Elements of astronomy

Front matter

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Introduction

General Vieic.

1. Astronomy is the science that treats of the heavenlybodies.

2. The Heavenly Bodies. — At night, if the sky be cloudless, we see it spangled with so many staes that it seems impossible to count them; and we see the same sight in whatever part of the world we may be. The Earth on which we live, is, in fact, surrounded by stars on all sides ; and this was so evident to even the first men who studied the heavens that they pictured the Earth standing in the centre of a hollow crystal sphere, in which the stars were fixed like golden nails.

3. In the daytime the scene is changed. In place of thousands of stars, our eyes behold a glorious orb whose rays light up and warm the Earth ; and this body we call the su]^. So bright are its beams that, in its presence, all the " lesser lights," the stars, are extinguished. But, if we doubt their being still there, we have only to take a candle from a dark room into the sunshine to understand how

1. What is Astronomy ? 2. Describe the appearance of tlie sky at night. By what is the Earth surrounded ? 3. In the daytime what do we behold in the sky J

10 INTEODUCTION.

their feeble light, like that of the candle, is " put out " by the greater light of the Sun.

4. There are, however, other bodies which attract our attention. The mook shines at night, now as a crescent and now as a full Moon, sometimes, like the Sun, rendering the stars invisible. Its changes show us that there is some difference between it and the Sun ; for, while the &un always appears round, because we receive light from all parts of its surface turned toward us, the shape of the bright portion of the Moon varies from night to night, that part only being visible which is turned toward the Sun.

5. Again, if we examine the heavens more closely still, we may see, after a few nights' watching, one, or perhaps two, of the brighter " stars " change their position with regard to the stars lying near them, or relatively to the Sun if we watch that body at its rising and setting. These are the planets; the ancients called them "wandering stars."

6. But the planets are not the only bodies which move across the face of the sky. Sometimes a comet may by its sudden appearance and strange form awaken our interest, and make us acquainted with a new class of objects, unlike any of those heretofore mentioned.

7. Such are the celestial bodies ordinarily visible. Far away, and comparatively so dim that the naked eye can make little out of them, lie the nebula (from the Latin nebula^ " a cloud ") ; so called because in the telescope they often put on strange cloud-like forms. They differ as much from stars in their appearance as comets do from planets.

There are other bodies, to which we shall refer by and by. We will here merely state in a general way what As-

What has become of the stars ? 4. What other body do we see at night ? What changes does the Moon undergo, and why? 5. On a closer examination of the heavens, what may we see? 6. What bodies sometimes suddenly appear? 7. What other heavenly bodies are mentioned ? Describe the nebulae. 8 What is

THE STABS. 11

tronomy teaches us concerning star and sun, moon and planet, comet and nebula.

8. The Stars. — To begin, then, with the stars. So far from being stationary and fixed, as it were, in a hollow glass globe, at nearly equal distances from us, they are all in rapid motion, and their distances vary enormously; though all of them are so very far away that they appear to be at rest, as a ship does when sailing along at a great distance from us. In spite, however, of their great and varying distances, science has been able to get a mental bird's-eye view of all the hosts of stars which the heavens reveal to our eyes, as they would appear to us if we could plant ourselves far on the other side of the most distant one. The telescope — an instrument described further on — has, in fact, taught us that all the stars which we see form but a cluster of islands, as it were, in an infinite ocean of space. We may therefore think of all the stars which we see, as forming our universe ; and, w^hen we have fixed that thought well in our minds, we may think of space being peopled with other universes^ as there are other cities besides New York in the United States.

9. Further, we know that our Sun is one of the stars that compose this cluster, and that the reason why it appears so much larger and brighter than the rest is simply because it is the nearest star to us.

We all know how small a distant house looks, or how feebly a distant gas-light seems to shine ; but the distant house may be larger than the one we are in, or the distant light be brighter than the one which, being nearer to us, renders the other insignificant. It is precisely so with the stars. Not only would they appear to us as bright as the Sun, if we were as near to them, but we know for a fact that some of them are larger and brighter.

the fact with respect to the motion and distances of the stars ? What does the telescope teach us respectins: the stars ? With what may we regard space as peopled ? 9. What is our Sun ? Why does it appear larger and brighter thao

12 INTEOBUCTION.

10. NoAV, why do the stars and the Sun shine? They shine, or give out light, because they are white-hoU They are globes of the fiercest fire ; on their surfaces, masses of metals and other substances are burning together more fiercely than any thing we can imagine.

