Love: Johannes Kepler
T
he year was 1571. Copernicus had been
dead for 28 years and his great idea of a
heliocentric universe had received virtually no public support. Tycho Brahe was a young
man of 25. Galileo and Shakespeare were both
7 years old. And Johannes Kepler was born, on
27 December (at 2.30 in the afternoon, according to a horoscope that he later cast for himself), the first child of Heinrich and Katharina
Kepler. Kepler was born in Weil der Stadt in
Germany. The main square now has a monument to its most famous son (figure 3), and the
Kepler Museum on the corner stands on the
site of the Kepler household. Much of what is
known about his early life comes from his own
writings (Caspar 1993).
Johannes Kepler had an unhappy childhood.
He described his father as “an immoral, rough
and quarrelsome soldier”, and his mother as
“small, thin, dark-complexioned, garrulous,
quarrelsome and generally unpleasant”. He
himself was not a particularly healthy child; he
nearly died of smallpox, aged three. His father,
the mercenary, left to fight in yet another war
when Kepler was in his mid-teens, and was
never seen by the family again.
Kepler did recollect, however, a few happy
moments in his early life. In 1577, when he
was five, his mother took him out one night
to see the bright comet of that year. This was
the same comet that was being observed in faraway Denmark by Tycho Brahe, who concluded
that – contrary to Aristotelian doctrine – it lay
beyond the sphere of the Moon. He also notes
that, in 1580, his father called him outdoors to
look at an eclipse of the Moon.
Kepler was a bright child who did very well at
school. In 1589 he had no difficulty in getting
into the Protestant stronghold of Tubingen University, where he intended to train to become a
Lutheran clergyman. It was here he met Michael
Maestlin, professor of mathematics and astronomy, and one of the few people who recognized
that the Copernican system was correct.
The initial tone of the Protestant reaction to
Copernicus was epitomized by his contemporary Martin Luther who declared: “This fool
[Copernicus] wishes to reverse the entire science of astronomy; but sacred scripture tells us
that Joshua commanded the Sun to stand still,
and not the Earth.” Other Protestant leaders
expressed similar views. Maestlin, as a member of a staunchly Protestant university, was
required to teach the Ptolemaic system to his
pupils. But in addition, perhaps only privately,
he also taught them about the Copernican
system, and the simplifications and greater
explanatory power which – in principle – it had
in comparison with Ptolemy.
Going to Graz
Thanks to Maestlin, Kepler became an early
and very public convert to Copernican ideas,
A&G • December 2009 • Vol. 50 1: Portrait of Kepler aged 38, artist unknown.
Who was
Johannes
Kepler?
David Love gives an introduction
to the life and achievements of
Johannes Kepler, who published
his first two laws of planetary
motion 400 years ago, in 1609.
although he still intended to become a Lutheran
clergyman. But the whole direction of his life
changed suddenly, by chance, in 1594. A maths
teacher at an obscure Lutheran school in Graz
died, and the school authorities turned to Tubingen University for advice on a successor.
Kepler was the obvious choice. Not only was
he a brilliant student, but he had also shown
some regrettably unorthodox tendencies, in
both his Copernicanism and his approach to
Calvinism. These hardly suited him to the job
of a Lutheran minister of religion. Kepler was
initially unwilling to move, but eventually saw
the benefit of the position.
So Kepler travelled to Graz, where he took
up the posts both of maths teacher and district
mathematician. Three astronomical problems
particularly fascinated him at that time: why
were there only six planets; why were they at the
distances that they were from the Sun; and why
did they travel more slowly the further they were
from the Sun? He could not possibly have known
that the first and second questions were fruitless,
but that the third would – 25 years later – lead
him to his third law of planetary motion.
But it was the first two questions that initially
fired his imagination and led him on a totally
false path, although it did in the end lead to
his first two laws of planetary motion. During
one of his classes he realized that an equilateral
triangle could be placed – more or less exactly
– between the orbits of Jupiter and Saturn, as a
result of the fact that the radius of the orbit of
Jupiter is half the radius of the orbit of Saturn
(give or take a few percent, or perhaps it would
fit exactly if only he had more accurate figures
than those used by Copernicus?). This was the
moment of Kepler’s revelation. It was clear to
him that God had created orbits of this size so
that a geometrical figure could be fitted exactly
between them. The triangle was not, of course,
literally there, but it was present in the mind of
God, Kepler reasoned.
He tried to find other two-dimensional shapes
to fit between the other planetary orbits, without success. However, by judicious choosing,
he found he could achieve his purpose with
three-dimensional shapes (the tetrahedron, the
cube, the octahedron, the dodecahedron, and
the icosahedron). Euclid had proved that there
were five and only five perfect solids, so Kepler
reasoned that there were six planets, only, precisely because there were five perfect solids to fit
between the five pairs of orbits of the six planets.
