Astronomy, a handy manual for students and others

Preface

In this little book I have attempted to give an account of the methods employed by astronomers and the reasons for some of the propositions they advance. Astronomical investigations frequently seem complicated owing to the amount of subsidiary detail, but the principles underlying them are simple and usually admit of a clear statement which can be followed by a general reader. In the introduction to his lectures delivered at Ipswich in 1848 Sir George Airy draws attention to an attitude towards Astronomy which is still prevalent. Such questions as the determination of the distance of the Sun or Moon are considered as beyond ordinary comprehension ; the instruments with which astronomical measurements are made are supposed to be based on obscure and difficult principles ; therefore the best a layman can do is to accept statements on the personal credit of the astronomer making them. He points out that this is an exaggerated view. The principles involved in measuring the distance of the Moon are no more abstruse than those employed to find the distance of a tree on the other side of a river. Astronomical instruments are as simple in principle and far less complicated in detail than a lathe or a steam-engine. It is quite true that in both instruments and methods many subsidiary details must be attended to when great accuracy is required in order that disturbing causes may be allowed for or eliminated. But an explanation of the essential principles may be given which can be readily understood with ordinary care and attention.

vi PREFACE

As far as possible an historical order has been followed. The reader's attention has been drawn to the desirability of making for himself certain observations of the sky which do not require the use of a telescope. Every educated person ought to see with his own eyes how Sun, Moon, Stars and Planets move in the sky, and be able to infer from his own observations the movement of the Earth about the Sun, the comparative nearness of the Moon, and other commonplaces of Astronomy.

It is difficult to acknowledge fully my obligations to the authors of books and papers which I have consulted. Mention should be specially made of Mr. Arthur Berry's History of Astronomy, Prof. Young's General Astronomy, and the articles by Prof. Newcomb on " Astronomy" and Prof. Hale on " Spectroscopy " in the Encyclopcedia Britannica.

I am indebted to the Astronomer Royal Sir William Christie, Prof. Barnard, Prof. Ritchey and other astronomers for permission to reproduce photographs published by them, and to Mr. W. B. Blaikie for the map taken from his Monthly Star Maps published by the Scottish Provident Association.

I wish to express my thanks to a number of friends for help in various directions. Mr. Heath, first assistant of the Royal Observatory, Edinburgh, copied a number of photographs and supplied me with the drawing on p. 172 ; Mr. Storey, assistant at the Observatory, and Mr. MacGregor assisted with the diagrams. I am much obliged to Mr. Storey and to Dr. J. Reynolds Green, who read the book in proof, for their valuable criticism and suggestions.

F. W. Dyson.

Royal Observatory ; Edinburgh, March 7, igio.

Contents

Chap.

I Ancient Astronomy

II The Copernican System

Chapter I

Astronomy is the oldest of the sciences. The orientation of the pyramids or of Stonehenge, the mythology of the Greeks and the religious festivals of the Jews are familiar evidences of astronomical knowledge in early civilizations. The constant repetition, day by day, month by month, or year by year, of similar phenomena both invited and aided study of the heavenly bodies. Before the dawn of history men wondered what caused the rising and setting of the Sun and Moon each day, why the Moon went through her phases each month, and why Orion reappeared each year in the sky as surely as the seasons returned. An out-of-door life was favourable to a knowledge of the heavens, and the tribes of Chaldea and Arabia two or three thousand years ago were, perhaps, better acquainted with the appearance of the sky than we are to-day. Modern conditions of life are not favourable to the general cultivation of practical astronomy, Buildings circumscribe the view of the sky, clocks and watches save us the trouble of observing the Sun and stars for time, and artificial illumination makes us independent of moonlight. But the following phenomena of the skies ought not to be merely read of in books, but should be verified by actual observation.

(i) The diurnal movement of the Sun; the different positions of the Sun in the sky in summer and winter.

(2) The phases of the Moon ; the rapid movement of the Moon among the stars.

(3) The diurnal movement of the stars ; the appearance of different constellations at different times of the year.