11. The Planets. — What, then, are the planets? We may first state that they are comparatively small bodies travelling round our Sun at various distances from him. Our Earth is one of them. There is, however, an important difference between the planets and the Sun. We have seen that the Sun is white-hot ; the surface, or outer crust, of our Earth, on the contrary, we know to be cold — all the heat we get coming from the Sun — and because it is cold, it cannot give out light. Astronomers have learned that all the other planets are like the Earth in this respect. They are all dark bodies — having no light in themselves ; and they all, like us, get their light and heat from the Sun. When, therefore, we see a planet in the sky, we know that its light is sunshine second-hand ; that, as far as its light is concerned, it is but a looking-glass reflecting to us the light of the Sun.

We have now got thus far : planets are dark or non-luminous bodies travelling round the Sun^ lohich is a bright body — bright because it is white-hot ; and the Sun is a star^ one of the stars which together form our universe ; the reason that it appears larger and brighter than the other stars being because it is nearer to us than they. It seems likely that the other stars have planets revolving round them, although they are so very far away that the telescopes we possess at present are not powerful enough to show us their planets, if they have any.

12. The Moon. — We now come to the Moon. What the other stars ? Ilhistrate this. 10. Why do the stars and the Sun shine ? 11. What are the planets ? What important difference is there between the planets and the San? Whence do the planets get their light and heat? Sum up what we have thus far learned. Are the other stars attended by planets ? 12. What

NEBULiS AND COMETS. 13

is it ? The Moon goes round the Earth, as the planets revolve round the Sun ; it is, in fact, a planet of the Earth ; it is to the Earth what the Earth is to the Sun. Like the Earth and planets, it is a dark body, and this is the reason it does not always appear round as the Sun does. We only see that part of it that is lit up by the Sun. In the Moon we have a specimen of a third order of bodies, called satellites^ or companions, as they accompany the planets in their courses round the Sun.

We have, then, to sum up again — (1) The Sun, a star, like all the other stars in motion ; (2) Planets revolving round the Sun ; (3) Satellites revolving round the planets.

13. Nebulse and Comets. — ISTebulse and comets are very different from the stars and planets, for they are masses of gas. The nebulaB lie far away from us, some of them perhaps out of our universe altogether. The comets rush for the most part from distant regions to our Sun, and having gone round him they go back again, and we only see them for a small part of their journey.

We saw in Art. 10 that the stars shine because they are white-hot ; so also nebulse and comets shine because they are white-hot : but in the case of the stars we are dealing with solid or liquid matter, in the case of the nebulae and comets with burning gas.

14. Further Facts. — Such, then, are some of the bodies with which the science of Astronomy has to deal; but astronomers have not rested content with the appearances of these bodies ; they have measured and weighed them, in order to assign to them their true place. Thus they have found that the Sun is 1,245,000 times larger than the Earth, and the Earth 50 times larger than the Moon. They have also discovered that, while we travel round the

is the Moon ? Of what order of bodies is it a specimeu ? 13. How do the nebulae and cornels differ from the stars and planets ? Why do they shine ? 14. What have astronomers found with respect to the comparative size of the Sun. Earth, and Moon ? What, with respect to the distance of the Moon and Sun from the

14 INTRODUCTION,

Sun at a distance of 91,430,000 miles, the Moon travels round us at a distance comparatively insignificant — only 240,000 miles. Thus the greater size of the Sun is balanced, so to speak, by its greater distance; the result being that the large distant Sun looks about the same size as the small near Moon.

1 5. We already see how enormous are the distances dealt with in Astronomy, although they are measured in the same way as a land-surveyor measures the breadth of a river that he cannot cross. The numbers we obtain when we attempt to measure any distance beyond our own little planetary system convey no impression to the mind. Thus the nearest fixed star is more than 20,000,000,000,000 miles away ; the more distant ones are so far away that their light, which travels at the rate of 185,000 miles in a second, requires 50,000 years to reach our eyes !

In spite, however, of this immensity, the methods employed by astronomers are so sure that the distances, sizes, weights, and motions, of the nearer bodies, are now well known. We can, indeed, predict the place that the Moon — the most difficult one to deal with — will occupy ten years hence, with more accuracy than we can obseiwe its position in the telescope.

16. Here we see the utility of the science, and how upon one branch of it. Physical Astronomy, which treats of the motions and structure of the heavenly bodies, is founded another branch. Practical Astronomy, which teaches us how their movements may be made to help mankind.

