Pioneers Of Astronomy: Johannes Kepler

PIONEERS OF ASTRONOMY: JOHANNES KEPLER

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In some ways, the life of Johannes Kepler followed a path similar to that of Tycho Brahe (see https://steemit.com/history/@extie-dasilva/pioneers-of-astronomy-tycho-brahe for his story) and in fact there paths would converge. But in other ways his life was very different. Kepler was born on the 27th December 1571 and had none of the privileges that Tycho enjoyed. Although the family had once ranked amongst the nobility and Kepler’s grandfather (Sebald) was highly regarded in the community, his father (Heinrich) was a mercenary soldier who had a drinks problem and was generally rather unsavoury. He had married young to a girl named Katherine and her argumentative nature made living with her difficult, a problem that was compounded by the fact that they shared a house with several of Heinrich’s brothers.

Due to his job as a soldier for hire, Heinrich was forever upping sticks to go and fight somewhere. The one time he had tried another career, which was running a tavern in the town of Elmingden in 1580, he ended up losing all his money. It was as a mercenary that he mysteriously disappeared and while it’s not known exactly what happened to him, it is quite clear that his lifestyle had a disruptive effect on his son. From the time he was two years old, Kepler’s parents had not been adverse to simply leaving him and his little bother with Sebald, only to want him back upon their return. Johannes was caught in the middle, passed from house to house and always having to change schools.

SCHOOL YEARS

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In 1557 Kepler saw a comet. This was the same comet Tycho had witnessed, but for Kepler some seemingly insurmountable obstacles stood in the way of a career in astronomy. For one thing, he had contracted smallpox as a boy and this had damaged his eyesight to the point that he could never observe the heavens as Tycho had done. Also, the family’s modest income placed severe restrictions on the ways Kepler could escape a life of toil and poverty. In fact, his only choice was to become a member of the clergy. When he was seven years old, Kepler was allowed to enter one of the new Latin schools at Leonberg that had been introduced after the Reformation, and whose purpose was to prepare learned men for a role in Church or State. Although his disruptive upbringing meant he took five years to complete a three year course, as a graduate of Latin school he was entitled to sit an exam that would be his passport to a life in the priesthood. He passed his exam in 1584 at the age of twelve and earned a place at Adleberg. Here, despite his often poor health, Kepler showed clear academic promise and was moved to a more advanced school at Maulbronn. By 1588 he had passed an entrance exam for the University of Tubingen, which he joined at the age of seventeen.

Unlike Tycho, Kepler was willing to follow the path that had been pre-prepared for him. But while he was at university a chain of events would begin that would result in them working together. Although he was training to be a priest, the university also required the students to learn mathematics, physics and astronomy. Kepler proved himself a talented student in all three disciplines and when he graduated from this part of the course he ranked second out of a class of fourteen. This put him in line for a rather special privilege. This being a university run by the Reformed church, the students were taught Ptolemy’s Earth-centric model of the universe. But the maths teacher (one Michael Maestlin) also taught the Copernican model to a select few, one of whom was Kepler. He soon realised that this model showed a lot more elegance and simplicity than the one the Church approved of. This was not the only way in which he disagreed with the church, since in private he had misgivings about the religious significance of some of the rituals and had taken the dangerous step of worshiping in his own way.

THE PEACE OF AUGSBURG

By 1594, Kepler was all set to finish his theological studies, when the next event to change his destiny occurred. In the distant town of Gruz in Austria, the professor of Mathematics passed away. The town had connections with the University of Tubingen and asked it to provide a replacement. Due to his outstanding performance, Kepler was recommended for the job. He accepted the position with some reluctance, on the condition that he could return and complete his theological studies should he need to. Kepler became the professor of mathematics at the age of twenty two on April 11th 1594. In a way, the place he moved to reflected his early childhood, since it was a rather disruptive area. This was due to its position in the Holy Roman Empire. In the northern parts of this empire, the Reformed churches were dominant and in the south it was the Catholic Churches that held sway. The city of Gruz was the capital of a statelet called Styria, situated where an invisible border existed between the two religious territories. This border was always shifting because of something called the Peace of Augsburg that had been settled in 1555. The Peace of Augsburg stated that a ruler of a particular region was free to choose the religion of his domain. In such turbulent times, when the death or overthrow of a ruler was by no means uncommon, it was quite the norm for the citizens to find themselves having to abandon their religion and adopt that of their new prince (or duke or whatever). When Kepler arrived the area was Protestant, but its ruler (Archduke Charles) had plans to crack down on this movement. Soon, this would make the situation unbearable for Kepler, but for now the Lutheran seminary was still tolerated.

