Lecture Ii

TYCHO BRAHÉ AND THE EARLIEST OBSERVATORY

We have seen how Copernicus placed the earth in its true position in the solar system, making it merely one of a number of other worlds revolving about a central luminary. And observe that there are two phenomena to be thus accounted for and explained: first, the diurnal revolution of the heavens; second, the annual motion of the sun among the stars.

The effect of the diurnal motion is conspicuous to every one, and explains the rising, southing, and setting of the whole visible firmament. The effect of the annual motion, i.e. of the apparent annual motion, of the sun among the stars, is less obvious, but it may be followed easily enough by observing the stars visible at any given time of evening at different seasons of the year. At midnight, for instance, the position of the sun is definite, viz. due north always, but the constellation which at that time is due south or is rising or setting varies with the time of year; an interval of one month producing just the same effect on the appearance of the constellations as an interval of two hours does (because the day contains twice as many hours as the year contains months), e.g. the sky looks the same at midnight on the 1st of October as it does at 10 p.m. on the 1st of November.

All these simple consequences of the geocentric as opposed to the heliocentric point of view were pointed out by Copernicus, in addition to his greater work of constructing improved planetary tables on the basis of his theory. But it must be admitted that he himself felt the hypothesis of the motion of the earth to be a difficulty. Its acceptance is by no means such an easy and childish matter as we are apt now to regard it, and the hostility to it is not at all surprising. The human race, after having ridiculed and resisted the truth for a long time, is apt to end in accepting it so blindly and unimaginatively as to fail to recognize the real achievement of its first propounders, or the difficulties which they had to overcome. The majority of men at the present day have grown accustomed to hear the motion of the earth spoken of: their acceptance of it means nothing: the attitude of the paradoxer who denies it is more intelligent.

It is not to be supposed that the idea of thus explaining some of the phenomena of the heavens, especially the daily motion of the entire firmament, by a diurnal rotation of the earth had not struck any one. It was often at this time referred to as the Pythagorean theory, and it had been taught, I believe, by Aristarchus. But it was new to the modern world, and it had the great weight of Aristotle against it. Consequently, for long after Copernicus, only a few leading spirits could be found to support it, and the long-established venerable Ptolemaic system continued to be taught in all Universities.

The main objections to the motion of the earth were such as the following:--

1. The motion is unfelt and difficult to imagine.

That it is unfelt is due to its uniformity, and can be explained mechanically. That it is difficult to imagine is and remains true, but a most important lesson we have to learn is that difficulty of conception is no valid argument against reality.

2. That the stars do not alter their relative positions according to the season of the year, but the constellations preserve always the same aspect precisely, even to careful measurement.

This is indeed a difficulty, and a great one. In June the earth is 184 million miles away from where it was in December: how can we see precisely the same fixed stars? It is not possible, unless they are at a practically infinite distance. That is the only answer that can be given. It was the tentative answer given by Copernicus. It is the correct answer. Not only from every position of the earth, but from every planet of the solar system, the same constellations are visible, and the stars have the same aspect. The whole immensity of the solar system shrinks to practically a point when confronted with the distance of the stars.

Not, however, so entirely a speck as to resist the terrific accuracy of the present century, and their microscopic relative displacement with the season of the year has now at length been detected, and the distance of many thereby measured.

3. That, if the earth revolved round the sun, Mercury and Venus ought to show phases like the moon.

So they ought. Any globe must show phases if it live nearer the sun than we do and if we go round it, for we shall see varying amounts of its illuminated half. The only answer that Copernicus could give to this was that they might be difficult to see without extra powers of sight, but he ventured to predict that the phases would be seen if ever our powers of vision should be enhanced.