17. Usefulness of Astronomy. — Let us first see what it does for our sailors and travellers. A ship that leaves our shores for a voyage round the world takes with it a book called the "Nautical Almanac," prepared three or four

Earth ? 15. What kind of distances are dealt with in Astronomy ? How far off is the nearest fixed star ? How far are the more distant ones ? 16. Of what does Physical Astronomy treat ? What branch of the science is founded on this ?

USES OF ASTRONOMY. 15

years in advance by government astronomers. In this book, the places the Moon, Sun, stars, and planets, will occupy at certain stated hours for each day are given, and this information is all that sailors and travellers require to find their way across pathless seas or unknown lands.

But we need not go on board ship or into new countries to find out the practical uses of Astronomy. It is Astronomy that teaches us to measure the flow of time — the length of the day and the year ; without Astronomy to regulate them, clocks and watches would be quite useless. It is Astronomy that divides the year into seasons for us, and teaches us the times of the rising and setting of the Moon, which lights up our night. It is to Astronomy that we must appeal when we would inquire into the early history of our planet, or wish to map its surface.

1 8. Such, then, is Astronomy — the science which, as its name, derived from two Greek words {aorrjp, a star, and vofiog, a law), implies, unfolds to us the laws of the stars.

Early History of Astronomy,

19. The establishment of the general facts just stated, and the various laws and principles which constitute the science of Astronomy at the present day, has been the work of centuries. The first astronomers were the Ancient Shepherds, who, as they tended their flocks beneath the canopy of heaven, naturally became interested in the orbs with which it was studded, observed their motions, and gave names to those that were most conspicuous. They knew, however, only such isolated facts as were apparent to the eye ; it was reserved for later ages to trace visible effects to their causes, and to build up theories ; and not till the improved instruments of comparatively recent

IT. Of what use is Astronomy to sailors ? Mention some of the other uses of Astronomy. 18. What is the meaning, and what the derivation, of the word astronomy? 19. Who were the first astronomers? What facts alone were

15 INTRODUCTION.

times extended the field of human vision almost beyond belief, was it possible to penetrate the mysteries of the science to their depths.

20. The Chaldeans and Egyptians were the first to make any material progress in Astronomy. The former, by continued observation, discovered that the eclipses of the Moon recur in the same order in periods of 18 years, and were thus able to predict them with considerable accuracy ; the latter investigated the motions of the planets, and established a sacred year of 365^ days.

The Chinese, also, paid great attention to this science in very early times. More than 2,300 years before the Christian era (according to their own records), a tribunal was established for the prosecution of astronomical studies, and particularly for the prediction of eclipses. Its members were held responsible with their lives for the correctness of their calculations ; and we are told that one of the emperors actually put to death his two chief astronomers for failing to predict an eclipse of the Sun.

21. From Egypt, the cradle of learning, art, and science, the Greeks obtained their first knowledge of astronomy, to which their wise men made important additions. Thales, about 600 b. c, taught that the world was round, and that the Moon shone with reflected light. His pupil Anaximander conceived the bold idea of a plurality of worlds — that is, that the planets are inhabited. A little later, Pythag'oras is said to have advanced the opinion that the Earth and other planets revolve round the Sun. Whether he did so or not, it is certain that this was taught by Aristarchus about 280 b. c. ; as, also, that the distance of the Sun from the Earth is insignificant in comparison

known to them ? 20. What nations were the first to make any material progress in astronomy ? What did the Chaldeans discover ? What did the Ej^yptians investigate ? What evidence is there that the Chinese paid great attention to astronomy in early times ? 21. Whence did the Greeks obtain tlieir knowledge of astronomy ? What was taught by Tl!ales ? What, by Anaximander? What, by Pythagoras ? What, by Aristarchus ? What was done by Eratosthenes ?

with that of the stars. Among other famous Greek astronomers were Eratos'thenes, who devised an accurate method of measuring the circumference of the Earth, and Hipparchus, who made a catalogue of all the stars visible above his horizon.

Ptolemy, an eminent Egyptian astronomer who flourished in the second century after Christ, rejected the theory of Pythagoras and Aristarchus respecting the solar system, and advanced one of his own, which soon met with general acceptance. He taught that the Earth was the centre of a system of eight immense hollow spheres of crystal, placed one within another : that the Moon was in the nearest sphere ; Mercury in the next ; Venus in the third ; the Sun in the fourth ; Mars, Jupiter, and Saturn, in the fifth, sixth, and seventh, respectively ; and that the eighth belonged to the stars, which, though most distant, were still visible through the transparent crystal. The revolution of this cumbrous system round the Earth from east to west, once in twenty-four hours, he thought would account for the succession of day and night, and the various phenomena of the heavens.

