The mathematics of the sky

Front matter

OB 44 .B9 I Copy 1

He Mathematics of the Sky

By

Preface

Reveling in the depths of space, reflecting on the grandeur of the universe and calculating on the vastness of its dimensions have brought many delightful hours while preparing the material for this book.

It is not a dry and prosy collection of numbers brought together for the sake of looking at them, but the study of the heavens which is back of the book fires the imagination and stirs the soul to grander conceptions of the magnificence of the universe, and to nobler aspirations and reverence for the God who made it. May every hour spent in reading this book fill the mind of the reader with more reverent thoughts concerning Him who created all things.

In locating various stars, clusters and nebulas I have generally spelled out the words degrees and minutes, because the signs for degrees and minutes of an arc are not ordinarily supplied by the linotype.

CHAS J. BURTON.

Minneapolis, Minn., May 1, 1920.

PRELIMINARY THOUGHTS

"Science interpreted is theology."

"Deity works by methods and means."

"Science prosecuted to its conclusion^ leads to God."

"The elucidation oi the great problems of philosophic or speculative theology ifc, indeed, the highest function of science."

"It is not for its facts, but for the significance of the facts, that science is valuable."

"To accumulate the data of science is good; to interpret them is the noblest prerogative of a thinking being."

"All our learning would in reality be but the "vanity* which it is sometimes reproached with being if it could reflect no light upon the origin, the nature, the duty, and the destiny of man." — Winchell.

NATURE A REVELATION

We cannot resist the conviction that Nature is intended as a revelation of God to all intelligences. If it be so intended, Nature must be capable of fulfilling the offices of a revelation, and a knowledge of her phenomena and laws must afford the data of a theology.

Despite the skepticism of a certain school of recent writers, the phenomena of the universe continue to inspire in the soul ot man emotions of religious reverence and worship. To the mass of mind, as to the intelligence of Socrates, and Plato, and Kepler, and Newton, and Galen, and Paley, and Buckland, the order or the Cosmos proclaims an infinite intelligence. — Winchell.

"Lift up your eyes on high, and behold who hath created these things, that brought out their host by number : He calleth them all by names by the greatness of His might, for that He is Strong in power, not one faileth. v Isa. 40:26.

"Is not God in the height of heaven? and behold the height of the stars, how high they are ! And thou sayest, how doth God know? Can He judge through the dark cloud? thick clouds are a covering to him, that he seeth not; and He walketh in the circuit of heaven." Job 22:12-14.

DONATI'S COMET

This comet which appeared in 1858 was a subject of universal wonder. Its tail was 50,000,000 miles in length, and its head was 250,000 miles in diameter. It parsed over the first magnitude star, Arcturus, Oct. 5, 1858, and came nearest the earth on Oct. 10 of the same year. It remained visible for more than 9 months, and will not appear again for nearly 2,000 years.

THE TELESCOPE AND JUPITER'S FAMILY

Not until June 7, 1610 was it known that Jupiter had any moons. Galileo found the 4 larger ones on that memorable night with his 30-inch "Optic Tube." A new era was then opened in astronomy. These 4 moons are known by the mythological names of Io, Europa, Ganymede, and Callisto. During nearly 300 years from Galileo's triumph to the Lick Refractor these 4 moons of Jupiter were supposed to be the full number, but a fifth satellite was added by E. E. Barnard at Mt. Hamilton in Sept., 1892. It has a period of 11 hours and 57 minutes and is 112,500 miles from the planet. Two additional moons were added to Jupiter's system in Dec. 1904 and Jan. 1905 by Prof. Perrine of the Lick Observatory. Finally on Feb. 28, 1908, P. Melotte of Greenwich Observatory, found an eighth moon of Jupiter. Its movement is retrograde, which anomaly is of va'st cosmical importance.

A TELESCOPE ON THE NEAREST STAR TO US

If you could stand on Alpha Centauri, the nearest star to the solar system, (4% light years away), and look at our sun, it would appear no brighter than Polaris does to us, "so great is its distance, and you could not see a single one of our planets even if you should look through Lord Rosse's great 60-foot telescope, which is 6 feet in diameter.