4. That if the earth moved, or even revolved on its own axis, a stone or other dropped body ought to be left far behind.

This difficulty is not a real one, like the two last, and it is based on an ignorance of the laws of mechanics, which had not at that time been formulated. We know now that a ball dropped from a high tower, so far from lagging, drops a minute trifle in front of the foot of a perpendicular, because the top of the tower is moving a trace faster than the bottom, by reason of the diurnal rotation. But, ignoring this, a stone dropped from the lamp of a railway carriage drops in the centre of the floor, whether the carriage be moving steadily or standing still; a slant direction of fall could only be detected if the carriage were being accelerated or if the brake were applied. A body dropped from a moving carriage shares the motion of the carriage, and starts with that as its initial velocity. A ball dropped from a moving balloon does not simply drop, but starts off in whatever direction the car was moving, its motion being immediately modified by gravity, precisely in the same way as that of a thrown ball is modified. This is, indeed, the whole philosophy of throwing--to drop a ball from a moving carriage. The carriage is the hand, and, to throw far, a run is taken and the body is jerked forward; the arm is also moved as rapidly as possible on the shoulder as pivot. The fore-arm can be moved still faster, and the wrist-joint gives yet another motion: the art of throwing is to bring all these to bear at the same instant, and then just as they have all attained their maximum velocity to let the ball go. It starts off with the initial velocity thus imparted, and is abandoned to gravity. If the vehicle were able to continue its motion steadily, as a balloon does, the ball when let go from it would appear to the occupant simply to drop; and it would strike the ground at a spot vertically under the moving vehicle, though by no means vertically below the place where it started. The resistance of the air makes observations of this kind inaccurate, except when performed inside a carriage so that the air shares in the motion. Otherwise a person could toss and catch a ball out of a train window just as well as if he were stationary; though to a spectator outside he would seem to be using great skill to throw the ball in the parabola adapted to bring it back to his hand.

The same circumstance enhances the apparent difficulty of the circus rider's jumping feats. All he has to do is to jump up and down on the horse; the forward motion which carries him through hoops belongs to him by virtue of the motion of the horse, without effort on his part.

Thus, then, it happens that a stone dropped sixteen feet on the earth appears to fall straight down, although its real path in space is a very flat trajectory of nineteen miles base and sixteen feet height; nineteen miles being the distance traversed by the earth every second in the course of its annual journey round the sun.

No wonder that it was thought that bodies must be left behind if the earth was subject to such terrific speed as this. All that Copernicus could suggest on this head was that perhaps the atmosphere might help to carry things forward, and enable them to keep pace with the earth.

There were thus several outstanding physical difficulties in the way of the acceptance of the Copernican theory, besides the Biblical difficulty.

It was quite natural that the idea of the earth's motion should be repugnant, and take a long time to sink into the minds of men; and as scientific progress was vastly slower then than it is now, we find not only all priests but even some astronomers one hundred years afterwards still imagining the earth to be at rest. And among them was a very eminent one, Tycho Brahé.

It is interesting to note, moreover, that the argument about the motion of the earth being contrary to Scripture appealed not only to ecclesiastics in those days, but to scientific men also; and Tycho Brahé, being a man of great piety, and highly superstitious also, was so much influenced by it, that he endeavoured to devise some scheme by which the chief practical advantages of the Copernican system could be retained, and yet the earth be kept still at the centre of the whole. This was done by making all the celestial sphere, with stars and everything, rotate round the earth once a day, as in the Ptolemaic scheme; and then besides this making all the planets revolve round the sun, and this to revolve round the earth. Such is the Tychonic system.

So far as relative motion is concerned it comes to the same thing; just as when you drop a book you may say either that the earth rises to meet the book, or that the book falls to meet the earth. Or when a fly buzzes round your head, you may say that you are revolving round the fly. But the absurdity of making the whole gigantic system of sun and planets and stars revolve round our insignificant earth was too great to be swallowed by other astronomers after they had once had a taste of the Copernican theory; and accordingly the Tychonic system died a speedy and an easy death at the same time as its inventor.

Wherein then lay the magnitude of the man?--not in his theories, which were puerile, but in his observations, which were magnificent. He was the first observational astronomer, the founder of the splendid system of practical astronomy which has culminated in the present Greenwich Observatory.

Up to Tycho the only astronomical measurements had been of the rudest kind. Copernicus even improved upon what had gone before, with measuring rules made with his own hands. Ptolemy's observations could never be trusted to half a degree. Tycho introduced accuracy before undreamed of, and though his measurements, reckoned by modern ideas, are of course almost ludicrously rough (remember no such thing as a telescope or microscope was then dreamed of), yet, estimated by the era in which they were made, they are marvels of accuracy, and not a single mistake due to carelessness has ever been detected in them. In fact they may be depended on almost to minutes of arc, i.e. to sixtieths of a degree.

For certain purposes connected with the proper motion of stars they are still appealed to, and they served as the certain and trustworthy data for succeeding generations of theorists to work upon. It was long, indeed, after Tycho's death before observations approaching in accuracy to his were again made.

In every sense, therefore, he was a pioneer: let us proceed to trace his history.