Again, the match was not exact, but Kepler put
this down to the quality of his data. He knew
that better data was held by Tycho Brahe, the
great observational astronomer.
Into print
The eager young Kepler rushed to publish a
book setting out his discovery. Mysterium Cosmographicum was published in 1597, when he
was 25. It was a beautiful theory, and totally
incorrect. Kepler circulated the book widely
and gained a reputation as a bright theoretical
astronomer. It is also noteworthy that, 54 years
after the publication of De Revolutionibus, this
was almost the first book to come out publicly
in favour of the Copernican universe, albeit
Kepler’s own version of this cosmology.
Kepler’s life was plagued by both religious
intolerance and family tragedy. In 1597 he married Barbara Muller who, although only 23, had
already been married and widowed twice. She
brought a daughter, Regina, to the marriage.
Religious intolerance first showed itself in the
decree of September 1598 that all Protestant
preachers and teachers were to leave Graz, ruled
by the devoutly Catholic Archduke Ferdinand,
who had declared: “I would rather rule a country ruined than a country damned.” Kepler
was among the many thrown out, but he was
alone in being allowed back only a month later,
6.15
Love: Johannes Kepler
perhaps because of his official role as district
mathematician, perhaps because he had friends
in high places. However, he knew that he would
not be able to stay in Graz for much longer.
Kepler tried and failed to get a job at his old
university in Tubingen; his tendency towards
unorthodox views meant that he was not
acceptable there. At this time he also received
a letter from Tycho Brahe thanking him for
a copy of his book, and expressing the hope
that he would soon apply the ideas in it to the
Tychonic system, and that Kepler would one
day call in on him. The Tychonic system was
a compromise between those of Ptolemy and
Copernicus, in which the Earth retained its central position in the universe, with the Sun and
the Moon in orbit about it, but the five planets
orbited the Sun. Kepler demolished it very effectively in his later writings.
To Prague and Tycho Brahe
In January 1600, at the age of 28, Kepler set
off for Prague to see if Brahe would offer him
employment. The two met in February. It was
a meeting of opposites who needed each other.
Brahe was a rich nobleman, whereas Kepler had
come from a much humbler background. Brahe
was primarily an observer, Kepler a theoretician. Brahe wanted Kepler to demonstrate the
truth of his Tychonic view of the universe, and
Kepler wanted Brahe’s observations to verify his
own version of the Copernican theory.
Things did not start off at all well. Kepler
was unhappy with his conditions of service. In
April, he had a blazing row with Brahe, and
walked out. He soon realized what a mistake
he had made, begged Tycho’s forgiveness, and
was received back into the fold. In June he
returned to Graz to collect his wife and possessions, and to settle his affairs there – just in
time. In August all Protestants in the city – not
just preachers and teachers – were required to
convert to Catholicism or get out. Kepler got out
and returned to Prague to work for Brahe. Just
over one year later, in October 1601, Brahe died,
and Kepler was appointed Imperial Mathematician to the eccentric Rudolph II in his place.
Good years
At this point in the story we can say goodbye to
Kepler the mystical speculator, and instead concentrate on Kepler the scientific genius – although
it has to be said that Kepler’s mystical side never
left him. The years from the time he started
working for Brahe to the publication of his first
two laws, in 1609, were highly productive. He
showed his genius in his fundamental approach
to the problem of working out planetary orbits.
Before Kepler, everybody – including Copernicus – had looked at the problem of planetary
orbits as purely a problem in geometry. If you
could find a geometrical model that replicated
the movements of the planets, then you had done
6.16
your job. There was no need to look for physical
causes. Kepler felt that this approach was wrong.
He suggested that there was some sort of force
coming out of the Sun that dragged the planets
round. The force faded with distance, which was
why the outer planets moved more slowly than
the inner planets. And the force was magnetic,
or something like it in its effects. Kepler was the
person who single-handedly moved astronomy
from geometry to physics.
His idea had an immediate practical consequence. He decided that he should measure all
planetary positions, angles and distances from
the Sun, rather than from the centre of planetary
orbits. He also had the good fortune to be given
the orbit of Mars to study. Mars, of course, has
the highest eccentricity of all the planets except
for Mercury, which is hard to observe. If you
can crack the orbit of Mars, you can crack the
orbit of any of the other planets.
His initial approach was conventional. He
assumed a circular orbit, with the Sun and the
equant – the point from which the planet would
be seen to move at a constant angular rate – offset from the centre. The idea of the equant came
from Ptolemy, who introduced it as an ingenious
fudge to help align theory and observation.
