Kepler and the Pathways of the Planets

1571–1635

The invention of the telescope prepared all minds for new wonders, and made astronomy the leading science of the day. The heavenly bodies were observed with a new interest, and their motions studied more intently; for, while the Copernican system proved that the earth and other planets moved around the sun as a centre, it left many mysteries unexplained which could not be accounted for by the fact of the daily rotation of the earth or its annual revolution. And while Galileo was startling the world by his magnificent discoveries in the heavens, the German astronomer Kepler was revolving in his mind a theory of the universe which would explain some these mysteries, and was destined to make his name as famous as that of his great contemporary.

The motions and nature of the heavenly bodies were questions that were puzzling the wisest heads, and many strange theories were advanced to account for the apparent irregularities in the movements of the planets and their relation to the fixed stars.

Tycho Brahe, the Danish astronomer, from his magnificent observatory, Uraniberg, had spent years in studying the order of planetary motion, and at his death left his observations recorded in a set of tables which he intrusted to the care of Kepler, his friend and pupil. Uraniberg, the city of the heavens, was built on the Island of Huen, in the Baltic, and under the patronage of the King of Denmark had become the resort of many of the most earnest scientific students, who gladly availed themselves of the teaching of Tycho Brahe. The observatory was furnished with the most complete set of astronomical instruments in the world, and was famous for its facilities for studying the heavens.

It was by means of these instruments, and by his great knowledge of mathematics, that Tycho Brahe was able to make those accurate observations which gave his tables a priceless value, and enabled Kepler to work out calculations that it would have been impossible to make without them.

Unlike many great scientists, Kepler had shown no special liking for any particular study when a child, and he was led to the study of astronomy only because he was appointed professor of that science in the university of Grätz. But while preparing his lectures, he became so deeply interested in the subject that before long it entirely occupied his mind, and nothing else seemed of any importance as compared with it.

Kepler possessed a very enthusiastic nature, and was always ready to listen to new theories, no matter how wild they might seem. He was among the first to rejoice over the splendid discoveries of Galileo, and was an ardent supporter of the Copernican system while it was yet being reviled by the authority of the Church and the disciples of Aristotle; and his originality and enthusiam made him capable of turning the earnest work of Tycho Brahe to the very best account.

The Copernican theory had been steadily gaining ground in the estimation of astronomers, and, as one after another gave up the old system, they ceased to speculate about the apparent movements of the sun and stars around the earth, and began to study the planets from a new point of view.

The path which a planet takes in revolving around the sun is called its orbit, and astronomers now became interested in the question of the size of the orbits and the rate of motion.

The idea that there was always to be found a certain harmony throughout all the works of nature, swayed the minds of men as much in the sixteenth century as it had done since the dawn of scientific thought, and no sooner was a new theory advanced, or a new discovery made, than the question arose as to how it would harmonize with the truths already known, or how, by following out some suggestion it contained, still other discoveries might be made.

Kepler possessed more than any of his contemporaries the gift of intuition, or the power of grasping a truth that has not been demonstrated by any known law of nature, and it is to this insight that he owed his success. He believed that the entire universe was governed by one great law or principle, and that there was a subtle relation existing between things that seemed to be utterly disconnected. All the great discoveries of science, all the wonderful operations of nature, every expression of beauty in the animal or vegetable world, and every useful invention of man, seemed alike to him to be controlled by some great harmonious principles that might be applied with equal appropriateness to the turning of a water-wheel, or the rise of the tides, or the rushing of a comet through illimitable space.

With this idea ruling his mind every new fact was at once made a basis for calculations that might lead to the discovery of the great secret law of the universe, and no toil was considered irksome that could help him on his way, for he believed that the relation existing between the different forces of nature was so strong that the discovery of the law of one would be the master-key that would unlock the whole mystery of creation.

This belief, which had haunted the minds of philosophers of all ages, seemed to Kepler of infinitely more importance than anything else, and the discovery of a new planet in the heavens meant to him not only a new wonder to be admired and gazed at, but a new instance of the harmonious working of the order of creation.

Pythagoras had claimed, two thousand years before, that he had discovered the world-secret, and that harmony, or proportion, was the law of the universe. He taught that the planets revolved around a central fire, moving with an inconceivable swiftness that caused them to be accompanied by mighty rushing sounds, but that the different velocities were so beautifully proportioned that the result was not mere noise, but the most exquisite music, which excelled in sweetness and power all earthly melodies. It was said that the reason that these harmonies were not heard by man was because they were unceasingly sounding in his ears from the moment of the birth, and that they would therefore be unnoticed by him. This notion was also held by many of the philosophers of the Middle Ages, and even at a much later day the astrologers and seers claimed that the music of the spheres might be easily distinguished by the initiated.

However absurd these theories may seem, it is nevertheless a fact that the love and study of the marvellous have in many cases led to the knowledge of some great truth of nature, and had it not been for Kepler's belief in the possibility of finding the secret that had forever eluded mankind, he might never have been led on to the discoveries that made him famous.

Calculations whose length and intricacy would have disheartened anyone else were cheerfully carried on him for months and years, to be as cheerfully abandoned if found incorrect, and the unwearied and painstaking labor of a life-time would have been counted as nothing in comparison to the discovery of some hitherto unknown truth.

