History of Science - 2
History of Science-2.
Tycho Brahe.
Johannes Kepler.
The person who most deserves the title of the first scientist is Galilieo.
He applied the modern scientific method to his work.
He fully understood what he was doing, and laid down the ground rules clearly,
for others to follow.
Galileo like all scientists, built on what was done before.
In this case the direct link is from Copernicus.
Copernicus began the transformation of astronomy in the renaissance.
It went on to Galileo via Tycho and Kepler.
Tycho was a typical example, in which profoundly significant scientific work,
could still be mixed up with mystical interpretations of the work.
Tycho and Kepler weren’t quite the last mystics.
They were certainly, in astronomy at least , transitional figures, between the mysticism of the ancients,
and the science of Galileo and his successors.
Tycho was born in 1546 in Sweden.
He came from an aristocratic family.
His father Otto was a privy counsellor to the king, and later became Governor of Helsingborg Castle.
Otto had a brother Joergen, an admiral in the Danish Navy.
He was married but childless.
The brothers agreed that if Otto had a son, he would handover the infant to Joergen,
to raise as his own son.
When Tycho was born Joergen reminded Otto of his promise.
But he received a frosty response, maybe because the twin brother of Tycho was stillborn.
The parents could have feared that Otto’s wife, might not be able to have more children.
Joergen waited till Otto had another son, and then kidnapped Tycho, and took him to his home.
Eventually Otto and his wife had five healthy sons, and five healthy daughters.
Tycho was raised by his paternal uncle.
He received a thorough grounding in Latin.
He went to the university of Copenhagen in 1559, when he was not yet 13 years old.
Joergen planned for Tycho to follow a career of service to the king.
A intervening event changed the course of his career.
In August 1560, there was an eclipse of the sun.
It was a total eclipse in Portugal, but only a partial eclipse in Copenhagen.
This caught the imagination of the 13 year old Tycho.
More than the eclipse, what fascinated him was, that the event had been predicted long before,
even in ancient times.
Tycho spent most of the rest of his time in Copenhagen studying astronomy and mathematics.
He bought a latin edition of the works of Ptolemy, and made many notes in it.
In 1562, Tycho left Denmark and went to the university of Leipzig.
He was accompanied by a young man Vedel, who was appointed by Joergen as his tutor.
Vedel was also supposed to keep Tycho out of mischief.
Tycho studied law in Leipzig.
His spent all his spare money on astronomical instruments and books.
He stayed up late to make his astronomical observations.
His knowledge of astronomy increased more than his knowledge of law.
Tycho realised the accuracy of the ancient astronomers was less impressive than what he thought.
In August 1563, there was a conjunction of Saturn and Jupiter.
This had great significance for astrologers.
This event happened on 24th August 1563.
But the ancient predictions were off by several days to a month.
From the beginning Tycho believed that a proper understanding of the movement of planets,
would be impossible without a long series of painstaking observations.
His predecessors did not believe in this, maybe because they had too great a respect for the ancients.
Tycho made observations of the motion of planets relative to fixed stars.
At the age of 16, Tycho’s mission in life was clear to him.
He did a prolonged series of observations, to get a more accurate picture of planetary motions.
This was in the days before the development of the astronomical telescope.
The instruments used required great skills to construct, and even greater skill to use.
This in contrast to modern telescopes, where it is the other way about.
One of the simplest techniques used by Tycho was to hold a pair of compasses, close to his eye,
with a point of one leg of the pair on a star, and another point on a planet.
By marking the distances of the compass on paper,
he could estimate the angular separation of the planet and the star.
This was a good beginning, but he wanted greater accuracy.
Tycho had a cross staff constructed, which was similar to those used in navigation.
It was possible to read off angular separation from a scale on this instrument.
Tycho’s instrument was not properly calibrated.
He had no money to have it recalibrated.
His tutor Vedel was still controlling his budget.
So Tycho worked out a correction table for his instrument.