Brahe had a huge collection of Mars observations, including 10 observations at opposition,
to which Kepler later added two more of his
own. His task was to find an orbit that fitted
the opposition observations. This was a lengthy
“Kepler was the person
who single-handedly
moved astronomy from
geometry to physics.”
and tedious trial and error exercise, involving
a series of ever closer approximations. Eventually he succeeded in finding a circular orbit for
Mars that fitted all the opposition observations,
to within 2 arcminutes, the level of accuracy of
Tycho’s pre-telescopic observations. Anybody
else might have stopped there, but not Kepler.
He checked his orbit further, against more of
Tycho’s observations, and found that it did not
fit. At worst, it was out by a full 8 arcminutes
– an error that simply could not be neglected.
He realized that he would have to throw out the
assumptions of his predecessors, and start all
over again. As he himself later put it: “These 8
minutes showed the way to a renovation of the
whole of astronomy.”
He recognized that he was going to have to
throw out in particular the assumption of circular motion that had been at the core of astronomical thinking for the past 2000 years. But
first, and more fundamentally, he was going to
have to check the Earth’s orbit; if the Earth did
not move at a uniform rate round the Sun, then
observations made from Earth based on this
assumption would be wrong.
But how do you find out whether the Earth
moves at a uniform rate? Kepler’s solution
was, as Einstein put it, “an idea of true genius”
(Baumgardt 1951). He measured the Earth’s
orbit as it would be seen by an observer on
Mars. He noted the position of Mars relative to
Earth (and therefore the position of Earth relative to Mars) every 687 days – the orbital period
of Mars. A succession of Tycho’s observations at
687-day intervals, when Mars was at the same
place, enabled Kepler to plot the true position of
Earth at various times in its orbit. He concluded
that the Earth does not revolve round the Sun
at a uniform rate, and that the Sun is not at the
centre of the Earth’s orbit. This led him to the
fact that the Earth and the other planets sweep
out equal areas in equal times, his second law,
which he discovered before his first law.
Having established this, he moved back to the
shape of the orbit of Mars. As he explained:
“The conclusion is quite simply that the planet’s
path is not a circle – it curves inwards on both
sides and outward again at opposite ends … The
orbit is not a circle, but an oval.” He battled
with the shape until the spring of 1605, when
he finally realized that the oval was in fact an
ellipse – his first law. The other part of his first
law – that the Sun was at one focus of this ellipse
– was only explicitly stated in his Epitome, published some 10 years later.
Both laws had to wait four more years for publication. There were two reasons for the delay.
First, the Emperor Rudolph II had no funds
available and, secondly, Brahe’s heirs were creating difficulties. Eventually, in 1609, the laws
appeared in Kepler’s book Astronomia Nova.
In the spring of 1610, news reached him that
Galileo had discovered four new planets. Kepler
immediately realized that these could not be
planets in their own right, but must be satellites
of a known planet, for he had proved in Mysterium Cosmographicum that there could only be
six planets. And sure enough, it soon emerged
that the new planets were satellites of Jupiter.
Bad years
The year 1611 was a disastrous one for the 39year old Kepler. Rudolph II, his patron, was
far from secure on his throne. And early in the
year, Kepler’s favourite child, Friedrich, died of
smallpox at the age of six. Kepler decided that it
was time to leave Prague, partly for the sake of
his homesick wife, and accepted a job as maths
teacher in Linz, in Austria. Later that year, his
wife also died.
Once settled in Linz, Kepler married for the
second time. His new wife was Susanna Reuttinger, some 17 years his junior. The marriage
seems to have been happier, except for the deaths
of more of his children. Kepler had twelve children, but eight of them died in infancy or early
A&G • December 2009 • Vol. 50
Love: Johannes Kepler
Table 1: Calculations using Kepler’s values for
the orbits of the Galilean moons of Jupiter
Kepler’s values
Kepler’s legacy
modern values
(using Europa distance = 5)
distance
time
D3/T2
distance
time
D3/T2
Io
3
1 d 18.5 hr
8.6
3.14
1.77 d
9.9
Europa
5
3 d 13.3 hr
9.9
5
3.55 d
9.9
Ganymede
8
7 d 2 hr
10.2
7.97
7.15 d
9.9
Callisto
14
16 d 18 hr
9.8
14.03
16.7 d
9.9
Barbara
Muller
=
Apr. 1597
Johannes
Kepler
2: Kepler’s
family tree,
showing
childhood
deaths.