The Mathematics of the Sky

CHAPTER ONE THE TELESCOPE AND THE UNIVERSE 1. The Telescope

While "the eye is not satisfied with seeing," (Eccl. 1:8), the telescope invented three hundred years ago ha$ come to assist the eye, and now enables it to look out into space and bring to view millions of suns that are known to be hundreds of light years from the solar system.

This instrument has given man a broader view of the bigness and magnificence of the Universe. The human eye unaided can see distinctly not more than seven thousand stars, but if one should look through one of the greaf telescopes, he would be astonished to find at lea^t a hundred millions of luminous suns in space. Sir William Herschel calculated that his twentyfoot reflector would penetrate into space and reach stars that are nine hundred times the distance of Sirius, and that his forty-foot reflector would bring to view stars that are twentyeight hundred time's the same distance. This is vast, simply enormous. Mr. Herschers forty- foot reflector, with an object glass of 48 inches, showed stars up to the eighteenth magnitude of our present day classifications. Sirius is known to be more than fifty trillions of miles from us, which means that it is eight and a half light years from the Solar System.

While the Yerkes and Lick telescopes have magnifying powers of more than three thousand diameters, Such instruments being intended to study the heavenly bodies in detail, the glasses that give the best satisfaction to the average person are of comparatively

OF THE SKY ll

moderate magnifying power, say about two hundred to three hundred diameters.

No minister, or other educated person, can afford to omit from his curriculum of study God's great Book of Nature. It should accompany the study of Revelation, the Holy Scriptures.

As we look out upon God's great universe and behold the beauty, the grandeur and the magnificence of His works, either with the naked eye or by the help of the telescope, we are constrained to Say in the language of the Psalmist, "O Lord, how manifold are Thy works! In wisdom hast Thou made them all; the earth is full of Thy riches." Psa. 104:24. 2. The Universe.

From the Latin Universum. Unus one and vertere to turn, that is, turned into one, combined into one whole; all created things viewed as one system.

I. What? 1. Stars or Suns.

(1) Luminous ones. The telescope finds at least 100,000,- 000.

(a) First magnitude start, 20 in all.

(b) Double stars, at least 12,-

000 couples have been found. Also many triples and quadruples.

(c) Variable stars.

(d) Temporary stars.

(e) The solar system, composed of the sun and 8 larger planets, 26 moons, and near 600 asteroids, also meteors and comets.

(2) Opaque. Probably millions of these also.

2. Nebulae. Ten thousand have been catalogued. Estimated to be at least one hundred and twenty thousand of them in the heavens. The most prominent are:

(1) The Great Nebula in Orion.

(2) Ring Nebula in Lyra.

(3) The Trifid Nebula.

(4) Dumb-bell Nebula.

(5) Great Spiral Nebula.

(6) Great Nebula in Andromeda.

3. Star Clusters. Most noted are,

(1) The Pleiades.

(2) The Hyades.

(3) The Praesepe.

(4) Great cluster in Hercules.

4. Comets. Many millions of these, some invisible to the naked eye, some few very bright and striking.

They are divided into short period and long period comets and those that never return to the solar system after one visit.

II. Extent f Known only to the Creator, but it is known to be vast. Sir Wm. HerSchel calculated that his 40-foot reflector reaches stars 2800 times the distance of Sirius, and this star is known to be fifty trillions of miles from the solar system, or eight and one-half light years' away from us.

III. How and When? "In the beginning God created the heavens and the earth." Gen. 1:1. Hence the universe did not come by chance, and it is not eternal.

CHAPTER TWO STUDIES IN CELESTIAL ARITH- METIC 1. The Moon. Our nearest neighbor, and the most interesting object in the sky to people on the earth, except the sun.

(1) Its diameter is 2163 miles; its volume is about 1/50 that of the earth while in mass it would take 81 moon's to make an earth. The pull of gravity on its surface is only 1/6 of what it is on the earth. Its sidereal revolution covers about 27% days, while its synodic period is about 29% days.

(2) It turns on its axis once while traveling around the earth and hence keeps the same face towards u's continually.

(3) Its average distance from the earth is about 240,000 miles, and an express train traveling at 60 miles per hour could go to the moon and back in 11 months. A round trip ticket at 3c a mile would cost $14,400.