Yes, it was a turbulent place that Kepler had moved to, and his financial situation did little to help. With no financial support from home, and his employers deciding to pay a three-quarters salary until he proved his worth, Kepler had to find a way to make ends meet. Tycho had become a celebrated astrologer and this was also the path chosen by Kepler, and he too was very adept at producing accurate tables. But there was a crucial difference between the two in that Kepler secretly thought the whole notion of astrology was codswallop. Despite his misgivings, and despite the fact he secretly considered his clients to be buffoons, Kepler was good at predicting future events. More precisely, he had a talent for making common-sense predictions and embellishing them with mystical jumbo-jumbo.

This may lead you to think that Kepler was less mystically inclined than Tycho. After all, Tycho had dismissed the Copernican model, whereas Kepler preferred it. Tycho fully believed in astrology and Kepler thought it was utter tosh. But really, Kepler at that time was just as much of the mystics’ school as Tycho had ever been. In fact, the influence of the Ancients’ teaching can be seen quite clearly in Kepler’s first attempt at modelling the universe. Because of his poor eyesight, Kepler was not really able to observe the heavens, and this meant he had to rely on imagination and reason, much like the ancient Greeks. Kepler knew that if one adopted the Copernican model, that gave you six planets orbiting the Sun. The question he wanted to answer was: Why six?

KEPLER’S FIRST MODEL OF THE UNIVERSE

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In 1595, Kepler came up with an idea that was decidedly ‘Ancient Greek’ in its concept. What he did was to equate the number of planets to the regular solid figures using Euclid geometry. These shapes are: A tetrahedron, which is a pyramid shape comprised of four triangles. A cube, the familiar ‘dice’ shape. The octahedron, which is comprised of eight triangles. A dodecahedron, which is made up of twelve identical pentangles, and finally an icosahedron, which is a twenty-one sided shape comprised of triangles. Kepler’s model of the universe used a combination of regular solid figures and spheres. Each shape was nested inside the other, and in each case the corners of a shape touched the inner surface of a sphere surrounding it, which in turn touched the inner sides of the next shape. Kepler imagined a sphere in the middle, followed by an octahedron, followed by a sphere, inside an icosahedron, then a sphere, in a cube, whose corners touched the inner surface of a final sphere. Arranged this way, Kepler arrived at a model where the space between each sphere more or less equal led the space of the orbits around the Sun.

KEPLER’S BOOK

This model was only ever approximate and there are several good reasons why it cannot work. But one fact stands above all others: There are actually more than six planets in our solar system. But this would not be known for centuries. During the year of 1595, Kepler continued developing his model, entering into correspondence with his maths teacher Michael Maestelin. The following year saw Kepler’s grandfather taken ill, and when he was granted leave of absence, Kepler took the opportunity to visit his former teacher. It was during this meeting that Maestelin encouraged his old student to write a book about his ideas, and even went as far as offering to pay the printing costs. The book itself came out in 1597, by which time his geometric model was under wide discussion. It was called ‘Mysterium Cosmographicum’ (Mystery of the Universe). As well as the now-discredited model, it contained another idea that was more of a step forward. This book marks the first time that somebody made a serious attempt to explain why the planets should be compelled to move in orbits. Previously, the nearest thing to an explanation was to state that Angels prodded them. Kepler reasoned that some kind of force must be coming from the Sun. As the planets moved slower the further out they were, that must mean that this force got less vigorous as one retreated from the Sun. Accordingly, Kepler named this force ‘vigour’. It’s also worth noting that Kepler explicitly stated that he considered the universe to run according to mechanistic principles. This way of thinking preempted Isaac Newton and in the near future Kepler would lay down the mathematical foundations upon which Newton would build modern science.

But first he had to overcome the problem of his eyesight and the fact that he had no observational data to work from. His book turned out to be part of the solution. Having written it, he sent copies to all of the great mathematicians of his day, a list that inevitably included Tycho. Although Tycho did not much think of a book that proposed a Copernican model, he nonetheless recognised the skills of the author. Kepler was invited to join his team of assistants. At the time, though, Kepler’s eagerness to share his ideas ended up causing a delicate situation. He had written to Reismarus Ursus, who was the Imperial Mathematician at that point in time. Perhaps wanting to flatter the man into a correspondence, Kepler praised him to the hilt, calling him ‘the greatest mathematician of all time’. This turned out to be a wrong move. Ursus never replied. Instead, he used Kepler’s praise out-of-context to endorse his own book, one that was critical of Tycho. Needless to say, several tactful correspondences were needed to heal the rift between Kepler and Tycho.