Susanna
=
Reutinger
Oct. 1613
Regina
b. 1590
d. 1617
Heinrich
b. 1598
d. 1598
Susanna
b. 1599
d. 1599
Susanna
b. 1602
Friedrich
b. 1604
d. 1611
Ludwig
b. 1607
Margarethe
b. 1615
d. 1617
Katharina
b. 1617
d. 1618
Sebald
b. 1619
d. 1623
Cordula
b. 1621
Friedmar
b. 1623
d. ~1635
childhood (figure 2). A further family problem came in 1615, when Kepler’s mother was
accused of witchcraft. It was six years before the
charge was finally dropped, but defending her
took a significant slice of Kepler’s time.
The year 1619 saw the publication of Harmonice Mundi, which contained Kepler’s third law
of planetary motion: that for any two planets,
the ratio of the cube of the mean distance from
the Sun to the square of the period is the same.
It is not generally realized that, in his Epitome
of Copernican [i.e. Keplerian] Astronomy, published in instalments in the years 1618–1621,
Kepler extended this law to include the four
newly discovered satellites of Jupiter. The constant of proportionality was of course different,
and the distances and periods that Kepler quotes
were (unsurprisingly) not totally accurate, but
table 1 shows that his third law held up well,
given the inevitable inaccuracies in his figures.
A fitting conclusion
Arguably, the culmination of all Kepler’s work
was the publication in 1627 of the Rudolphine
Tables, dedicated to the late Rudolph II. Based
on his laws of planetary motion, these enabled
the prediction of planetary positions well into
the future. It was the fact that they were more
accurate than any other tables that led to the
gradual and no doubt reluctant acceptance of
A&G • December 2009 • Vol. 50 1634 Kepler’s Somnium, the story of
a journey to the Moon, is published
posthumously.
1638 Kepler’s second wife, Susanna, dies
in poverty at the age of 49.
1687 Newton publishes Principia, which
includes his gravitational inverse square
law, from which he derives Kepler’s
three laws.
2009 The Kepler mission is launched,
to search for Earth-like planets around
other stars.
Hildebert
b. 1625
d. 1635
Anna Maria
b. 1630
Kepler’s ellipses. This took some time – for
example, Galileo’s Dialogue on the Two Chief
World Systems, published in 1632, contains no
mention of elliptical orbits, even though he must
have been fully aware of Kepler’s discoveries.
The frontispiece to the tables was drawn up
according to Kepler’s instructions, and shows a
gathering of astronomers – a Babylonian, Hipparchus, Ptolemy, Copernicus and Tycho. On
the base, on the left, is a picture of Kepler, working away. Above hovers an eagle, the symbol of
the emperor, dropping coins, perhaps symbolizing the fact that poor Kepler was still owed
substantial sums of money for his efforts.
The forecast in the tables that there would be a
transit of Mercury across the face of the Sun in
1631 was duly observed by the French astronomer Pierre Gassendi. Sadly, Kepler himself did
not live to see or hear about this. One can only
hope that his last year of life brought some happiness – his oldest daughter, Susanna, was married in March 1630, and his youngest daughter,
Anna Maria, was born in April. Kepler himself
was passing through Regensburg when he fell ill,
and later died on 15 November 1630. In 1632 the
churchyard where he was buried was destroyed
during the 30 Years’ War. So we can visit the
tombs of Galileo and Newton, but not that of
Kepler. The inscription he had arranged to have
placed on his tombstone is, however, known:
3: Kepler’s statue in Weil der Stadt, Germany.
“I measured the skies, now the shadows I
measure.
Sky-bound was the mind, earth-bound the
body rests.” ●
David Love graduated in astronomy at University
College London; [email protected].
References
Baumgardt C 1951 Johannes Kepler: Life & Letters
(Philosophical Library).
Caspar M 1993 Kepler (Dover).
Further reading
● Max Caspar’s excellent and detailed biography
provided much of the biographical information,
but a shorter and more readable account is Arthur
Koestler’s The Watershed (part of The Sleepwalkers),
published by Heinemann in 1961.
● Information about science and the church in
Kepler’s time comes from Andrew D White’s A
History of the Warfare of Science with Theology, chapter
III (1993, Prometheus) and Owen Chadwick’s The
Penguin History of the Church, Vol. 3 – The Reformation
(1964, Penguin).
● A summary of Kepler’s arguments is given in
Selections from Kepler’s Astronomia Nova by William H
Donahue (2004, Green Lion Press), who is currently
preparing a new and revised translation of the
complete Astronomia Nova. Essential further reading
on this topic are Kepler’s Physical Astronomy by Bruce
Stephenson (1987, Princeton University Press) and
The Composition of Kepler’s Astronomia Nova by James
R Voelkel (2001, Princeton University Press).
6.17