Born the eldest son of a noble family--"as noble and ignorant as sixteen undisputed quarterings could make them," as one of his biographers says--in a period when, even more than at present, killing and hunting were the only natural aristocratic pursuits, when all study was regarded as something only fit for monks, and when science was looked at askance as something unsavoury, useless, and semi-diabolic, there was little in his introduction to the world urging him in the direction where his genius lay. Of course he was destined for a soldier; but fortunately his uncle, George Brahé, a more educated man than his father, having no son of his own, was anxious to adopt him, and though not permitted to do so for a time, succeeded in getting his way on the birth of a second son, Steno--who, by the way, ultimately became Privy Councillor to the King of Denmark.

Tycho's uncle gave him what he would never have got at home--a good education; and ultimately put him to study law. At the age of thirteen he entered the University of Copenhagen, and while there occurred the determining influence of his life.

An eclipse of the sun in those days was not regarded with the cold-blooded inquisitiveness or matter-of-fact apathy, according as there is or is not anything to be learnt from it, with which such an event is now regarded. Every occurrence in the heavens was then believed to carry with it the destiny of nations and the fate of individuals, and accordingly was of surpassing interest. Ever since the time of Hipparchus it had been possible for some capable man here and there to predict the occurrence of eclipses pretty closely. The thing is not difficult. The prediction was not, indeed, to the minute and second, as it is now; but the day could usually be hit upon pretty accurately some time ahead, much as we now manage to hit upon the return of a comet--barring accidents; and the hour could be predicted as the event approached.

Well, the boy Tycho, among others, watched for this eclipse on August 21st, 1560; and when it appeared at its appointed time, every instinct for the marvellous, dormant in his strong nature, awoke to strenuous life, and he determined to understand for himself a science permitting such wonderful possibilities of prediction. He was sent to Leipzig with a tutor to go on with his study of law, but he seems to have done as little law as possible: he spent all his money on books and instruments, and sat up half the night studying and watching the stars.

In 1563 he observed a conjunction of Jupiter and Saturn, the precursor, and cause as he thought it, of the great plague. He found that the old planetary tables were as much as a month in error in fixing this event, and even the Copernican tables were several days out; so he formed the resolve to devote his life to improving astronomical tables. This resolve he executed with a vengeance. His first instrument was a jointed ruler with sights for fixing the position of planets with respect to the stars, and observing their stations and retrogressions. By thus measuring the angles between a planet and two fixed stars, its position can be plotted down on a celestial map or globe.

In 1565 his uncle George died, and made Tycho his heir. He returned to Denmark, but met with nothing but ridicule and contempt for his absurd drivelling away of time over useless pursuits. So he went back to Germany--first to Wittenberg, thence, driven by the plague, to Rostock.

Here his fiery nature led him into an absurd though somewhat dangerous adventure. A quarrel at some feast, on a mathematical point, with a countryman, Manderupius, led to the fixing of a duel, and it was fought with swords at 7 p.m. at the end of December, when, if there was any light at all, it must have been of a flickering and unsatisfactory nature. The result of this insane performance was that Tycho got his nose cut clean off.

He managed however to construct an artificial one, some say of gold and silver, some say of putty and brass; but whatever it was made of there is no doubt that he wore it for the rest of his life, and it is a most famous feature. It excited generally far more interest than his astronomical researches. It is said, moreover, to have very fairly resembled the original, but whether this remark was made by a friend or by an enemy I cannot say. One account says that he used to carry about with him a box of cement to apply whenever his nose came off, which it periodically did.

About this time he visited Augsburg, met with some kindred and enlightened spirits in that town, and with much enthusiasm and spirit constructed a great quadrant. These early instruments were tremendous affairs. A great number of workmen were employed upon this quadrant, and it took twenty men to carry it to its place and erect it. It stood in the open air for five years, and then was destroyed by a storm. With it he made many observations.

On his return to Denmark in 1571, his fame preceded him, and he was much better received; and in order to increase his power of constructing instruments he took up the study of alchemy, and like the rest of the persuasion tried to make gold. The precious metals were by many old philosophers considered to be related in some way to the heavenly bodies: silver to the moon, for instance--as we still see by the name lunar caustic applied to nitrate of silver; gold to the sun, copper to Mars, lead to Saturn. Hence astronomy and alchemy often went together. Tycho all his life combined a little alchemy with his astronomical labours, and he constructed a wonderful patent medicine to cure all disorders, which had as wide a circulation in Europe in its time as Holloway's pills; he gives a tremendous receipt for it, with liquid gold and all manner of ingredients in it; among them, however, occurs a little antimony--a well-known sudorific--and to this, no doubt, whatever efficacy the medicine possessed was due.