STABLE MARRIAGE, UNSTABLE WORLD

This all happened in 1597, and it was also during this year that Kepler took a wife. Her name was Barbara Muller and she was the daughter of a wealthy merchant. Although Kepler was on a full salary by now, his new wife’s family was definitely of a higher class than himself and some assume that it was a need for financial security that played a role in his choice of spouse. If so, this didn’t work out as planned because Barbera’s family withheld money she was due at protest to her marrying below her station. Even so, the marriage was happy enough and would produce three children (and two more who died in infancy).

But, if Kepler’s married life was reasonably stable, the same thing could not be said for the political situation in Styria. In 1596, Archduke Ferdinand became its ruler, and this devout Catholic began the customary task of reconfiguring the religious framework according to his tastes. The Protestant community first got wind of these changes when they found the taxation system had been changed to favour Catholics at their expense. This prompted them to write up a formal list of complaints and deliver it to the new regime, but Ferdinand used this as evidence that the Reformers were a bunch of trouble makers. In the spring of that year, Archduke Ferdinand travelled to Italy and held audience with the Pope. When he returned to Graz in September, he really stepped up his plans to wipeout Protestantism, ordering all professors and teachers to convert to Catholicism or go into exile. Kepler chose exile, but for some reason he was allowed back within a month. This may be because he was district mathematician and the post required he live in Graz. It is not known, however, why he was not sacked in favour of another district mathematician.

KEPLER MEETS TYCHO

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It is known that the situation in Graz had grown uncomfortable to intolerable. For instance, when Kepler’s daughter passed away and he didn’t perform the ceremony of last rites, he was forbidden from burying her until he paid a fine for his omission. All of which must have made leaving to work for Tycho doubly appealing. Not only did he have a wealth of observational data that Kepler needed, but by now he had also moved to Prague, which was far more relaxed when it came to religious freedom. In January of 1600, Kepler met with a Styrian nobleman by the name of Baron Hoffman, whom he soon impressed with his skills. It so happened that this nobleman was a councilor to the Holy Roman Emperor, Rudolph II, whose chief mathematician was Tycho Brahe. As he had to go to Prague on court business, he offered to take Kepler along and introduce him to Tycho. This meeting took place at Benatky castle on February 4th 1600. Tycho had amassed the greatest collection of accurate astronomical data, but the 53 year old was not as fit as he once was and needed help in analysing the data. Kepler was a 23-year-old, and a superb mathematician whose burning desire was to get his hands on astronomical data and analyse it. He couldn’t collect the data himself, so teaming up with Tycho was the obvious solution.

But, Tycho did not see things the same way, and for a long time he only allowed very restricted access to his data. One reason for this may be because he feared Kepler’s undeniable mathematical skills would allow him to far surpass his achievements. On the other hand, maybe he was simply unwilling to fully trust a relative stranger with his life’s work. Whatever the reason, Kepler only received the data in dribs and drabs, and there was certainly no question of his taking it out of the castle. This was doubly annoying, since it was hard to concentrate, what with all the construction work going on. Well aware that nobody in Tycho’s extensive entourage could match his mathematical skills, Kepler wrote up a list of conditions, and asked a third party to act as mediator. Meanwhile, Tycho had been negotiating with Rudolph II with the aim of securing a paid position for Kepler. But when the list somehow fell into his hands, he took exception at what he thought were high-handed demands. It took a while to smooth things over, but eventually Tycho promised that the emperor would soon come good with a paid position. It would turn out, though, to be roughly as easy as getting blood from a stone.

Kepler returned to Graz in June 1600. He had never resigned from his post as district Mathematician and the visit to Benatky castle was only meant to be a short stay. So, when he returned after an extended period, his officials were by now tired of his absences. Kepler was given a choice: Resign or go to Italy, train as a physician and so something useful for the community. By summer, however, the decision was out of his hands. It was decreed that any citizen who had not yet converted to Catholicism did so at once. Kepler was one amongst sixty one who refused and, as a result, he lost his job on 2nd August 1600. He also lost what little property he had and was given six weeks and two days to leave Graz. Desperate for help, Kepler wrote to Maestelin and Tycho. The latter was confident that the Emperor would soon come through with his promise of a paid position and advised Kepler to come to Prague. He and his family did so in mid-October and were housed by Baron Hoffman. This was a tough period for them. Back then, the city of Prague was a filthy place and that winter both Kepler and his wife were seriously ill with a fever. Also, their finances were fast running out and by February 1601 there was still no sign of an appointment from the Emperor.