Observation of the Sun. — In the latitude of London the Sun rises on midsummer day at about 3 h. 45 m. at a point on the horizon considerably north of east. At midday, when due south, it is high in the sky. If we take a stick and point it horizontally and turn it gradually towards the . vertical, we shall not be pointing to the Sun till the stick has been turned through rather more than two-thirds of the right-angle between the horizontal and vertical directions. It sets in the evening about 8h. 19 m. at a point on the horizon considerably north of west. From midsummer to midwinter it rises later and sets earlier each day; the point of the horizon where it rises gradually shifts from north of east to due east, and then to south of east ; and the point where it sets shifts in the other direction from north of west to due west, and then to south of west. In midwinter the Sun rises at 8 h. 7 m. and sets at 3 h. 51 m., and at noon, instead of being high up in the sky, it is only 15 , or one-sixth of a right-angle, above the horizon.

From midwinter to midsummer the days lengthen and the Sun at noon is higher each day. Midway between midsummer and midwinter, on March 22 and Sep. 22, the Sun rises due east and sets due west, and day and night are equal in length. This succession of phenomena repeats itself year by year, and is more striking in the latitude of the British Isles than in the more southern countries from which our astronomical knowledge was derived.

Diagram I illustrates the path of the Sun across the sky at different times of the year. The circle NES is the horizon, and NPZS the meridian or circle of the sky cut by a vertical plane in a direction due north and south. The diagram represents the eastern half of the sky — the part above NES being above the horizon and visible, and the part below r NES below the horizon and invisible, On midsummer day the Sun travels from A to C between midnight and midday, crossing the horizon at B (i.e. rising) at 3 h. 45 m. All points of the circle ABC are 66J° from P, i. e. if we divide the arc of the sphere from the pole P to the opposite one into 180 parts, all points of the

circle ABC are 66J parts from P. But on Septem-

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Diag. I.

ber 22 the Sun is 90 from P. At midnight on that day it is at D, rises at E (due east) at 6h. om., and is at its highest point F (due south) at 12 h. om. When we come to December 22 the Sun is 113J from P. At midnight it is at G, does not reach H, i. e. does not rise till 8 h. 7 m., and is at K (due south) at 12 o'clock.

Solar Day. — It is not quite correct to say that the Sun is due south exactly at 12 o'clock, but this is sufficiently true for the explanation given in the last paragraph. The interval of time between the moment when the Sun is due south one day to the moment when it is due south the next is called the solar day, and is the natural unit of time. The length of the solar day is not quite constant, but varies to the extent of one minute at different times of the year. Its average length throughout the year is the mean solar day, and is exactly the 24 hours of our clocks and watches.

Year. — The exact time the Sun takes to go through the cycle of changes described above is the year. The length of the year can therefore be found approximately by counting the number of days from a particular day in any year to the day in the following year when the Sun is the same height in the sky at noon. When the Sun's height at noon, or, in technical language, its altitude, is measured accurately, it is found that after 365 days have elapsed from March 22 the Sun is not quite so high, but after 366 days is higher. Thus the year does not consist of an exact number of days.

The Greek astronomer, Hipparchus, made accurate observations which showed that the year w<as rather less than 365J days — a year of 365J days giving, according to his calculations, an error of only one day in 300 years.

Calendar. — It is hardly necessary to refer to the difficulties different nations experienced with their chronology till a civil year was devised, whose average length was equal to that of the actual solar or tropical year. Our calendar is derived from the one introduced by Julius Caesar with the advice and assistance of Sosigenes. Every fourth year on this system is a leap year, and consists of 366 days. The error, according to this reckoning, is more than was supposed by Hipparchus, and is very approximately 3 days in 400 years. In course of time this small error accumulated, till in 1582, the equinoxes, midsummer day, etc., all fell on dates 10 days different from those on which they had fallen in a.d. 325, the year of the Council of Nice. In the reformation of the calendar, which was then introduced by Pope Gregory XIII, it was ordained that the centurial years should not be counted as leap years unless the number of centuries is divisible by 4 without remainder. Thus 1700, 1800, 1900 are not leap years, but 2000 is a leap year. With this correction the average length of the civil year only differs from the solar year by one day in about 3300 years.

Observation of the Moon. — Each month the Moon changes from new to full and from full to new.

These changes in the Moon's appearance are called its phases, and observation shows that as the phase of the Moon changes the angle between the directions of the Sun and Moon changes also. The new Moon is always seen in the west near the setting Sun ; when half illuminated its direction makes a right-angle with that of the Sun ; and when full, its direction is diametrically opposite to that of the Sun. The correct interpretation of the Moon's phases was given by Aristotle (384-322 B.C.), viz. that it is a spherical body, illuminated by the very distant Sun. One half of the sphere is bright and the other dark. The appearance of the Moon from the Earth depends on whether the Earth is in a position from which much or little of the illuminated part is visible.