So he might have gone on wasting his time, were it not that in November, 1572, a new star made its appearance, as they have done occasionally before and since. On the average one may say that about every fifty years a new star of fair magnitude makes its temporary appearance. They are now known to be the result of some catastrophe or collision, whereby immense masses of incandescent gas are produced. This one seen by Tycho became as bright as Jupiter, and then died away in about a year and a half. Tycho observed all its changes, and endeavoured to measure its distance from the earth, with the result that it was proved to belong to the region of the fixed stars, at an immeasurable distance, and was not some nearer and more trivial phenomenon.

He was asked by the University of Copenhagen to give a course of lectures on astronomy; but this was a step he felt some aristocratic aversion to, until a little friendly pressure was brought to bear upon him by a request from the king, and delivered they were.

He now seems to have finally thrown off his aristocratic prejudices, and to have indulged himself in treading on the corns of nearly all the high and mighty people he came into contact with. In short, he became what we might now call a violent Radical; but he was a good-hearted man, nevertheless, and many are the tales told of his visits to sick peasants, of his consulting the stars as to their fate--all in perfect good faith--and of the medicines which he concocted and prescribed for them.

The daughter of one of these peasants he married, and very happy the marriage seems to have been.

Walker & Boutallse.]

Now comes the crowning episode in Tycho's life. Frederick II., realizing how eminent a man they had among them, and how much he could do if only he had the means--for we must understand that Tycho, though of good family and well off, was by no means what we would call a wealthy man--Frederick II. made him a splendid and enlightened offer. The offer was this: that if Tycho would agree to settle down and make his astronomical observations in Denmark, he should have an estate in Norway settled upon him, a pension of £400 a year for life, a site for a large observatory, and £20,000 to build it with.

SEXTANS ASTRONOMICVS TRIGONICVS PRO DISTANTIIS rimandis.

FIG. 22.--Tycho's large sextant; for measuring the angular distance between two bodies by direct sighting.]

Well, if ever money was well spent, this was. By its means Denmark before long headed the nations of Europe in the matter of science--a thing it has not done before or since. The site granted was the island of Huen, between Copenhagen and Elsinore; and here the most magnificent observatory ever built was raised, and called Uraniburg--the castle of the heavens. It was built on a hill in the centre of the island, and included gardens, printing shops, laboratory, dwelling-houses, and four observatories--all furnished with the most splendid instruments that Tycho could devise, and that could then be constructed. It was decorated with pictures and sculptures of eminent men, and altogether was a most gorgeous place. £20,000 no doubt went far in those days, but the original grant was supplemented by Tycho himself, who is said to have spent another equal sum out of his own pocket on the place.

FIG. 23.--The Quadrant in Uraniburg; or altitude and azimuth instrument.]

For twenty years this great temple of science was continually worked in by him, and he soon became the foremost scientific man in Europe. Philosophers, statesmen, and occasionally kings, came to visit the great astronomer, and to inspect his curiosities.

QVADRANS MVRALIS SIVE TICHONICUS.

FIG. 24.--Tycho's form of transit circle.

The method of utilising the extremely uniform rotation of the earth by watching the planets and stars as they cross the meridian, and recording their times of transit; observing also at the same time their meridian altitudes (see observer F), was the invention of Tycho, and constitutes his greatest achievement. His method is followed to this day in all observatories.]

And very wholesome for some of these great personages must have been the treatment they met with. For Tycho was no respecter of persons. His humbly-born wife sat at the head of the table, whoever was there; and he would snub and contradict a chancellor just as soon as he would a serf. Whatever form his pride may have taken when a youth, in his maturity it impelled him to ignore differences of rank not substantially justified, and he seemed to take a delight in exposing the ignorance of shallow titled persons, to whom contradiction and exposure were most unusual experiences.

For sick peasants he would take no end of trouble, and went about doctoring them for nothing, till he set all the professional doctors against him; so that when his day of misfortune came, as come it did, their influence was not wanting to help to ruin one who spoilt their practice, and whom they derided as a quack.