(4) One of the highest mountains on the moon is called Leibnitz, and is fully 6 miles high. The Surface of the moon contains several thousand craters and some of these are from 14 to 100 miles across. Copernicus, one of its great craters, is fully 13,000 feet high. The mountains of the moon are much higher in proportion than those upon the earth.

(5) The moon in its revolution around the earth travels at the rate of 3355 feet per second, 38 miles per minute, 2288 milts per hour, and completes a revolution around the earth in 27% days. It travels from west to east and covers about 13° on the face of the sky daily. It would take more than 600,000 full moorts to equal the light of the sun as its shines upon the earth.

(6) If a person should stand on the moon and look at the earth, it would look 14 times a's large as the moon looks to us upon the earth. While it takes nearly 50 moons in volume to equal the earth, it takes more than 60,- 000,000 moons to equal the sun. While it takes 81 moon's to weigh as much as the earth, it takes 26,892,000 moons to weigh as much as the sun.

2. The Sun. To us he i*s the most magnificent of all the heavenly bodies.

(1) His distance is 93,000,000 miles from the earth. A passenger train running 30 mile's per hour would require 352 years to make a journey to the sun, and a round trip ticket at 3c a mile would cost $5,580,000. Preachers traveling at half fare would have to pay $2,790,000. A cannon ball traveling at 1760 feet per second would require nearly 9 years to reach the sun.

(2) The sun and moon appear about the Same size, but if the sun could be brought as near the earth as the moon, it would seem to us as large as 160,000 moons, resulting in practically no night, for it would fill the whole heavens. Furthemore, the earth would be 160,000 times as hot as it is now, and nothing could live upon it tor a moment.

(3) The amount of light and heat given off by the sun has been calculated. The annual amount of heat received by the earth is sufficient to melt a layer of ice over its entire surface 114 feet thick; but the amount the earth receives must be multiplied by 2,170,000,000 to get the whole amount of solar radiation for the same time — one year.

(4) The sun is 750 times greater than all the planets combined — , the 8 larger planets, nearly 600 asteroids and 26 moons. If we should represent the earth by a marble one inch in diameter, the sun would be represented by a ball nine feet in diameter, and on this scale the earth would be 968 feet from the sun. On the same 'scale, Neptune would be Sy 2 miles away, and the nearest star would be 49,500 miles distant, while Polaris would be at least 495,000 mile's away.

(5) To get a better idea of the vast volume of the sun, remember that it is 866,000 mile's in diameter which is 109 times that of the earth's diameter; its surface is 12,000 times that of the earth; while its volume is 1,300,000 times that of the earth. Its mass is 332,000 time* that of the earth. While its density is only one-fourth as much as the earth's, its superficial gravity is 27.6 time's greater than that of the earth. In other words a body weighing 100 pounds on the earth would weigh 2760 pounds if carried to the surface of the sun. If an aeroplane could circle the earth in 10 days it would require 3 years for it to circle the sun.

If the earth were as large as the sun, and all objects on the earth were correspondingly as large, a man 6 feet tall would be increased to one-eighth of a mile; his arms from his Shoulders to the tips of his fingers would be more than 160 feet long ; his legs would be more than 250 feet long; his eyeS would be 9 feet in diameter, while his nose would be about 14 feet long. The Mississippi River would be 140,000 miles long, and at Memphis, Tenn., it would be 109 mile's across; Pike's Peak would be 292 miles high, while mount Everest would be over 500 miles above sea level. The Atlantic Ocean would be 327,000 miles wide, and from one side of Chicago to the other would be more than 2000 miles. A train of cars containing 10 coaches would be more than 8 miles long.

Chapter Three The Bigness Of The Solar

SYSTEM

The Ptolemaic system of astronomy gave way about the time of the discovery of the new world by Columbus. The Copernican system then came into popular favor. It was shown and proved that the diurnal movement of the heavens was due to the rotation of the earth on its axis. Real and apparent motion were pointed out and explained by Copernicus. The earth was given its true position in the universe, with the sun as the center of the solar System. A family of 8 larger planets and nearly 600 asteroids have been found to revolve around the sun in regular times and at definite distances.