During this time war broke out between Sweden and Denmark.
Tycho and Vedel left Leipzig and returned home.
Soon after he went back to Copenhagen.
A little later Joergen passed away.
Most of his family frowned on Tycho’s interest in astronomy.
They wanted him to pursue a career, suited to his high status in society.
But Tycho had a inheritance from Joergen, and he could not be held back,
from his interest in astronomy.
Tycho continued his studies, which included astrology, chemistry and medicine.
There was so little known about this subjects, that there was no point in trying to be a specialist.
In those days it was believed that astrological events were related to what happened to humans,
and the human body.
Tycho became adept at casting horoscopes.
In 1566 there was a eclipse of the moon.
Tycho based on his horoscope, predicted the death of the Ottoman Sultan,
Sulaiman the magnificent.
The Ottoman empire was at a peak under Sulaiman.
He was proving a threat to eastern parts of Christian Europe.
Sulaiman was any way 80 years old.
When news reached that Sulaiman had died, Tycho’s prestige soared.
It didn’t seem to matter that the eclipse happened a few weeks before he died.
A Danish aristocrat is believed to have mocked Tycho’s prediction,
of the death of the sultan, who was already dead.
This lead to a quarrel, which could only be settled by a duel.
In the duel, Tycho received a blow, which cut away part of his nose.
He tried to conceal his disfigurement for the rest of his life.
This reveals something about the 20 year old Tycho’s character.
He was a firebrand, arrogantly aware of his own abilities,
and not willing to follow the path of caution.
This caused much grief to Tycho, later in life.
In 1568, Tycho received an offer from king Frederick II, to become a canon of a cathedral.
There were no religious duties attached to the post.
It was a way to support men of learning.
The post was entirely the gift of the king to Tycho, a potential, ‘man of learning’.
After his studies, Tycho settled in Augsburg in 1569.
He began a series of observations there.
He had a huge version of the instrument called a quadrant made for him.
It had a radius of 6 meters.
The circular rim could be calibrated in minutes of arc, for accurate observations.
In 1570 Tycho returned to Denmark, when his father was seriously ill.
He continued to make observations even then.
Tycho’s father Otto died in 1571, when he was 58 years old.
Tycho went to live with his mother’s brother called Steen.
Steen was the only member of the family who encouraged Tycho’s interest in Astronomy.
Steen introduced paper making and glass manufacture, on a large scale to Denmark.
Till 1572 Tycho devoted himself to chemical experiments.
He did continue his interest in astronomy.
In November 1572, Tycho was returning home from his laboratory.
He was observing the panorama of stars along the way.
He realised that there was something odd about the constellation Cassiopeia.
There was a new star in the constellation, and it was particularly bright.
At that time stars were regarded as fixed, external and unchanging lights,
attached to a crystal sphere.
It was part of the concept of the perfection of the heavens.
A new star would shatter this age old belief of the perfect heaven.
What looked like a star could have been a comet.
At that time comets were thought to be atmospheric phenomena,
occurring only a little way above the surface of the Earth.
It was believed that comets were much closer than the moon.
The moon itself was believed to be at the end of the Earth’s atmosphere.
The way to tell the difference would be to measure the relative position of the new object,
relative to nearby stars in the constellation.
If it changed position it could be a comet or a meteor.
Tycho had just completed the construction of another very large sextant.
He concentrated on observing this new star.
It stayed visible for 18 months.
During this time, it never moved relative to other stars.
It was indeed a new star.
It was as bright as Venus and could be seen in daylight.
It gradually started to fade in December 1572.
Many other people saw this star, and there were many fanciful stories about it.
Tycho had written his own account of the phenomenon.
He was reluctant to publish it for a combination of reasons.
He was concerned how others will react to the shattering of heavenly perfection.
The star was still visible, so the observation is not complete.
People might regard it as unseemly for a nobleman to be involved in such studies.