In the same month, the Keplers moved to Benatky castle. Living with Tycho was an uneasy experience, because Kepler did not like being dependent on Tycho, who interpreted this as ingratitude. Eventually, Kepler was formerly introduced to the Emperor and obtained that long-awaited paid position. As Tycho’s official assistant, Kepler would help him compile the Rudolphine Tables. Named in honour of the Emperor, these tables would chart planetary positions.

Although Kepler was now Tycho’s official assistant, the situation was much the same as before. He was still only allowed a small sample of the data and the relationship between the two men was always a little awkward. But then, things changed dramatically. This started on 13th October 1601, when Tycho fell dangerously I'll. In his delirium, the astronomer was heard crying out that he hoped his life’s work had not been in vain. By the 24th October, his mind had cleared, but by now it was obvious that these were his final hours. His life’s work remained unfinished, and Tycho needed a worthy successor to complete his work. He appointed Kepler. Looking at it in terms of ability, it was the best choice, but one can imagine how shocking the announcement must have been. It was not long ago that Kepler had been a penniless mathematician, struggling to understand the universe without the benefit of data or instruments. Now, with this and the subsequent appointment by Rudolph II as Imperial Mathematician, Kepler was fully responsible for all of Tycho’s data, instruments and unpublished works. The baton had fully passed to him, and now he could set about solving the riddle of planetary motion.

SOLVING THE RIDDLE OF THE PLANETS

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But, this turned out to be easier said than done, for several reasons. Because Kepler was responsible for Tycho’s data and unpublished works, this made him a target for the deceased astronomer’s relatives. They were eager to see his work published, knowing that they would make money from it. They were also as against Copernicanism as Tycho had been, and in their eyes it seemed likely that Kepler would distort Tycho’s data in order to invalidate Ptolemy. Another problem was Kepler’s role as Imperial Mathematician. It might sound like a job that entailed doing sums and equations, but in reality it meant ’astrologer to the Emperor’. Much of Kepler’s time was spent in the nonsense task of reading the heavens for portentous signs. Finally, Kepler had great difficulty in obtaining his wages, a problem that would rear its ugly head time and again.

Even if there had been no distractions, the calculations themselves would have been immensely challenging. In the days before computers and calculators, it was a truly Herculean task to go through the mountain of data, checking and rechecking for the slightest mathematical slip up. The orbit of Mars was particularly bothersome. Tycho had passed the problem onto Kepler while he had been alive and, according to some, this was because he knew it would occupy him long enough for Tycho to complete his tables. But actually, it was a special property of the orbit of Mars that would force Kepler to abandon the central theme of Aristotelian thinking: The idea of circular orbits. He tried hard to avoid this, only arriving at this conclusion after a step by step process that lasted for years. One of the first things he tried was to offset the orbit of Mars, and in doing so had one half of the orbit closer to the Sun than the other. This approach was at least partly successful because it matched data that showed the planet moved faster when nearer the Sun. In technical terms, the point closest to the Sun is called the ’Perihelion’ and its furthest point is called the ’Aphelion’.

Kepler developed this ’eccentric orbit’ idea in 1602. It was in the same year that he came up with the second of his Three Laws of Motion (it was the second law that lead Kepler to the first, as we shall see). The Second Law of Motion states:

‘A line joining the planet to the Sun sweeps out equal areas in equal times as the planet moves around in an ellipse’.

Do take note of the last word. It is very important and forms the basis of the First Law. Kepler came to this realisation when he worked out that an imaginary line joining a planet to the Sun sweeps out equal areas in equal times. This means a planet is moving faster at its perihelion because its radius line is shorter and has to cross a bigger angle if it is to cover the same area that a longer radius line would cover when it moves across a smaller angle. This constantly changing angular speed results in the planet executing elliptical motion as it orbits the Sun.