22. During the Dark Ages, Astronomy was cultivated chiefly by the Arabians, who made no advance as regards theory, but were diligent observers, and devised some improvements in instruments and methods of calculation. Even after the termination of this period, comparatively little progress was made until the time of Coper'nicus, a Prussian priest, about 350 years ago. He ventured to reject the system of Ptolemy, which then generally prevailed; and, reviving the teachings of Pythagoras and Aristarchus, set forth what is called from him the Copernican system, now very generally received as true, though at first bitterly denounced as visionary and even irreli-

What, by Hipparchus? What theory was advanced by Ptolemy? 22. By whom was astronomy chiefly cultivated durin^^ the Dark Ages ? What improvements were made by the Arabians ? When and by whom was the present theory of the

18 INTEOBUCTION.

gious. Its three fundamental points are, (1) that the Earth is round ; (2) that it turns on its axis from west to east; and (3) that the Earth and other planets revolve round the Sun.

23. After Copernicus came the great Italian philosopher Galileo, who first used the telescope, and was thus enabled to make many important discoveries, all tending to support the theory of Copernicus. The day on which Galileo died was memorable for the birth of Newton, whose great discovery of the law of gravitation explained the planetary motions, while his mathematical researches gave a new impetus to the science.

Mathematical Definitions.

Certain mathematical terms used in Astronomy must be understood.

24. A Line is a magnitude conceived as having length without breadth or thickness.

25. A Straight Line is one that has the same direction Fig. 1. o throughout. It is the shortest distance

r~ between two points, ^^and G JD are

straight lines.

A Curved Line, or Curve, is a line that changes its direction at every point, ^ ^ as^i^

Parallel Lines are such as maintain the same distance from each other at all points, as A B and (7Z> in Figure 1.

26. An Angle is the difierence in direction of two straight lines that meet. The point at which they meet is called the Vertex of the angle.

An angle is named from the letter at its vertex, if but

universe advanced ? What are its three fundamental points ? 23. By what two philosophers was Copernicus succeeded, and what discoveries did they make ? 24. What is a Line ? 25. What is a Straight liine ? What is a Curved Line ? 26. What is an Angle ? How is an angle named ? 27. When are two lines said

Fig. 2.

MATHEMATICAL DEFINITIONS. 19

one angle is formed there. Otherwise, it is named from the letters on each side and at the vertex, that at the vertex Fig. 3. being placed in the middle. The angle in

Fig. 3 is called K ; if more than one angle were formed there, it would be distinguished as IKL or L KL The size of an angle depends not at all on the length of its sides, but simply on their difference of direction. The angle ^will become no larger, however far we may extend its sides.

Fig. 4, 27. When one straight line meets

another in such a way as to make the two adjacent angles equal, the lines are said to be perpendicular to each other, and

^ the angles formed are called Right Angles.

The angles JSf JP and N Q^ being equal, are right angles ; and the lines N 0^ P Q-i ^i*^ perpendicular to each other.

Fig. 5. An Obtuse Angle is one that is

greater than a right angle, as B S T.

An Acute Angle is one that is less than "s V a right angle, as i? /S K

28. A Surface is a magnitude conceived as having length and breadth without thickness.

A Plane is a surface with which a straight line that joins any two of its points will coincide altogether.

A Convex Surface is one that swells out in a rounded form, as the outside of an egg-shell.

A Concave Surface is one that curves in, as the inside of an egg-shell.

29. A Plane Figure is a plane bounded by a line or lines.

to be perpendicular to each other ? What are the angles formed by lines that are perpendicular to each other called? What is an Obtuse Angle? What is an Acute Angle? 28. What is a Surface? What is a Plane? What is a Convex Surface ? What is a Concave Surface ? 29. What is a Plane Figure ? 30. Whalt

INTEODUCTION.

30. A Triangle bounded by three XTZ.

A Circle is a plane figure bounded is a plane figure straight lines, as

Fig. 7.

V z

by a curve, every point of which is equally distant from a point within, called the Centre.

The Circumference of a circle is the line that bounds it. Any part of the circumference is called an Arc. Fig. 7 represents a circle ; A is the centre, BE C I) the circumference; E B, B I), BE, etc., are arcs.

A Diameter of a circle is a straight line passing through its centre, and terminating at each end in the circumference, as B E in Fig. 7. Every circle has an infinite number of diameters, all equal.