But some of the great ignorant folk who came to visit his temple of science, and to inspect its curiosities, felt themselves insulted--not always without reason. He kept a tame maniac in the house, named Lep, and he used to regard the sayings of this personage as oracular, presaging future events, and far better worth listening to than ordinary conversation. Consequently he used to have him at his banquets and feed him himself; and whenever Lep opened his mouth to speak, every one else was peremptorily ordered to hold his tongue, so that Lep's words might be written down. In fact it was something like an exaggerated edition of Betsy Trotwood and Mr. Dick.

"It must have been an odd dinner party" (says Prof. Stuart), "with this strange, wild, terribly clever man, with his red hair and brazen nose, sometimes flashing with wit and knowledge, sometimes making the whole company, princes and servants alike, hold their peace and listen humbly to the ravings of a poor imbecile."

To people he despised he did not show his serious instruments. He had other attractions, in the shape of a lot of toy machinery, little windmills, and queer doors, and golden globes, and all manner of ingenious tricks and automata, many of which he had made himself, and these he used to show them instead; and no doubt they were well enough pleased with them. Those of the visitors, however, who really cared to see and understand his instruments, went away enchanted with his genius and hospitality.

I may, perhaps, be producing an unfair impression of imperiousness and insolence. Tycho was fiery, no doubt, but I think we should wrong him if we considered him insolent. Most of the nobles of his day were haughty persons, accustomed to deal with serfs, and very likely to sneer at and trample on any meek man of science whom they could easily despise. So Tycho was not meek; he stood up for the honour of his science, and paid them back in their own coin, with perhaps a little interest. That this behaviour was not worldly-wise is true enough, but I know of no commandment enjoining us to be worldly-wise.

If we knew more about his so-called imbecile protégé we should probably find some reason for the interest which Tycho took in him. Whether he was what is now called a "clairvoyant" or not, Tycho evidently regarded his utterances as oracular, and of course when one is receiving what may be a revelation from heaven it is natural to suppress ordinary conversation.

Among the noble visitors whom he received and entertained, it is interesting to notice James I. of England, who spent eight days at Uraniburg on the occasion of his marriage with Anne of Denmark in 1590, and seems to have been deeply impressed by his visit.

Among other gifts, James presented Tycho with a dog (depicted in Fig. 24), and this same animal was subsequently the cause of trouble. For it seems that one day the Chancellor of Denmark, Walchendorf, brutally kicked the poor beast; and Tycho, who was very fond of animals, gave him a piece of his mind in no measured language. Walchendorf went home determined to ruin him. King Frederick, however, remained his true friend, doubtless partly influenced thereto by his Queen Sophia, an enlightened woman who paid many visits to Uraniburg, and knew Tycho well. But unfortunately Frederick died; and his son, a mere boy, came to the throne.

Now was the time for the people whom Tycho had offended, for those who were jealous of his great fame and importance, as well as for those who cast longing eyes on his estate and endowments. The boy-king, too, unfortunately paid a visit to Tycho, and, venturing upon a decided opinion on some recondite subject, received a quiet setting down which he ill relished.

Letters written by Tycho about this time are full of foreboding. He greatly dreads having to leave Uraniburg, with which his whole life has for twenty years been bound up. He tries to comfort himself with the thought that, wherever he is sent, he will have the same heavens and the same stars over his head.

Gradually his Norwegian estate and his pension were taken away, and in five years poverty compelled him to abandon his magnificent temple, and to take a small house in Copenhagen.

Not content with this, Walchendorf got a Royal Commission appointed to inquire into the value of his astronomical labours. This sapient body reported that his work was not only useless, but noxious; and soon after he was attacked by the populace in the public street.

Nothing was left for him now but to leave the country, and he went into Germany, leaving his wife and instruments to follow him whenever he could find a home for them.

His wanderings in this dark time--some two years--are not quite clear; but at last the enlightened Emperor of Bohemia, Rudolph II., invited him to settle in Prague. Thither he repaired, a castle was given him as an observatory, a house in the city, and 3000 crowns a year for life. So his instruments were set up once more, students flocked to hear him and to receive work at his hands--among them a poor youth, John Kepler, to whom he was very kind, and who became, as you know, a still greater man than his master.

But the spirit of Tycho was broken, and though some good work was done at Prague--more observations made, and the Rudolphine tables begun--yet the hand of death was upon him. A painful disease seized him, attended with sleeplessness and temporary delirium, during the paroxysms of which he frequently exclaimed, Ne frustra vixisse videar. ("Oh that it may not appear that I have lived in vain!")