But before the year 1781 it was not known that there were any planets beyond the orbit of Saturn. While the first real telescope was invented and used by Galileo in 1610, no new planet was discovered till 171 years later when Uranus was discovered in 1781 A. D. by the great astronomer Herschel. It was found by accident and with a relatively small telescope of 7-foot length. This leads me to say that small telescopes have been used in the past and may be used in the future in making important discoveries. The instrument that found the 4 larger moons of Jupiter was a 30-inch instrument. Do not despise the small glass. Secure one for your own use if possible and use it indujtriou'sly and enthusiastically. It will repay you many times in both pleasure and profit.

But I am digressing. Let us get back to Herschel and the planet Uranus. Anciently and up till 1781, Saturn was considered the outside planet of the solar system. This planet revolves around the sun at a distance of 886,000,000 miles from him. Double these figure's and you have the dimensions of the solar system as known at that time. It will be 1,772,000,000 miles and represents the diameter of Saturn's orbit. But an hour or two before midnight of March 13, 1781 the solar system was suddenly doubled, and Wm. Herschel was suddenly made famous. His small telescope had done the work. He was industriously looking for other objects, searching among some stars in the constellation of Gemini when the discovery was made. The dimensions of the solar system were thus doubled, for Uranus' orbit was found to be about double that of Saturn's, 1,800,000,000 miles from the sun. This was a great triumph and created much attention and excitement among tstronomers. The study of astronomy became popular, telescopes were in demand and everybody wanted one.

Thus Wm. Herschel was brought out of obscurity into universal popularity and renown. Not only so, but he was lifted from poverty and inconvenience into favor and influence in many ways. Remember that Herschel by industry and perseverance became one of the world's greatest astronomers in the face of seemingly insurmountable obstacles. He was without a university education, but he made up for this by diligence, hard work, enthusiasm and a perseverance that conquered all difficulties. He learned to grind lenses and build telescopes, and after the discovery of Uranus the king gave him the means to build his great 40-ft. reflector. This was the crowning work of his life, for with it he penetrated into space and found stars of the 18th magnitude and so far away that it take's their light thousands of years to reach the human eye. He became a Fellow of the Royal Society, was given an observatory by the king and received a salary of $1000 a year, which was quite respectable in those days. But back to Uranus again. This planet is just about at the limits of visibility to the unaided eye. though it is 32,000 miles in diameter and fully 64 times as large as the earth. It makes a journey around the sun in nearly 84 years traveling at the rate of 4% miles per second. A child is born, it passes its youth into young manhood, then into married life, middle life, old age and dies at the age of 84 while Uranus makes one revolution around the sun. But it is never tired. It goes on and on and on.

The planet Uranus is so far away from the earth at its nearest approch that a limited fast-line expres's train running 1000 miles a day would require more than 4600 years to span the distance.

But 65 years after the discovery of Uranus, the diameter of the Solar system was extended 2,000,000,000 miles. On Sept. 23, 1846 the planet Neptune was discovered. It was not found by accident a's Uranus had been, but its discovery came about because two men searched for it and calculated its place in the heavens, though the planet was invisible. One of these men wa5 Leverrier of France, the other was Adams, an English astronomer. These men spent nearly two years making their drawings and calculations to find the place in the sky where the planet was believed to be. It is remarkable that neither of these men knew that the other was making calculations to find an unknown planet. But the result of their calculation's almost agreed. These men did not, and could not, know that there was another planet farther out than Uranus, by means of their natural eyes; but they did know or 'strongly believed through their mathematical eyes that there was such a planet. Hence their search by means of two years of laborious calculations. It wa's the behavior of Uranus that led them to believe there was another planet outside his orbit. They could see an invisible body pulling on Uranus, disturbing him in his journey around the fcun, hastening him or holding him back in certain portions of his orbit. They therefore prepared to find the unknown body. After the drawings and calculations were all completed, Leverrier requested the astronomer Galle to direct the telescope to a certain point in the constellation of Aquarius, and he would find the unknown body. It wa's found within a half hour and within less than a degree of the place where Leverrier said it would be. This discovery is regarded as one of the greatest mathematical achievements of the human mind. Such feats as this strengthen and confirm our faith in the mathematics of the heavens. And now since Neptune has been found, what are the great mathematical le k ssons forced upon our minds? This brings the dimensions of the solar system to twice the distance of Neptune from the sun. Neptune's distance being 2,800,000,000 miles from the sun, the diameter of his orbit is 5,600,000,000 miles. He circles the 'sun in nearly 165 years, and travels in an orbit 3-1/7 times the diameter of his orbit, at the rate of 3% miles per second. His distance from the Sun is so vast that the light of the sun requires 4 hours and 10 minutes to reach Neptune. Now remember that light travels through space at the inconceivable rate of 186,000 miles per second.