His friends however persuaded him to publish it.
The result was a book called ‘De Nova stella’ , or ‘The new star’, published in 1873.
It gave us the new astronomical word, ’Nova’.
Tycho showed that the object was not a comet or a meteor.
It must be a star in the crystal sphere.
He compared this to an object seen in the heavens by Hipparchus in 125 BC.
He also saw astrological significance in the new star, because Europe was in turmoil at that time,
with many bloody battles going on.
Tycho made an intensive study to see if there was any trace of parallax shift,
which would have been there, if the Earth really did move around the Sun.
He could find no evidence of parallax.
This convinced him that the Earth is fixed, with the stars rotating about it, in the crystal sphere.
In 1573 Tycho settled down with a girl called Christine.
She was a commoner.
Maybe because of this they didn’t formally get married.
In 16th century Denmark, marriage was an optional extra.
The couple produced 4 surviving daughters and 2 sons.
Tycho was not happy in Denmark, and wanted to move abroad,
where he could get better support for his work.
He wanted to settle in Basle.
King Frederick was keen to keep him in Denmark.
He offered him a royal castle, which Tycho turned down.
The king then offered him an Island called Hveen.
He offered to build a house for him, and give him an income.
This was an offer Tycho could not refuse.
In 1576, Tycho moved to the island Hveen and setup his observatory there.
The observatory was named Uraniborg, after Urania the muse of astronomy.
Over years it became a major scientific institution, with observing galleries, library, and studies.
The instruments were the best that money could provide.
Tycho also established a press to publish his astronomical data, and also his pretty good poetry.
His mysticism was reflected in the layout of the buildings,
which was intended to reflect the structure of the heavens.
Tycho spent 20 years, night after night,
measuring the position of planets relative to the fixed stars.
It takes 4 years to track the Sun’s movement through the constellations.
It takes 12 years for Mars and Jupiter.
It takes 30 years for Saturn.
His work came into fruition later,
when Kepler used Tycho’s tables to explain the orbit of planets,
many years after Tycho had died.
In 1577, Tycho observed a bright comet.
By careful analysis he concluded that it could not be a local phenomena, close to the Earth.
It was clear that they travel among the planets, even crossing their orbits.
This was a shattering blow to the old ideas about the heavens.
It destroyed the notion of crystal spheres, since the comet moved right through the places,
the spheres were supposed to be.
The comet studies and his earlier observations of the supernova,
encouraged Tycho to publish a book, in 2 volumes,
‘Introduction to the new astronomy’, in 1587 and 1588.
His model in the book was halfway between the Ptolemaic system and the Copernicus system.
Tycho’s idea was that the Earth is fixed at the centre of the universe,
and the Sun, moon, and fixed stars orbit around the Earth.
The Sun was seen as the centre of the orbits of 5 planets.
Mercury and Venus were moving in orbits, smaller than the orbit of the Sun around the Earth.
Mars, Jupiter and Saturn included both the Sun and the Earth in their orbits.
The system did away with epicycles.
The explanation seemed to be simpler, but obviously was wrong,
because it was basically an Earth centric model.
The significant improvement of the model, was that it did not associate itself with anything physical,
like a crystal sphere.
He was the first astronomer to imagine planets hanging unsupported in empty space.
Tycho was adamant in believing that it was absurd to think, that the Earth could be moving.
At this time, the most virulent opposition to the copernican model, came from the protestant church.
The catholic church more or less ignored it at this time.
Tycho also did not subscribe to copernican ideas.
King Frederick II died in 1588.
His son Christian was only 11 years old.
Four Danish nobles were elected, to act as his protector, till he was 20 years old.
There was no change in attitude towards Tycho.
He was still regarded as a great national institution.
Tycho had many distinguished visitors.
Tycho managed to offend several members of the nobility, whom he did not like.
He flouted protocol by allowing a low born wife, a place of honour in the dining table.
He had many quarrels with many people.
