Astronomy before Kepler had been a purely descriptive geometry of the
skies. The motion of stars and planets had been represented by the
device of epicycles and eccentrics -- an imaginary clockwork of circles
turning on circles turning on circles. Copernicus, for instance, had used
forty-eight wheels to represent the motion of the five known planets
around the sun. These wheels were purely fictitious, and meant as such
-- they enabled astronomers to make more or less precise predictions,
but, above all, they satisfied the dogma that all heavenly motion must
be uniform and in perfect circles. Though the planets moved neither
uniformly nor in perfect circles, the imaginary cog-wheels did, and
thereby 'saved the appearances'.
Kepler's discoveries put an end to this state of affairs. He reconciled
astronomy with physics, and substituted for the fictitious clockwork a
universe of material bodies not unlike the earth, freely floating and
turning in space, moved by forces acting on them. His most important
book bears the provocative title:
A New Astronomy Based on Causation
Or Physics of the Sky
(1609). It contains the first and second of
Kepler's three laws. The first says that the planets move around the sun
not in cirdes but in elliptic orbits; the second says that a planet moves
in its orbit not at uniform speed but at a speed that varies according
to its position, and is defined by a simple and beautiful law: the line
connecting planet and sun sweeps over equal areas in equal times. The
third law establishes an equally elegant mathematical correlation between
the length of a planet's year and its mean distance from the sun.
Kepler did not start his career as an astronomer, but as a student of
theology (at the Lutheran University of Thuebingen); yet already as
a student he was attracted by the Copernican idea of a sun-centred
universe. Now Canon Copernicus's book,
On the Revolutions of the
Heavenly Spheres
, had been published in the year of his death,
1543; that is, fifty years before Kepler first heard of him; and
during that half century it had attracted very little attention. One
of the reasons was its supreme unreadabillty, which made it into an
all-time worst-seller: its first edition of a thousand copies was never
sold out. Kepler was the first Continental astronomer to embrace the
Copernican theory. His
Mysterium Cosmographicum
, published in 1597
(fifty-four years after Copernicus's death), started the great controversy
-- Galileo entered the scene fifteen years later.
The reason why the idea of a sun-centred universe appealed to Kepler
was repeatedly stated by himself: 'I often defended the opinions of
Copernicus in the disputations of the candidates and I composed a careful
disputation on the first motion which consists in the rotation of the
earth; then I was adding to this the motion of the earth around the
sun
for physical or, if you prefer, metaphysical reasons
.' [2]
I have emphasized the last words because they contain the leitmotif
of Kepler's quest, and because he used the same expression in various
passages in his works. Now what were those 'physical or, if you prefer,
metaphysical reasons' which made Kepler prefer to put the sun into the
centre of the universe instead of the earth?
My ceaseless search concerned primarily three problems, namely, the
number, size, and motion of the planets -- why they are just as they
are and not otherwise arranged. I was encouraged in my daring inquiry
by that beautiful analogy between the stationary objects, namely, the
sun, the fixed stars, and the space between them, with God the Father,
the Son, and the Holy Ghost. I shall pursue this analogy in my future
cosmographical work. [3]
Twenty-five years later, when he was over fifty, Kepler repeated his credo:
'It is by no means permissible to treat this analogy as an empty
comparison; it must be considered by its Platonic form and archetypal
quality as one of the primary causes.'
He believed in this to the end of his life. Yet gradually the analogy
underwent a significant change:
The sun in the middle of the moving stars, himself at rest and yet the
source of motion, carries the image of God the Father and Creator. He
distributes his motive force through a medium which contains the moving
bodies, even as the Father creates through the Holy Ghost. [4]
Thus the 'moving bodies' -- that is, the planets -- are now brought into
the analogy. The Holy Ghost no longer merely fills the space between the
motionless sun and the motionless fixed stars. It has become an active
force, a
vis motrix
, which
drives
the planets. Nobody before
Kepler had postulated, or even suspected, the existence of a physical
force acting between the sun and the planets. Astronomy was not concerned
with physical forces, nor with the causes of the heavenly motions, merely
with their description. The passages which I have just quoted are the
first intimation of the forthcoming marriage between physics and astronomy
-- the act of betrothal, as it were. By looking at the sky, not through
the eyes of the geometrician only, but of the physicist concerned with
natural causes, he hit upon a question which nobody had asked before,
The question was: 'Why do the planets closer to the sun move faster than
those which are far away? What is the mathematical relation between a
planet's distance from the sun and the length of its year?'