The possession of Tycho Brahe's tables aided him greatly in the work, for so accurate had been the observations of the Danish astronomer, and so reliable his deductions, that Kepler was able to depend upon them almost absolutely, and to decide that in every case his theories must be rejected if they did not agree with the statements in the tables.

Having always in mind the discovery of the law of harmony that governed the universe, Kepler bent the whole energies of his mind to the study of the number of the planets, their motions, and the sizes of their orbits. It seemed to him that there must be some proportion between the sizes of the orbits, and he made many calculations to prove the truth of this conjecture. There were at that time but five planets known, and after having failed to prove any relation existing between the sizes of their orbits, Kepler imagined a new planet between Venus and Mercury, and another between Mars and Jupiter, and then made a new calculation to see if he could discover the proportion he was looking for; but he failed also here, and, after many months spent in fruitless toil, he was obliged to give up the the work without having proved that there was any regular rate of increase between the orbits of the planets nearest the sun and those farthest from it.

In all his calculations Kepler started from the old theories of the relations which were supposed to exist between the different solid and plane figures, and when he began the study of the planets' orbits he pursued the same plan.

Up to this time the belief had always been that the motions of the heavenly bodies were described in circles. The circle, which was considered the most beautiful of all curves, had always had a mystic meaning for the old philosophers, and was always associated in some manner with their religious belief. It was the emblem of eternity, and was carved on the tombs of kings, and inscribed in sacred books, and many things in nature seemed to mark it with special significance. The arch of the heavens stretching from earth to earth again, the cycle of the seasons, the expansion of the moon, which was worshipped as a deity, from the crescent form to the perfectly rounded figure, the circular disc of the sun, and many other things all enveloped the circle with a sacred meaning which had by no means losts its power when astronomy was invested with new interest by the genius of Copernicus.

And when it was conceded that the planets revolved around the sun it was at once assumed that their orbits were circular, for this shape alone would enable them to harmonize with the popular belief in regard to the mystic importance of the circle.

Kepler, starting with this idea, tried in vain to account for the irregularities of the planets' motions which had puzzled other astronomers. If the planets moved in circles about the sun, each always taking the same time for a revolution and moving at a perfectly, regular rate, then, by knowing their positions at any one time and the rate at which they were moving, it would be easy for an astronomer to calculate where they would be at any other time.

But this was found not to be the case. Mars was the planet most convenient for making observations upon, and Kepler made this planet the subject of careful study for years, in order to determine the reason for its irregularity of motion. Mars, travelling round the sun in a circular orbit should reach a certain point on a certain date, and because this did not happen the astronomers were sorely puzzled and invented many ingenious reasons to account for it.

Kepler made nineteen different theories to explain the irregularity of the motion of the planets, but none of them could be considered entirely satisfactory. Each theory was made the subject of the most careful calculation, but all failed, and planetary motion remained as great a mystery as ever.

At last Kepler was forced to think that possibly the planets did not move in circular orbits, although the circle was the most beautiful of curves, and he began to imagine the orbits to be of a different shape than had hitherto been supposed. The careful study that he had made the orbit of Mars seemed to show that it was of an oval form, and as the ellipse was the simplest form of oval, Kepler chose this curve as a basis for new calculations.

He had already become convinced, from his study of the earth's motion, that the planets did not move in their orbits at a regular rate of motion, but that the moved faster when they were nearer the sun and slower when farther from it; this in itself was a most important discovery.

On applying this rule to calculate the motion of Mars, Kepler found, to his surprise and delight, that when its orbit was taken to be an ellipse the planet would reach any point in its path just at the moment calculated, but that this would not be so if any other form of orbit were assumed. This was also found to be the case with the other planets.

These two great discoveries startled the world by their originality, and placed Kepler among the greatest astronomers of the day. Hitherto his theories had been regarded rather indifferently, as his contemporaries thought him always too eager to run after new ideas, and his method of starting a new hypothesis and making one intricate calculation after another to test it, did not correspond with their more sober way of proceeding.

But Kepler kept on in his own manner of working, and continued his study of the planets' orbits. He was still desirous of proving his old theory of some proportion existing between them, and after many months of unremitting toil he was at length rewarded by the discovery of a law which at once established a most beautiful harmony in the solar system; for although he had failed to find any relation existing between the sizes of the orbits, he now found that there was a very direct and beautiful proportion between the times of the revolutions of the planets and their distances from the sun, and that one, knowing the distance of any one planet from the sun and the time it occupied in its revolution, could calculate the distance of any other planet whose period was given, or the period of any planet whose distance was known.

These three great discoveries—the shape of the planets' orbits, the rate of their motion, and the relation existing between their distances and periods of revolution—are called Kepler's Laws, and were the basis for all astronomical calculations from that time. Their discovery was of incalculable value to astronomers, and they contained, besides, the first proof of the ancient belief in the harmony that prevailed throughout the universe.

The thought of the old philosophers was found to be no dream, but a reality as beautiful as the conception that raised the walls of cities by the power of music or changed the loved of the gods to constellations, whose solemn motion through the heavens possessed infinite power over the destinies of mankind; and although the great discoverer of these laws lived a life of the greatest hardship and died in extreme poverty, he is yet to be envied as one who realized all the hopes of his life and saw his greatest wish brought to a satisfying completion.