His observations continued as before.
He cataloged the positions of thousand fixed stars in 1595.
In 1596, Christian was crowned as King Christian 4.
He wanted to make economies in every area of state activity.
He withdrew the mainland estates granted to Tycho, by Frederick II.
He thought that Uraniborg could be run with a smaller budget.
Tycho took this as an insult, and threat to his work.
In 1597, the king cut off Tycho’s annual pension.
Tycho made plans to move out of the Island.
He was arrogant with the king, the king was quiet glad to let him go.
Tycho moved to Wandsbeck near Hamburg.
He resumed his observations here.
He then received an invitation from the holy Roman empire Rudolph II.
Rudolph II was more interested in science and arts than politics.
This was good for Tycho, but bad for middle Europe.
His poor political skills, resulted in the 30 year war.
Tycho arrived in Prague, the capital of the empire, in 1599.
He was appointed as the imperial mathematician.
He was granted a good income, and a castle to make his observations.
He sent his son, to Denmark to fetch 4 large observing instruments, from Hveen.
Tycho in his 50’s did not make significant observations here, before his death.
He however ensured that, his life’s work would be put to the best possible use,
by the ablest member of the next generation of astronomers, namely Kepler.
Kepler had none of the advantages of birth, which gave Tycho a head start in life.
Kepler’s grandfather was a furrier.
He was a hard worker and rose to the position of mayor.
His eldest son Heinrich Kepler was a wastrel.
His only employment was as, a mercenary solider.
He married a young woman called Katherine.
The marriage was not a success.
Apart from the faults of Heinrich, Katherine was argumentative and difficult to live with.
She had a great faith in the healing powers of folk remedies.
This would contribute to her eventual imprisonment as a suspected witch.
Her son Johannes Kepler, had a disturbed childhood.
He was born in 1571, in Germany.
His father unsuccessfully tried his hand at various businesses and failed.
He lost all his money.
He eventually set off to try his luck as a mercenary.
This time he disappeared altogether.
Kepler was tossed about from household to household, and school to school.
At a young age he caught smallpox, which left him with a bad eyesight for the rest of his life.
His brain was however not affected.
At the age of 7, he entered a Latin school.
These schools were primarily meant to prepare men for service in the church, or the state administration.
Only Latin was spoken in the schools, as it was the language of educated men at that time.
When he graduated, he was entitled to take an examination to enter a seminary, to train for priesthood.
This was the obvious and traditional route out of poverty.
Kepler got interested in astronomy after he saw the same comet seen by Tycho in 1577.
He also saw another comet and an eclipse of the moon.
In 1584 he passed the examination for a seminary.
He was admitted to the school at the age of 12.
The Language of the school was Latin, in which Kepler became fluent.
The discipline in the school was harsh, and Kepler was a sickly youth, who often took ill.
He showed such promise academically, that he was moved to more advanced school.
His tutors prepared him for entry into the university of Tubingen,
to complete his theological studies.
He entered the university at the age of 17.
Although training to be a priest, he was required to take, in the first 2 years, courses in mathematics,
physics and astronomy.
Kepler was a outstanding student in these subjects.
He graduated in 1591, standing 2nd in a class of 14.
He then moved on to his theological studies.
Kepler learnt something, that was not in his curriculum.
The professor of mathematics, Michael taught his students in public the Ptolomaic system,
because it was approved by the church.
In private Michael explained the Copernician system to promising students,
including Kepler.
This made a deep impression on young Kepler.
He saw the power in simplicity of the Sun centric model of the universe.
In this way he deviated from the strict Lutheran teaching of his time.
Though he believed in the existence of God, but the rituals of the church did not make sense to him.
This was a distinctly dangerous attitude at that time.
In 1594, when he was about to complete his theological studies,
something happened that changed his life.
There was a seminary in Graz, which had close academic connections with the university of Tubingen.
The mathematic professor in the Graz seminary died.