In order to get perhaps a clearer idea of the meaning of this distance, consider the following illustration. Sound travels through the air at the rate of 1090 feet per second. Suppose there is an explosion on the sun, and suppose that the sound of this explosion could be carried through space at the same rate of 1090 per second till it reached the planet Neptune. It would require more than 430 years for the report of the explosion to be heard on Neptune.

Another illustration. Suppose that aeroplanes were used away back in Old Testament times, and one of these machines actually started from the earth to the planet Neptune via the intervening planets — , Mars, Jupiter, Saturn, and Uranus, passing them in regular order, but never making a stop at any one of them. Suppose the machine started from the earth in the days of Judges, in 1170 B. C, near the time of Jephthah, the 9th judge, (Judges 11th chap.), and traveled all the way at 100 miles per hour, or 2400 miles per day. The first part of the journey was from the earth to Mars, a distance of 48,500,000 miles when that planet is nearest the earth. It required 55 years and passed the planet Mars, therefore, in 1115 B. C, within a few years of the death of Samson. The

Second part of the journey was from Mars to the planet Jupiter, a distance of 342,000,000 miles. This paffof the journey required 390 years and it passed Jupiter in 725 B. C, four years before Shalmanezer carried the ten tribes into captivity. The third part of the journey was from Jupiter to the planet Saturn, a distanve of 403, 000,000 miles. It required 460 years and passed Saturn in 265 B. C. within a few years of the date when the Septuagint version of the Old Testament was made. The fourth part of the journey was from Saturn to the planet Uranus, a distance of 914,000,000 miles. The time required was 1043 years and it pas'sed Uranus in 778 A. D., the year in which Charlemagne made an invasion of Spain and annexed the country between the Ebro and the Pyrenees under the name of the "Spanish March." The fifth part of the journey was from Uranus to the planet Neptune, a distance of 1,000,000,- 000 miles. It required 1142 years and arrived on the planet Neptune in A. D. 1920, this present year of grace. In other words, the distance from the earth to Neptune (2,707,000,000 miles) is so vast that the aeroplane which Started from the earth to Neptune in the year B. G. 1170, traveling constantly night and day at the rate of 100 miles per hour, finished the excursion at the completion of 3090 years, arriving on Neptune in 1920 A. D.

Chapter Four Weight Of The Sun And

PLANETS The amount of matter in each planet and moon of the solar system as well as that of the sun himself has been calculated. In other words, each one of these bodies has been weighed. And this is one of the most wonderful achievements that astronomer's have been able to accomplish. The problem of finding their weight, or of finding the amount of matter in each, is really a very difficult task. Yet the problem has been solved and the principle on which it has been done is as simple as that which has been used in finding their dimensions. The following figures express the weight of the earth in tons: 6,000,000,000,000,000,000,000, or six sextillion tons. Of course these figures are meaningless to us because the mind cannot grasp so stupendous a number, yet they represent the amout of matter which the earth contains. To find the weight of the sun, multiply the earth's weight by 332,000, because the sun contains 332,000 times as much material as the earth.

Comparing the sun with the other planets we have the following: It takes 27,000,000 moons to weigh as much as the sun; 7,000,000 Mercuries; 407,000 worlds like Venus to equal the weight of the sun; 3,000,000 bodies like Mars ; 1048 Jupiters ; 3502 Saturns ; 22,760 worlds like Uranus; and 19,500 Neptunes to weigh as much as the 'sun.

Comparing the earth with the other planets we have the following: It takes nearly 82 moons to equal the earth in weight; 21 Mercuries; Venus weighs 8/10 as mucn as the earth; it takes 9 worlds like Mars to weigh as? much as the earth ; it takes 317 earth's to weight as much as Jupiter; 95 earths to weigh as much as Saturn; 14% earths to equal Uranus in weight; and 17 earth's to weigh as much as Neptune.

