or else degrees (°), minutes ('), and seconds ("). The Great Bear's tail or Dipper-handle is about 16 degrees long, the long side of the Dipper-bowl is about 10 degrees, the shorter sides are 4° or 5° ; the moon is about half a degree, or 30', in diameter.

11. The student will remember that a degree is one three-hundredand-sixtieth of the circumference of a circle, so that a quarter of the circumference, or the distance from the point overhead to the horizon, is 90° ; also, that a minute is the sixtieth part of a degree, and a second the sixtieth part of a minute. The radian is the angle measured

360° by an arc of the circumference equal to its radius. It is , or

It is very important, also, that the student in Astronomy as soon as possible should accustom himself to estimate celestial measures in these angular units. 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 a flattened vault, so that all estimates of angular distances for objects near the horizon are apt to be exaggerated. The moon when rising or setting looks to most persons much larger 1 than when overhead, and the " Dipper-bowl "

. x This is due to the fact that when a heavenly body is overhead there are no intervening objects by which we can estimate its distance from us, while at the horizon we have the whole landscape between us and it. This

8 DISTANCE AND APPARENT SIZE. [§ 12

when underneath the pole seems to cover a much larger area than when above it.

12. Relation between the Distance and Apparent Size of an Object. — Suppose a globe of the radius BG, Fig. 2, equal to r. As seen from the point A its "apparent" (that is, angular) semi-diameter will be the angle BAG, or s, its distance being

AC, or R. Evidently the nearer A is to G, i.e., the smaller R may be, the greater will be the angle s. If the angle s is 1°, R will be 57.3+ times as great as ?*; and if it were only 1", R would then be 206,265 times r. As long as the angle s does not exceed 1° or 2°, we may without sensible error take

The distances i? and r are of course measured in units of length, or "linear" units, such as miles, kilometers, or feet. In makes it seem remoter when low down, and as the angular diameter is unchanged, it makes it seem to us larger (Art. 12). It may be mentioned as a rather curious fact that people unaccustomed to angular measurements say, on the average, that the moon (when high in the sky) appears about a foot in diameter. This implies that the surface of the sky appears to them only about 110 feet away. Probably this is connected with the physiological fact that by the muscular sense, by means of the convergence of the eyes, we can directly estimate distances up to about 100 feet with more or less accuracy. Beyond that we depend for our estimate mainly on intervening objects.

§ 12] CIRCLES OF THE SPHERE. 9

general, therefore, for r, the radius 1 (in linear units) of a globe whose angular semi-diameter is s", we have r" r

We see therefore that the apparent diameter of the object varies directly as the linear diameter, and inversely as the distance. In the case of the moon, R equals about 239,000 miles, and r, 1081 miles ; whence, from the formula just given, her semi-diameter, which equals 933" — a little more than \°.

0IE0LES OP THE SPHERE.

13. In order to be able to describe intelligibly the position of a heavenly body in the sky, it is convenient to suppose the inner surface of the celestial sphere to be marked off by circles traced upon it, — imaginary circles, of course, like the meridians and parallels of latitude upon the surface of the earth. Three distinct systems of such circles are made use of, each of which has its own special adaptation for its special purposes.

SYSTEM WHICH DEPENDS UPON THE DIRECTION OF THE FORCE OF GRAVITY AT THE POINT WHERE THE OB- SERVER STANDS.

14. The Zenith and Nadir. — If we suspend a plumb-line (consisting simply of a slender thread with a heavy ball attached to it) , the thread will take a position depending upon

1 The exact trigonometric equation is sins=— , whence r = R sins.

R This equation is exact, even if s is a large angle.

10 THE HORIZON. [§ 14

the direction of the force of gravity. If we imagine the line of this thread to be extended upward to the sky, it will pierce the celestial sphere at a point directly overhead, known as the astronomical zenith, 1 or " the zenith " simply, unless some other qualifier is annexed.

As will be seen later (Art. 82), the plumb-line does not point exactly to the centre of the earth, because the earth rotates on its axis and is not strictly spherical. If an imaginary line be drawn from the centre of the earth upward through the observer, and produced to the celestial sphere, it marks a point known as the " geocentric zenith," which is never very far from the astronomical zenith, but is not identical, and must not be confounded, with it. For most purposes the astronomical zenith is the better practical point of reference, because its position can be determined directly by observation, which is not the case with the geocentric zenith.

The nadir (also an Arabic term) is the point opposite to the zenith in the invisible part of the celestial sphere directly underneath.

15. The Horizon. — If now we imagine a great circle drawn completely around the celestial sphere half way between the zenith and nadir (and therefore 90° from each of them), it will be the horizon. 2 Since the surface of still water, according to hydrostatic principles, is always perpendicular to the direction of gravity, we may also define the horizon as the great circle in which a plane, tangent to a surface of still water at the place of observation, cuts the celestial sphere; or, in slightly different words, the great circle where a plane passing through the observer's eye, and perpendicular to the plumb line, cuts the sphere.

1 The word " zenith" is derived from the Arabic, as are many other astronomical terms. It is a reminiscence of the centuries when the Arabs were the chief cultivators of science.

2 Pronounced ho-ri'-zon ; beware of the vulgar pronunciation hor'-i-zon.

§15]

VISIBLE HORIZON.

Sensible and Rational Horizon. — Many writers distinguish between the "sensible" and "rational" horizons, the former being defined by a horizontal plane drawn through the observer's, eye, while the latter is defined by a plane, parallel to this, but drawn through the centre of the earth. Since, however, the celestial sphere is infinite in diameter, the two lines traced upon it by these planes, though 4000 miles apart, confound themselves to the observer's eye into a single great circle, 90° from both zenith and nadir, agreeing with the first definition given above. The distinction is not necessary.

16. Visible Horizon. — The word " horizon " means literally " the boundary" that is, the limit of landscape, where sky meets earth or sea ; and this boundary line is known as the Visible Horizon. On land it is of no astronomical importance, being usually an irregular line broken by hills and trees and other objects; but at sea it is practically a true circle, nearly, though not quite, coinciding with the horizon as above defined. If the observer's eye were at the water-level, the coincidence would be exact ; but if he is at an elevation above the surface, the line of sight drawn from . his eye tangent to the water inclines or " dips " downward by a small angle, on account of the curvature of the earth. This is illustrated by Fig. 3, where OH is the line of the true level from the observer's eye at 0, situated at an elevation, h } while OB is the line drawn to the visible horizon.

The visible horizon, therefore, is not a great circle of the celestial sphere, but technically a small circle, parallel to the true horizon and depressed below it by an amount measured by the angle HOB, which is called the Dip of the Horizon. 1 In marine astronomy this visible horizon is of great importance, because it is the circle from which the observer measures with his

Fig. 3. — Dip of the Horizon.

1 The Dip (in minutes) = y/h (in feet) nearly.