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Diag. II.

In the right half of Diagram II the appearance of the Moon is shown : (1) a few days after it is new; (2) shortly after first quarter; (3) full; (4) shortly before third quarter; (5) a few days before it is new. In the left half the illuminated and unilluminated parts of the Moon are shown at corresponding times.

Another observation which the reader should make consists in noting the position of the Moon with reference to the stars on two consecutive nights. In this way its rapid movement across the sky will be duly appreciated. The distance moved in 24 hours will be found to be very considerable, approximately 12 , or ^th part of the whole circumference of the sky. Diagram III illustrates this : if the Moon is at M 1 one night, it will be at M 2 at the same time on the following night.

Further observations of the Moon will show that it is always to be found in a certain narrow belt of stars. This belt is called the zodiac, and its central line is the ecliptic. The eclipm

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Diag. III.

tic is an imaginary circle which divides the whole sky into two equal portions, and is exactly like the line formed on a globe by its intersection with a plane passing through the centre.

Month. — It is well worth while to verify for oneself that when the Moon is new, it is in the same part of the sky as the Sun, and that it travels round the sky and reaches the Sun again in one month. The length of the month is approximately 29J days, but varies a little from month to month. The times of new and full Moon were carefully investigated by the ancient astronomers for purposes of chronology.

Meton's Cycle. — As a lunar month consists of approximately 29J days, twelve months will contain approximately 354 days, and as this is 11J days short of the year, considerable difficulty was experienced in harmonizing a system of chronology depending on the Moon with one depending on the Sun. Meton, who lived between 400 and 500 B.C., discovered (if, indeed, the discovery is not older) that in 6940 days there are almost exactly 19 years, and also 235 lunar months. Consequently, if the dates of new and full Moon are known for 19 years, the same dates will serve for the next 19 years, and so on. A little complication arises in practice from the way leap years happen to fall ; but this cycle discovered by Meton is still the basis by which Christian countries fix the festival of Easter. As showing the accuracy attained by Meton in the measure of the length of a month, it may be noted that modern observations show that 235 months is about 7 J hours less than 6940 days, or that Meton's rule makes the month only two minutes too short.

Observation of the Stars. — We will now make a preliminary observation of the stars. In the northern hemisphere the Great Bear is one of the most strikingconstellations. Its appearance is well described by its American name, the Dipper. When it is once recognized it can always be found without any difficulty. Its position in the sky is different at different times of the night and at different times of the year. But it always preserves the same form; the stars do' not change their relative positions, but the constellation moves as a whole.

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The character of this movement is easily seen. If a line be drawn, as in Diagram IV, and produced, it passes nearly through another star. This star, called the Pole Star, is always to be found by looking due north and (in the latitude of Great Britain) at an altitude of about 53 , or somewhat above the point midway between the zenith and the northern horizon. If the Great Bear be watched at intervals for a few

IO hours it will be seen to be turning about the Pole Star. In the diagram its position, marked A, B, C, is shown at 6 p.m., midnight, and 6 a.m. on January i . Not only the Great Bear, but all the stars are seen to partake of this motion at the same rate. The time they take to make a complete revolution is evidently not very .far from a day, for on consecutive days at the same hour they are in nearly the same positions.

If we take a constellation further from the North

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Pole, like Orion, we find that, unlike the Great Bear, it cannot be seen at all times of the year. On January

ANCIENT ASTRONOMY n

i Orion is a little to the west of south at midnight ; on April i it is nearly setting in the west at midnight ; on July i it is not seen, and October i it is rising in the east at midnight. But its appearance shows no change, and its position is always midway between Aldebaran and Sirius. At whatever part of the year it is observed it describes the same journey in the sky, rising at the same point of the horizon, reaching the same altitude when due south and setting at the same point of the horizon. The stars of this constellation, like those of the Great Bear, keep at constant distances from the pole.