The Tubingen authorities recommended Kepler for the post,
just as he was about to start life as a clergyman.
This surprised Kepler, but he eventually agreed to take up the post.
The 22 year old Kepler, became a professor in 1594, in Austria.
By moving to Graz, Kepler had crossed an invisible border.
In the northern states, the reformed churches were dominant.
In the southern region, the catholic church was dominant.
This invisible border was constantly changing.
The peace of Augsburg treaty was signed in 1555.
According to this each prince or duke or head, was free to decide the appropriate religion in his domain.
There were dozens of princes ruling individual statelets within the holy empire.
When a prince died or changed, the religion could change.
Some princes allowed freedom of worship, while other did not.
Graz was the capital of a statelet called Styria.
It was ruled by Archduke Charles, who was determined to crack down on the protestant movement.
Kepler was a poor man, with no financial resources from his family.
His university studies was paid by a scholarship.
He had to borrow money to travel to Graz.
The Graz seminary decided to put him on 3 quarter salary, until he proved his worth.
There was only one way to improve his finances.
That was by casting horoscopes.
He used this for most of his life to supplement his inadequate income.
He knew that astrology was utter tosh, but he became skilful in the art of talking in vague generalities,
and telling people what they wanted to hear.
In private to his friends, he called his clients ‘fatheads’.
His skill in dressing up common sense predictions up in astrological mumbo jumbo,
established his reputation in Graz.
His salary was also increased.
Though Kepler was less superstitious, he was mystically inclined in many ways.
Kepler was never able to be a effective observer of the heavens, because of his bad eyesight.
He followed the mental footsteps of the ancients, by using reason and imagination,
to come up with an explanation of the nature of the cosmos.
He puzzled over the fact of the Copernican model, that there were only six planets in the universe.
He came up with the model which involved geometrical shapes.
He used a sphere, cube, octahedron, icosahedron, dodecahedron, and tetrahedron,
in a complicated arrangement to explain the orbits of the planets around the Sun.
His model was based on the mystical belief that the heavens must be governed by geometry.
His model fell apart when Kepler himself showed that the orbit of planets is elliptical.
When Kepler came up with the model in 1595, it seemed to him like a divine revelation.
Kepler’s sun centric model, was against the Lutheran beliefs.
It is ironic that Kepler himself was somewhat of a Lutheran.
Kepler published his model in 1597, in a book called ‘The mystery of the universe’.
There was an interesting new idea in his model.
Copernicus had observed that the planets which were further from the sun, moved slower.
Kepler suggested that they were kept moving in their orbits by a force called ‘vigour’.
He explained that the vigour force would be less vigorous, further from the sun.
This would push the distant planets more slowly.
The idea was partly stimulated by the work of Gilbert on magnetism.
This was an important step forward.
Earlier it was believed that planets were pushed around by angels.
Kepler stated that his aim was to show that the machinery of the universe,
is not a divine animated being, but similar to a clock.
Kepler sent copies of his book to eminent thinkers of the time.
This included Galileo and Tycho.
Tycho was impressed with Kepler’s mathematical skill, and replied to Kepler with a detailed critique,
though he did not believe in a sun centric model.
Tycho was impressed enough to suggest that Kepler join as one of his assistants.
In 1597 Kepler married Barbara, a young widow, and daughter of a wealthy merchant.
Barbara’s family felt that she had married beneath her status, and withheld money she was entitled to.
Barbara found it tough to live on Kepler’s salary.
Kepler was eager to consolidate his new reputation, by associating with other mathematicians.
He wrote a letter to the imperial mathematician Ursus, seeking his opinion about his work.
He also sycophantically praised Ursus as the greatest mathematician of all time.
Ursus did not bother to reply, but took Kepler’s praise as an endorsement of his own work.
His work was critical of Tycho.
This offended Tycho’s feelings.
It took a lot of tactful correspondence from Kepler to soothe Tycho’s feelings.