Thus did Kepler become the first astronomer to realise that the orbits of planets are not circular like everyone prior to 1605 assumed they were. As Kepler’s model is based around ellipses, it’s worth taking a look at some of their basic properties, but first let’s see why there was a gap of three years between the discovery of the Second Law and the First. The reason was simply because Kepler was distracted from his main task by his other duties, including his secretly hated role as Imperial Astrologer. In 1604, a new star appeared in the night sky. To be precise, a very long time before Kepler existed, a star died in a supernovae and its light hit his retina in 1604, giving the impression that a new star had presented itself in the heavens. Just as Tycho had done, Kepler calculated that this star was indeed part of the fixed stars and therefore invalidated the notion of their eternal nature. He was also required to report on the supposed astrological significance of this event, which he did so in the usual way of disguising common-sense predictions with mumbo-jumbo. As well as his mystical duties, the year of 1604 also saw Kepler undertaking the more practical role of writing a book about optics, explaining how eyeglasses worked. Although three hundred years had passed since their invention, it was not known exactly how they corrected eyesight. Kepler worked out that people with poor eyesight have imperfections in their retina that cause light rays to be focused at a point behind or in front of it. Eyeglasses corrected this so that the rays are focused on a single point on the retina.

So, Kepler was busy doing work that was both scientific and mystical, and his work on elliptical orbits definitely fitted into the second category. Now, let’s take a look at the basic properties of ellipses.

ELLIPSES

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The first thing you notice about an ellipse is that it resembles a flattened circle. The amount of flattening is termed the ’eccentricity’ and is measured from zero to one. So, a circle is a special kind of ellipse whose eccentricity is zero. As for the orbit of planets, they are true ellipses with an eccentricity between zero and one, but it is so slight that one can only determine they are not circular by carefully examining their geometry.

Now, think of a clock face (a traditional one as opposed to one with a digital display). It has twelve numbers arranged in a circular pattern, with dashes marking five minute intervals between each number. Imagine the minute hand sweeping around the clock face. As it does so, it always maintains the same distance from the markers denoting the minutes. But, if the clock face were elliptical, this would not be the case. The hand would be nearest the markers at the ’12’ position, then move away until it was at its furthest at ’3’. Now it moves back in as ’6’ approaches, out as it moves to ’3’ and finally moves back in as ‘12’ comes round again. What does this teach us? It teaches us that an ellipse has two axes, and one is shorter than the other. The short axis is called the minor axis and the long one is known as the major axis. In a circle, any line drawn from the centre to the outer edge denotes its radius. But, in an ellipse the radius is the semi-major axis, which is one half of the major axis. It is the semi-major axis that marks the average distance of a planet from its Sun, so the ’radius’ of a planetary orbit usually means the length of the semi-major axis.

So, a planet orbits the Sun, tracing out an ellipse as it does so, with the semi-major axis marking the average distance from the parent star. The next important point is that the Sun is not placed at the centre of the ellipse. In the case of a circle, there is a single focus point- right at the centre- from which any point on the circle is a constant. An ellipse, though, has two focus points. These foci are situated to the left and right of where you would intuitively place the ’centre’. The sum of the distances to the foci from any point on the ellipse is a constant. To put it another way, the ellipse is defined in terms of its distances to focus points ’a’ and ’b’. This is expressed in the simple equation: a+b=constant.

The Sun is not placed at the centre of the ellipse but is instead at one focus point ( and there is generally nothing at the other). This is Kepler’s First Law of Planetary Motion:

‘The orbits of planets are ellipses, with the Sun at one focus of the ellipse’.

With just these two laws, Kepler was able to do away with all the complicated baggage that had plagued other astronomers from Ptolemy to Tycho. He had no need of epicycles, quadrants or even the nested solids of his own model (though he never accepted this). By looking at the universe in a different way, Kepler had found the universe to be more elegant than previously thought. This would not be a one-off in science, either. For instance, in the 20th century the Scot James Clerk Maxwell produced eight equations that showed light was an electromagnetic wave. Henceforth any student learning electricity and magnetism had to memorise his eight awkward and clumsy equations. But when Einstein proposed that Time was not different to Space, but rather constituted a fourth spatial dimension, Maxwell’s eight equations collapsed into a single one not much bigger than an inch long.

As for Kepler, problems with printing and a lack of finances delayed publication of his ideas until 1609. When they were published in the book Astronomica Nova, the world of astronomy was not changed as you would expect. People stubbornly refused to believe that the planets moved in ellipses, or that the Earth moved at all. It took a mathematician of considerable skill to see that Kepler’s ideas were born of observation as opposed to being just another piece of mystical thinking. The calibre of mathematician needed is highlighted in the fact that Kepler only achieved the accolades he deserved when one of the greatest mathematicians that ever lived used his model as the foundations of his own work: Isaac Newton.