Now remember as has been stated before that the sun is 750 times as great as all the planets and moons of the solar system combined. Is it any wonder, then, that the sun has such tremendous pulling power, holding all the planets in their orbits and compelling them to revolve around him?

Is it any wonder hat he has the power to reach out and take hold of far-away Neptune, 2,800,000,000 miles distant, and say to him, you may continue to travel around me, but you shall not get any further away? Remember, that while Neptune fa 32,000 miles in diameter, it takes 19,500 Neptunes to weigh as much as the sun. But this is not all. The sun's power of attraction does not stop with Neptune. There are a number of comets that go out into space hundreds of times' the distance of Neptune, and in every part of their journey they are under the influence and power of the sun's attraction. They go on journeys of hundreds or even thousands of years, but they are compelled by the superiority of the sun to return.

Chapter Five Alpha Centauri And Its

MATHEMATICAL LESSONS The four preceding chapters have been devoted mainly to the sun and his family, and we have been led to get a view of the vast dimensions of our !solar system, expressed by the awiful grasp of figures that tell us of its boundary. While the outer planet of this system is at the inconceivable distance of 2,800,000,000 miles from the sun this distance is but a step, a mile, a measuring unit so to speak as compared with the vastness of the great void separating us from the nearest fixed star. When we have covered the space from the sun to the orbit of Neptune, we have just arrived at the front gate of our own premises, getting ready to start toward Alpha Centauri. This is a first magnitude star in the southern heavens and cannot be seen in this country except in the southern portion of the Gulf states. It is situated in right ascension 14 hrs. 32 mi., and 60d 25m southern Declination. It is a double star, and its components revolve around their common center of gravity at a mean distance of almost 25 times the radius of the earth's orbit, or 2,325,000,000 miles. The period of this binary system is 81 years. It is a great light-giving sun, and believed to be a little larger than our own sun. At any rate it is fully equal to it in luminuosity.

But what can be said of the enormous distance of Alpha Centauri from us? How are we to get any idea of what is meant by 25,500,000,000,000 miles? This distance is so vast that light traveling through space at the rate of 186,000 miles per second would require 4% years to span it. But this does not satisfy us and we must try another illustration. This star is 9000 time the distance of Neptune from us, and we found in a preceding chapter that an aeroplane traveling at 100 miles per hour would spend 3090 years in going from the earth to the planet Neptune. We must therefore, multiply 3090 by 9000 in order to find how long it would take the aeroplane to travel from the earth to Alpha Centauri. You will probably be asstonished to find by calculation that the time will be 27,810,000 years. Let us try another. We consider that sound is traveling at a rapid rate when it covers 1090 feet in a second of time, but at this rate if sound could be carried through space, it would require more than 3,000,000 years to travel from the earth to Alpha Centauri.

Here is another illustration. The Alpha star in the Centaur is in motion traveling through space at 14 miles per second. Let us suppose it is coming towards us at that rate, and will continue to come in this direction till it reaches the solar system. How long will it take? Dividing the distance to Alpha star by 14, the result will be seconds; divide this by 60 and the result will be minutes; divide this by 60 and the result will be hours; divide this by 24 and the result will be days; divide this by 365 and the result will be years. You will find that it will require more than 57,000 years for the star to reach this part of the universe. Still another illustration. Suppose a. passenger train starts from the earth to Alpha Centauri, traveling continually and making 1 mile per minute. How long will at take to reach the star? By performing the calculation you will find that 48,200,000 years will be required. Now suppose that a ticket on this excursion one way costs lc per mile, what will be the fare to the star? The fare will be $255,000,000,000, as much as the great world war cost during the 4 years and 3 months it was running. Suppose the money for this ticket was put into standard silver dollars and piled one upon another, how far above the surface of the earth would the top dollar be? as it takes nine silver dollars to make an inch divide by 9 and reduce the inches to miles. The dollar on top of the column would be 445,000 miles high. It would reach to the moon and 207,000 miles beyond. It would make a string of dollars all around the world 18 times, these dollars hugging each other as closely as it is possible for them to be.