Kepler was keen to get his hands on Tycho’s wealth of observational data.
He wanted to test his model with Tycho’s data.
In 1596, Ferdinand, a devout catholic became the ruler of Styria.
He ordered all teachers a theologians to convert to catholicism, or leave the state.
Kepler had to move to neighbouring state.
For some reason, maybe because of his stature as a mathematician,
Kepler alone was allowed to return.
In 1599, the situation in Graz became intolerable for Kepler.
Tycho was near Prague, where people were free to worship in their own manner.
In 1600, a Styrian nobleman, who was the counsellor of the emperor Rudolph II,
took Kepler along to meet Tycho.
Tycho was 53 years old and Kepler was 28.
Tycho had a huge collection of accurate astronomical data.
He needed help to analyse it.
Kepler was desperate for an income, and he was also very keen to get his hands on Tycho’s data.
Kepler took on the role of an assistant with Tycho, though he did not resign his post at Graz.
In 1600, Kepler returned to Graz.
At this time all citizens of Graz were required to convert to Catholicism.
He was one of the 61 prominent citizens who refused to do so.
He was dismissed from his post, and asked to leave the state.
He had to forfeit what little property he had.
Kepler wrote to Tycho asking for help.
Tycho replied positively, that he was negotiating with the emperor for a post for Kepler.
He asked Kepler to move, to Prague.
Kepler along with his family went to the stinking, unhealthy city of Prague.
He and Barbara became severally ill with fever.
His limited supply of money rapidly diminished.
There was still no appointment from the emperor.
In 1601, Kepler moved in with Tycho, in his new residence.
Eventually, the emperor appointed him as Tycho’s official and paid assistant.
He was to compile a new set of tables of planetary positions,
called in the emperor’s honour, as Rudolphine tables.
Tycho parted with his observational data to Kepler in small packages.
He did not give him free access.
The relationship of Kepler and Tycho was not very friendly.
Tycho became severely ill and close to death.
On his death bed, Tycho handed over the task of completing the Rudlophine tables to Kepler.
He bequeathed his life’s work to the stunned Kepler.
He however urged Kepler to demonstrate the truth of Tychonic model, and not the Copernician model.
A little later Kepler was appointed as Tycho’s successor, as an imperial mathematician for Rudolph II.
He was made responsible for all of Tycho’s instruments and published work.
Kepler faced many challenges in his work.
Tycho’s heirs feared that he may promote Copernician ideas.
As a imperial mathematician, which in reality meant imperial astrologer,
he had to keep advising Rudolph on the significance of heavenly portents.
Kepler’s astronomical work, involved laborious arithmetic calculations of planetary orbits.
It is difficult to imagine how he did this, without calculators or computers.
It took many years to solve the riddle of the orbit of mars.
Kepler made a highly significant, step of carrying out some of his calculations,
from the perspective of an observer on mars, looking at Earth’s orbit.
This was a huge conceptual leap, which presages the idea that all motion is relative.
In 1602, while he was working with his eccentric circular orbit,
Kepler came up with what is now known as his second law.
An imaginary line joining the Sun to a planet moving in its orbit around the Sun,
sweeps out equal areas in equal times.
This is a precise way of expressing how much faster the planet moves, when closer to the Sun.
A shorter radius line has to sweep across a bigger angle to cover the same area.
It was after this discovery, that Kepler realised that the shape of the orbit is actually elliptical.
In 1605, he came up with, what is now known as the first law.
Each planet moves in its own elliptical orbit around the Sun.
The Sun is at one of the two foci of the ellipse.
This model did away with all the old models, with the epicycles, equants,
including Kepler’s mystical idea of nested solids.
His new ideas was published in 1609 in the book Astronomia Nova.
Kepler did not receive instant acclaim.
Many people had not accepted that the Earth was not at the centre of the universe.
Only skilled mathematicians could appreciate Kepler’s model.