The movement of the stars in the sky is exactly what we should see if we were at the centre of a vo

Diagram of Circles (VI).

great globe on which they were fixed, and the globe turned about an axis pointing to the pole. Thus, in Diagram VI, which represents the eastern half of a globe, 1 1 1 is the path of a star which never sets ; 222 of a star which is just at such a distance from the pole that it rises at the north point of the horizon ; 333 is the path of a star still farther from the pole, which rises to the north of east and is above the horizon for the greater part of its path but below it for a shorter (dotted) part; 444 is the path of a star which is go° from the pole, and for half of its path it is above the horizon, for the other half below it and invisible ; 555 shows the path of a star more than 90 from the pole, the part of its path during which it is above the horizon is less than half, and such a star rises at a point south of east ; 666 is the limiting path of a star which never rises in the latitude for which the diagram is drawn.

This representation of the stars as fixed points on a turning sphere agrees with the facts that the stars do not change their relative positions, and that all describe parallel circles in the sky in the same time. This time is approximately 4 minutes less than 24 hours. Thus each star is at the same point of its daily path 4 minutes earlier than it was on the preceding day. In a month this makes the very perceptible difference of two hours, and those stars which rise and set, rise and set two hours earlier each month. Thus the stars which are seen due south at midnight at one time of year are due south at midday after six months. They are not seen, owing to the glare of the sunlight, but that is the only reason, and with a telescope fairly bright stars may be seen in the middle of the day.

The stars, then, do not change their positions in the sky relatively to one another, but they all move together like so many points pricked on a vast sphere which turns uniformly about an axis pointing to the pole. This very ancient discovery is important because it states these everyday phenomena of the fixed stars succinctly and accurately. It also furnishes us with a new point of view with regard to the movements of the other heavenly bodies, the Sun, Moon and planets. Instead of considering their movement across the face of the sky, we may consider their movements with reference to the stars. That the five planets, Mercury, Venus, Mars, Jupiter and Saturn do not remain in the same position relatively to the fixed stars, but wander among them, is very readily seen. Their motion is not nearly so quick as that of the Moon, illustrated in Diagram III, but is evident for some of them when their positions are compared after an interval of a few days, and for others after a few weeks. The Sun, however, presents a difficulty. Its light obscures the stars, and prevents a direct determination of its position on the celestial sphere. By carefully observing the position of the Sun just before it sets relatively to Venus or the Moon, and afterwards when the night was dark enough for the stars to be seen, observing the position of Venus or the Moon relatively to the stars, early astronomers were able to mark the position

H of the Sun day by day on the celestial globe. This is a very easy task in a modern observatory, thanks to the instruments we now possess for measuring angles, and clocks for accurately measuring time. But with the simple apparatus possessed by the Chaldeans, Egyptians and Greeks it was far from being an easy task.

In the accompanying map, which represents two halves of a celestial globe on which all the brightest stars are marked, the position of the Sun is marked for the first day of each month. It will be seen that these positions all lie on the dotted line called the

Diag. VII.

ecliptic. This line is an imaginary circle dividing the sphere into two equal parts. It is a fixed line among the stars and goes through the constellations enumerated in the doggerel lines —

The Ram, the Bull, the Heavenly Twins, And next the Crab, the Lion shines,

The Virgin and the Scales ; The Scorpion, Archer, and He-Goat, The Man that bears the watering-pot,

And Fish with glittering tails.

It is important to notice that the Sun makes this same journey among the stars each year and that its journey is intimately associated with the changes of its position in the sky referred to on pp. 2, 3, and illustrated in Diagram I. For the circle of the ecliptic on the globe is in some parts nearer to the north pole than in others. It cuts the equinoctial or circle in the sky midway between the poles in two points which are 90 away from the poles, and half-way between them is, as shown in the map, 23^° nearer to or farther from the poles. On March 22 the Sun's position in the ecliptic is at one of the points where the equinoctial is cut. It is then 90 from the poles, and its path in the sky on that day is the circle DEF of Diagram I. The days and nights are equal, and the Sun rises due east and sets due west. The Sun moves along the ecliptic through Pisces, Aries and Taurus, and on June 22 it has reached a point 66J° distant from the north pole. During this period the days have lengthened and the nights shortened in the northern hemisphere.

The converse process goes on in the next three months while the Sun passes through Gemini, Cancer and Leo, till on September 22 the days and nights are again equal. The Sun continues to move farther from the north for the next three months till December 22, when the shortest day in the northern and longest in the southern hemisphere occurs. It then moves northward, and on March 22 completes its circle.

This annual movement of the Sun accounts for the changing of the constellations visible at night at different times of the year. For example, in June at midday Orion is in the southern sky below the Sun, and with a telescope the brighter stars may sometimes be seen, but it is in December, when the Sun is at the opposite part of the sky, that Orion is seen towards the south at midnight.