Quietly, however, at last, and surrounded by his friends and relatives, this fierce, passionate soul passed away, on the 24th of October, 1601.

His beloved instruments, which were almost a part of himself, were stored by Rudolph in a museum with scrupulous care, until the taking of Prague by the Elector Palatine's troops. In this disturbed time they got smashed, dispersed, and converted to other purposes. One thing only was saved--the great brass globe, which some thirty years after was recognized by a later king of Denmark as having belonged to Tycho, and deposited in the Library of the Academy of Sciences at Copenhagen, where I believe it is to this day.

The island of Huen was overrun by the Danish nobility, and nothing now remains of Uraniburg but a mound of earth and two pits.

As to the real work of Tycho, that has become immortal enough,--chiefly through the labours of his friend and scholar whose life we shall consider in the next lecture.

SUMMARY OF FACTS FOR LECTURE III

Life and work of Kepler. Kepler was born in December, 1571, at Weil in Würtemberg. Father an officer in the duke's army, mother something of a virago, both very poor. Kepler was utilized as a tavern pot-boy, but ultimately sent to a charity school, and thence to the University of Tübingen. Health extremely delicate; he was liable to violent attacks all his life. Studied mathematics, and accepted an astronomical lectureship at Graz as the first post which offered. Endeavoured to discover some connection between the number of the planets, their times of revolution, and their distances from the sun. Ultimately hit upon his fanciful regular-solid hypothesis, and published his first book in 1597. In 1599 was invited by Tycho to Prague, and there appointed Imperial mathematician, at a handsome but seldom paid salary. Observed the new star of 1604. Endeavoured to find the law of refraction of light from Vitellio's measurements, but failed. Analyzed Tycho's observations to find the true law of motion of Mars. After incredible labour, through innumerable wrong guesses, and six years of almost incessant calculation, he at length emerged in his two "laws"--discoveries which swept away all epicycles, deferents, equants, and other remnants of the Greek system, and ushered in the dawn of modern astronomy.

LAW I. Planets move in ellipses, with the Sun in one focus.

LAW II. The radius vector (or line joining sun and planet) sweeps out equal areas in equal times.

Published his second book containing these laws in 1609. Death of Rudolph in 1612, and subsequent increased misery and misfortune of Kepler. Ultimately discovered the connection between the times and distances of the planets for which he had been groping all his mature life, and announced it in 1618:--

LAW III. The square of the time of revolution (or year) of each planet is proportional to the cube of its mean distance from the sun.

The book in which this law was published ("On Celestial Harmonies") was dedicated to James of England. In 1620 had to intervene to protect his mother from being tortured for witchcraft. Accepted a professorship at Linz. Published the Rudolphine tables in 1627, embodying Tycho's observations and his own theory. Made a last effort to overcome his poverty by getting the arrears of his salary paid at Prague, but was unsuccessful, and, contracting brain fever on the journey, died in November, 1630, aged 59.

A man of keen imagination, indomitable perseverance, and uncompromising love of truth, Kepler overcame ill-health, poverty, and misfortune, and placed himself in the very highest rank of scientific men. His laws, so extraordinarily discovered, introduced order and simplicity into what else would have been a chaos of detailed observations; and they served as a secure basis for the splendid erection made on them by Newton.

Seven planets of the Ptolemaic system-- Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn.

Six planets of the Copernican system-- Mercury, Venus, Earth, Mars, Jupiter, Saturn.

The five regular solids, in appropriate order-- Octahedron, Icosahedron, Dodecahedron, Tetrahedron, Cube.

Table illustrating Kepler's third law.

+---------+---------------+-----------+---------------+----------------+ | | Mean distance | Length | Cube of the | Square of the | | Planet. | from Sun. | of Year. | Distance. | Time. | | | D | T | D^3 | T^2 | +---------+---------------+-----------+---------------+----------------+ | Mercury | ·3871 | ·24084 | ·05801 | ·05801 | | Venus | ·7233 | ·61519 | ·37845 | ·37846 | | Earth | 1·0000 | 1·0000 | 1·0000 | 1·0000 | | Mars | 1·5237 | 1·8808 | 3·5375 | 3·5375 | | Jupiter | 5·2028 | 11·862 | 140·83 | 140·70 | | Saturn | 9·5388 | 29·457 | 867·92 | 867·70 | +---------+---------------+-----------+---------------+----------------+

The length of the earth's year is 365·256 days; its mean distance from the sun, taken above as unity, is 92,000,000 miles.