It wasn’t only Kepler’s work that played a part in Newton’s eventual rise as the World’s greatest scientist. The political situation in Central Europe played its part as well. Combined with the suppression of Galileo’s ideas by the Catholic Church, the turmoil that would soon be unleashed in Central Europe would stunt the growth of scientific ideas, and the full flowering of Kepler’s model would take place in the more settled academic setting of Newton’s England. Even as Kepler struggled to compile his Three Laws, a situation was developing that would lead to the 30 years war.

POLITICAL AND RELIGIOUS TROUBLES

The political and religious situation began to deteriorate in the years following the supernova. In 1608, several Protestant states merged to form a coalition known as the Protestant Union. The Catholics responded in kind the following year by forming the Catholic League. With these old enemies stronger than before, the Holy Roman Empire needed a leader who was an adept politician able to pour oil on troubled waters. Unfortunately, it had Rudolph II. More interested in his art collection than the disorder outside his walls, he had barely been fit to act as emperor even during relatively peaceful times, and some say he went mad in later life. He was also running out of money and his power was gradually passing to his brother, Matthius. It was he who became emperor when Rudolph II died in 1612.

Kepler had realised things were falling apart long before the emperor died, and he planned to leave Prague. And at the same time that Society was experiencing troubled times, Kepler had plenty to worry about at home, because in 1611 Barbara developed epilepsy and one of their three children died of smallpox. Kepler’s initial escape route was to apply for a position at his old university in Tubingen, but because of his unorthodox beliefs he was rejected out of hand. His fortunes changed for the better when he travelled to Linz and applied for a job as district mathematician. He was accepted in June, but when he returned to Prague to prepare for the move he found his wife had contracted typhus. She died a few days later.

This would be the pattern for the remainder of Kepler’s life: Periodically, fortune would smile on him, but then his life would take a downturn. Things seemed more promising once Matthius became emperor. After Barbara died, Kepler became depressed and uncertain about the future. But when Matthius became emperor, he retained Kepler as Imperial Mathematician and also gave him leave to take up the post in Linz as well. Then, things took a downturn. At that point in time, Linz was under the influence of the extreme orthodox Lutheran Church. Kepler was a Lutheran, but a rather unorthodox one. The chief priest had come from Tubingen and was well aware that Kepler held non-mainstream opinions. He refused to allow him to take holy communion. Kepler may have been unorthodox, but in his own way he was a very religious man. Not being able to take holy communion was very stressful and repeated appeals did little to resolve the situation. It also got in the way of his mathematical work. Nonetheless, Kepler was doing such work at this time. For one thing, he was involved in calendar reform. The modern calendar had been invented by Pope Gregory XIII in 1582 and Protestant states were reluctant to make the change. Kepler also used his mathematical skills for more religious work, when he used an eclipse of the moon recorded in Herod’s time to show Christ was born in 5 BC.

On a personal level, the up and down pattern persisted. On a happy note, Kepler remarried to a woman 24 years of age, who bore him six children (three died in infancy). But then, in 1615, his mother was accused of witchcraft. Were she to be found guilty, he would lose his position as Imperial Mathematician. But surely, the thing that was uppermost in his mind was that a guilty verdict would result in his mother being burned at the stake. To emphasise just how real a threat this was, six so-called witches had met this grisly end in his mother’s town of Leonberg that year. Kepler spent years appealing on her behalf. She was not formally accused of witchcraft until 1620, and eventually it was decided that there was enough evidence to arouse suspicion, but not enough to return a definitive verdict. She was kept in jail until October 1621 and died six months after her release.

KEPLER’S LAST LAW

With Kepler’s life as troubled as the political situation in Central Europe during the Thirty Years war, it seems ironic that he should title one of his last great works Harmonica Mundi (Harmony of the Worlds). Of course, the title referred to the solar system, still going about its business and caring little for the troubled Earth. Although this book was largely a mystical work of no scientific value, it did make one important contribution in that it contained the last of Kepler’s Three Laws. He thought of it on 8th March 1618 and it states:

‘The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of the semimajor axes’.