The discovery of the movement of the Sun among the stars is the first great landmark in the history of astronomical science. The date of the discovery is very uncertain, and has to be inferred from slender evidence like the names of the constellations through which the Sun passes. It is probably between 2000 and 3000 B.C.

Eclipses of the Sun and Moon. — Eclipses of the Sun and Moon, especially of the Sun, are very striking phenomena. Excluding the Chinese accounts, the earliest eclipse of which we have any record is referred to on a Babylonian tablet and has been identified with one which occurred in 1062 B.C. Some verses in the Book of Amos, e.g. chapter viii., ver. 9, "to darken the earth while it is yet day," may be taken as an indication that the writer had seen the total eclipse of the Sun which passed across Samaria on June 19, 763 B.C.

From the fact that Thales is said to have predicted an eclipse which occurred in 584 B.C., it is clear that considerable knowledge of these phenomena was possessed at that time in Ionia. But to the Babylonians belongs the honour of having discovered a law in these apparently very irregular occurrences. It was doubtless perceived soon after records were kept that eclipses of the Sun occurred at the time of new Moon, and those of the Moon at the time of full Moon. The correct explanation was given, viz. the interposition of the Moon between the Earth and Sun in the case of a solar eclipse ; and the interposition of the Earth between the Sun and Moon in the case of a lunar eclipse. But as the path of the Moon among the stars does not coincide with that of the Sun, but is inclined to it at a small angle, the three bodies are not sufficiently in a straight line for eclipses to occur at every new and full Moon. The path of the Moon in the sky is a circle inclined at about 5 degrees to the ecliptic, the path of the Sun (seep. 23). The two points of intersection of these circles are called the nodes of the Moon's orbit. If the Moon is sufficiently near a node when it is new or full an eclipse of the Sun or Moon respectively will occur. From our present knowledge of the movements of the Moon and of its nodes — which move round the ecliptic in 18 years and 7 months — it can be shown that after 223 months the relative positions of the Sun, Moon, and the nodes of the Moon's orbit will be nearly the same. Thus after this period eclipses will recur. This very curious cycle, called the Saros, was discovered by the Babylonian astronomers from their observations of eclipses of the Moon. The period is 223 months or 6585*3 days, or approximately 18 years and 11 days. If, then, the eclipses are recorded which occur in one period of this duration, those in the next period may be predicted, and so on. As the relationship between the numbers is not quite exact, an eclipse may in some cases occur which is not predicted by the cycle, and in some cases an eclipse predicted in this way may not occur, but the extreme cases where the rule fails from one cycle to the next are very few. The date of the discovery of the Saros cannot be fixed with" certainty, but must have been some centuries before the Christian era.

The Planets. — Besides the Sun and Moon there are five other celestial bodies visible to the naked eye which move among the stars. Of these Mercury is only occasionally seen in Great Britain. Venus is best known as a brilliant evening star which is sometimes visible in the west about the time of sunset. At other times it is a morning star and rises before the Sun. The identity of the evening and morning star is said to have been discovered by Pythagoras. Venus is always seen in a direction not far from that of the Sun, the largest angle between them being 47 . The planet passes from side to side of the Sun as the Sun pursues its circuit of the sky, and when on one side is seen as the morning star and when on the other as the evening c 2 star. Next to Venus, Jupiter is the most brilliant of the planets. If its position among the stars is plotted down each day on a celestial globe or on a map of the stars, it will be seen to be sometimes moving round the sky in the direction of the Sun's annual motion, but sometimes to be moving in the opposite direction. Its total movement in a sufficiently long interval is in the same sense as the Sun's motion, but the irregularities of its movement will be seen from Diagram VIII, giving its movement from 1908, Sept. 20, to 1909, July 10. Mars and Saturn exhibit a similar irregular

movement among the stars. The most important difference between the movements of these three planets is that Mars takes 2 years, Jupiter 12 years and Saturn 29J years to complete the circuit of the sky.

The Greek astronomers succeeded in expressing the observed movements of the planets, as well as of the Sun and Moon, by mathematical formulas, so that their position could be calculated and predicted. This was an immense step in the progress of astronomy. A formula, however empirical it may be, which correctly represents the facts, simplifies their statement and brings them into orderly arrangement and small compass. As an example we may take the representa-