Kepler achieved the status he deserves, only after Newton used Kepler’s laws,
in his theory of gravity.
In his own time Kepler was more famous as an astrologer, rather than an astronomer.
In 1604, a new star as bright as Jupiter appeared.
It was visible till 1606.
Kepler had to interpret its significance of this astrological event, as the imperial mathematician.
However Kepler knew that it was a supernova, like Tycho had seen.
In 1604, Kepler published a book on optics.
He explained how the eye works, by refracting light rays that enter the pupil to focus them on the retina.
All the rays coming from single point, are focused at a single point on the retina.
He also explained that some people have bad eye sight, because the imperfect eye,
causes the rays to be focused in front of or behind the retina.
We recollect that Kepler himself had bad eyesight.
Though eyeglasses had been in use for more than 300 years, nobody understood how it worked.
Kepler was able to explain how eyeglasses worked.
After Galileo used the telescope for astronomy,
Kepler developed his ideas to explain how the telescope works.
Some years after the supernova was sighted, there was political and religious strife in Europe,
resulting in a 30 year war.
In 1608, several protestant states joined together as the protestant union,
while their rivals form the catholic league.
Rudolph was by now a semi-recluse.
He was obsessed by his art collection, and was almost mad.
He ran out of money, and power passed on to his brother Matthias, who became emperor in 1612.
Kepler had domestic troubles.
His wife Barbara, became ill with epilepsy.
One of his three children died of smallpox.
His wife died of typhus.
To his surprise, the new emperor Matthias appointed him as imperial mathematician.
Kepler was also allowed to work in Linz as a district mathematician.
He soon remarried a young woman of 24, who bore him six children.
Three of them died in infancy.
Kepler studied the eclipse of the moon in Herod’s time, to show that Jesus was actually born in 5BC.
He was also involved in calendar reform.
In 1582, pope Gregory XIII introduced the modern calendar,
but many protestants states were reluctant to adapt it.
There was another major setback in Kepler’s life after 1615, when his mother was accused of witch craft.
In 1620 she was arrested and imprisoned.
In 1621, she was released, and she died 6 months later.
Inspite of all his troubles Kepler published a book called ‘Harmony of the world’
The idea of Kepler’s third law started with this book.
The law relates to the time it takes for a planet to go around the Sun, to its distance from the Sun.
The time that a planet goes around the sun is a planet year or period.
It quantifies this in a precise way, the general pattern that Copernicus discovered.
It says that the squares of the periods of any two planets, are proportional to the cube of the distance,
from the Sun.
For example, Mars is 1.52 times as far from the Sun as Earth.
1.52 cubed is 3.51.
The length of the year on Mars is 1.88 times the length of the year on Earth.
1.88 squared is about 3.53.
The difference is due to rounding off.
Kepler published another book in three volumes called ’The epitome of Copernican astronomy’,
between 1618 and 1621.
This book was more widely read.
Logarithm was invented by Napier around this time.
It eased the burden of arithmetic calculations.
Kepler used it to publish the Rudolphine tables in 1627.
The tables made it possible to calculate the position of planets,
30 times more accurately than the tables of Copernicus.
In 1631, French astronomer Gassendi observed the transit of Mercury,
which was predicted by Kepler’s tables.
The transit of Mercury happens when it passes in front of the Sun.
This was the first transit of Mercury that was ever observed.
In 1619, Ferdinand II became the holy Roman Emperor, after Matthias died.
He was a fervent catholic, and there was pressure on Kepler to convert.
In 1628 Kepler secured a position, with a duke who was very tolerant,
and who never made a move without consulting his astrologers.
The best thing about this job was that he was paid regularly.
Kepler found time to write a science fiction story ’The dream of the Moon’.
In 1630, Kepler died, just short of his 59th birthday.
He lived in a time when kings depended on the prediction of astrologers.
Kepler was poised between the mysticism of the past, and the logical science of the future.