A Radius of a circle is a straight line drawn from the centre to the circumference ; sl^ A B, A B', A G, A E, in Fig. 7. Every circle has an infinite number of radii, all equal, and each just half its diameter.

A Tangent is a straight line that touches the circumference of a circle in a single point, without cutting it at either end when produced ; as ^ ^ in Fig. 8.

32. The circumference of every circle may be divided into 360 equal parts, called Degrees (marked °). Each degree may be divided into 60 equal parts, called Minutes (^) ; and each minute into 60 equal parts, called Seconds ('').

A circumference may also be divided into 12 equal parts, of 30 degrees each. These are called Signs.

is a Triangle? 31. What is a Circle? What is the Circumference of a circle? What is an Arc ? What is a Diameter ? What is a Radius ? What is a Tangent ? %2. Into what may the circumference of every circle he divided ? What is a Sign ?

MATHEMATICAL DEFINITIONS.

33. A Semicircle is one-half, a Quadrant one-fourth, and a Sextant one-sixth, of a circle.

34. An angle is measured by the number of degrees in the arc that subtends it. A right angle is subtended by one-fourth of the circumference (see C D E in Fig. 8), and is therefore an angle of 90 degrees.

35. An Ellipse is a curve every point of which is at such distances from two points within, called its foci, that the sum of these distances is in each case the same. AB C'\% an ellipse ; I) and JS'are its foci. AD ^ AE ^JBB-VBE^CJD + CE.

An ellipse may be described by fastening the ends of a piece of thread 6t any two points (the foci) whose distance from each other is less than the length of the thread, and then drawing a line around these points with a pencil placed against the thread, and kept stretched out as far as the thread will allow. The process is shown in Fig. 10.

Fig. 10.— Mode or describing an Ellipse.

The thread here represents the sum of the distances from each point of the ellipse to the foci, and remains the same while the ellipse is described. Draw an ellipse according to these directions.

The Centre of an ellipse is the point midway between the foci in the straight line that connects them, as in Fig. 10. A Diameter is a line passing through the centre and terminating at each end in the ellipse ; as 6^ ^ I J,

33. What is a Semicircle ? What is a Quadrant ? What is a Sextant? 34. How is an anoxic measured ? Illustrate this in the case of a right angle. 35. What is an Ellipse ? How may an ellipse be drawn ? What is the Centre of an ellipse?

INTEODUCTION.

The Major Axis of an ellipse is its longest diameter, as GH, The Minor Axis is its shortest diameter, as IJ.

The Eccentricity of an ellipse is the distance of either focus from the centre, divided by half the major axis. Hence the greater the aforesaid distance, the greater the eccentricity, and the more the ellipse deviates from a circle. In Fig. 11, if i>jf^ the distance of one of the foci from the centre, is to G F^ half the major axis, as 2 to 3, the eccentricity of the ellipse will be I, or .66+.

36. A Solid is a magnitude that has length, breadth, and thickness.

37. A Sphere is a solid bounded by a curved surface every point of which is equally distant from a point

Fig. 12. within, called the centre. A

Hemisphere is half a sphere.

A Diameter of a sphere is a straight line passing through its centre, and terminating at each end in its surface.

The Axis of a revolving

sphere is the diameter round

which it turns. The Poles are

the extremities of the axis. In

** the sphere represented in Fig.

12, the straight line connecting A and jB is a diameter;

and also the axis, if the sphere revolves round this

diameter ; in which case A and B are the poles.

What is a Diameter ? What is the Major Axis ? The Minor Axis ? What is meant by the Eccentricity of an ellipse ? 36. What is a Solid ? 37. What is a Sphere ? What is a Hemisphere ? What is a Diameter of a sphere ? What is the Axis of a revolving sphere ? What are the Poles ? 38. What is a Great

MATHEMATICAL DEFINITIONS. 23

. 38. Circles on the surface of a sphere are distinguished

as Great and Small. A Great Circle is one whose plane

divides the sphere into two equal parts ; as A H B G and

G 11^ in Fig. 12. A Small Circle is one whose plane

Fig. 13. divides the sphere into two unequal parts,

as CB and EF.

The Circumference of a sphere is one of its great circles. The Equator of a sphere is that great circle which is equally distant from the two poles, as G H in Fig. 12.

39. A Spheroid is a solid which differs Fig. 14.

but little from a sphere.

An Oblate Spheroid is a sphere flattened at the poles, as in Fig. 13.

A Prolate Spheroid is a sphere lengthened out at the poles, as in Fig. 14.