Sounds complicated, but it’s simply a way of working out how long a planet takes to orbit the Sun by measuring its distance from the parent star. The length of the ’year’ increases dramatically with the radius of a planet’s orbit. Consider Mars. It is 1.52 times as far from the Sun as the Earth is and its year is 1.88 times the length of ours. According to Kepler’s law, we work out what 1.523 is and the answer is 3.51108 which we round off to 3.5. But if we work out the square of 1.88 we get 3.5344 which we again round off at 3.5. Thus:

‘The ratio of the squares of the revolutionary periods for (Earth and Mars) is (3.5, which ) is equal to the cubes of their semimajor axes (also 3.5)’.

This was not an entirely novel idea, since a similar pattern had been discovered by Copernicus. Harmonica Mundi was published in 1619 at a time when the Thirty Years War was well underway. Kepler also published another book called Epitome of Copernicanism, but because of the troubles caused by the unstable political situation (as well as that of his personal life) the work was published in three volumes in 1618, 1620 and 1621. The book was far more accessible than others and so it brought Copernican ideas of a Sun-centric universe to a wider readership.

POLITICAL TROUBLE (AGAIN)

Somewhere between the publication of the second and third volumes, the religious map underwent yet another alteration. This change came about because in 1619 emperor Matthius died and was succeeded by Ferdinand II. You may remember him: It is the same Ferdinand who had made life impossible for Lutherans like Kepler and threw him out of Graz in the early 1600s. Now, in 1625, he brought Catholic dominance to all of Austria and Kepler found himself being persecuted for being too Lutheran, whereas before he faced persecution for not being Lutheran enough! However, it should be pointed out that the new emperor was quite well disposed towards Kepler on a personal level. Although he insisted Kepler (and all Lutherans) converted to Catholicism, it would have been Ok if Kepler only paid lip service to such a conversion. But Kepler would not even entertain the idea and Ferdinand II would not have a Lutheran in the role of Imperial Mathematician. Once again, Kepler was out of a job.

Before he did lose his post, though, Kepler managed to fulfil his duty to the Empire by completing the Rudolphine Tables. They were published in 1627 after being delayed by all kinds of strife, including a siege of Linz. Kepler managed to complete the task thanks largely to one John Napier (born 1550). He had recently invented a new mathematical tool called logarithms which made Kepler’s job a lot easier. With the publication of the Rudolphine Tables, it was possible to track the planets with an accuracy thirty times greater than that offered by Copernican tables. A year after the tables were completed, Kepler managed to secure a new position with the Duke of Wallenstein. Like most people in positions of power (he commanded Ferdinand’s army) the Duke always consulted his astrologers before he made a move. In his day, Kepler was more famous for his astrological work than anything else and Duke Wallenstein was well aware of his abilities in this field. Kepler and his family moved to the Silesian town of Sagan on July 1628 to begin a new life and Kepler’s luck took a temporary turn for the better. His new employer actually paid his salary on a regular basis, and he also permitted all kinds of religious worship, provided they were Christian. It was during this time that Kepler produced Dreams of the Moon, which was the first of many science fiction stories.

KEPLER’S DEATH

But then, things took their usual downturn soon after Kepler arrived. In order to curry favour with the emperor, the Duke decided to go along with the Counter Reformation and this resulted in new laws that ruined the Protestant community and had it living in fear. As an employee of the Duke, Kepler was exempt from these laws, but in the summer of 1630 Wallenstein was dismissed from his post as Commander of the Army. Once more facing an uncertain future, Kepler had to pool his resources in anticipation of yet another move. There was some money owed to him in Linz and the authorities arranged for a meeting on 11th November. He set off on the long journey from Sagan in October but he never completed his journey. Kepler got as far as Regensburg on 2nd November 1630, where he was struck down with a fever. He was confined to bed and died on 15th November 1630. But it was not long before the work that was his legacy was enabling others to make new discoveries. In 1631, a French astronomer called Pierre Gassendi became the first person to witness a transit of Mercury. A transit is when a planet passes in front of the Sun and this particular example had been predicted by Kepler using the new Rudolphine Tables.

In our story, Kepler represents the last of the transitional figures that bridge the gap between mysticism and science. And transitional figure he was: Living at a time when there was little distinction between astrology and astronomy and when work on providing accurate astronomical data could be interrupted by charges of Witchcraft.

An essay such as this cannot be written without relying on the hard work of prior writers who have recorded important information like dates and names. My reference was an excellent book by John Gribbin called 'Science: A History'.