These questions could only occur to one who had conceived the
revolutionary hypothesis that the motion of the planet -- and therefore
its velocity and the duration of its year -- was governed by a physical
force emanating from the sun. Every astronomer knew, of course, that the
greater their distance from the sun the slower the planets moved. But
this phenomenon was taken for granted, just as it was taken for granted
that boys will be boys and girls will be girls, as an irreducible fact of
creation. Nobody asked the cause of it because physical causes were not
assumed to enter into the motion of heavenly bodies. The greatness of
the philosophers of the scientific revolution consisted not so much in
finding the right answers but in asking the right questions; in seeing
a problem where nobody saw one before; in substituting a
why
for a
how
.
Kepler's answer to the question why the outer planets move slower than
the inner ones, and how the speed of their motion is related to their
distance from the sun, was as follows:
There exists only one moving soul in the centre of all the orbits;
that is the sun which drives the planets the more vigorously the closer
the planet is, but whose force is quasi-exhausted when acting on the
outer planets because of the long distance and the weakening of the
force which it entails. [5]
Later on he commented:
If we substitute for the word "soul" the word "force", then we get
just the principle which underlies my Physics of the Skies. As
I reflected that this cause of motion diminishes in proportion to
distance just as the light of the sun diminishes in proportion to
distance from the sun, I came to the conclusion that this force must
be substantial -- "substantial" not in the literal sense but . . . in
the same manner as we say that light is something substantial, meaning
by this an unsubstantial entity emanating from a substantial body. [6]
We notice that Kepler's answer came
before
the question -- that it
was the answer that begot the question. The answer, the starting point,
was the analogy between God the Father and the sun -- the former acting
through the Holy Ghost, the latter through a physical force. The planets
must obey the law of the sun -- the law of God -- the mathematical law
of nature; and the Holy Ghost's action through empty space diminishes,
as the light emanating from the sun does, with distance. The degenerate,
purely descriptive astronomy which originated in the period of the
Greek decline, and continued through the Dark and Middle Ages until
Kepler, did not ask for meaning and causes. But Kepler was convinced
that physical causes operate between heavenly, just as between earthy,
bodies, and more specifically that the sun exerts a physical force on
the planets. It was this conviction which enabled him to formulate his
laws. Physics became the auxiliary matrix which secured his escape from
the blocked situation into which astronomy had manoeuvred itself.
The blockage -- to cut a very long story short -- was due to the fact that
Tycho de Brahe had improved the instruments and methods of star-gazing,
and produced observational data of a hitherto unequalled abundance
and precision; and the new data did not fit into the traditional
schemes. Kepler, who served his apprenticeship under Tycho, was given
the task of working out the orbit of Mars. He spent six years on the
task and covered nine thousand folio-sheets with calculations in his
small handwriting without getting anywhere. When at last he believed he
had succeeded he found to his dismay that certain observed positions of
Mars differed from those which his theory demanded by magnitudes up to
eight minutes arc. Eight minutes arc is approximately one-quarter of
the apparent diameter of the moon. This was a catastrophe. Ptolemy,
and even Copernicus, could afford to neglect a difference of eight
minutes, because their observations were accurate only within a margin
of ten minutes, anyway. 'But,' Kepler wrote in the
New Astronomy
,
'but for us, who by divine kindness were given an accurate observer such
as Tycho Brahe, for us it is fitting that we should acknowledge this
divine gift and put it to use. . . . Henceforth I shall lead the way
towards that goal according to my ideas. For if I had believed that we
could ignore these eight minutes, I would have patched up my hypothesis
accordingly. But since it was not permissible to ignore them, those eight
minutes point the road to a complete reformation of astronomy. . . .' [7]
Thus a theory, built on years of labour and torment, was instantly thrown
away because of a discord of eight miserable minutes arc. Instead of cursing
those eight minutes as a stumbling block, he transformed them into the
cornerstone of a new science. For those eight minutes arc had at last
made him realize that the field of astronomy in its traditional framework
was well and truly blocked.
One of the recurrent frustrations and tragedies in the history of thought
is caused by the uncertainty whether it is possible to solve a given
problem by traditional methods previously applied to problems which seem
to be of the same nature. Who can say how many lives were wasted and good
minds destroyed in futile attempts to square the circle, or to construct
a "perpetuum mobile"? The proof that these problems an insoluble was
in each case an original discovery in itself (such as Maxwell's second
law of thermodynamics); and such proofs could only be found by looking
at the problem from a point of view outside its traditional matrix.
On the other hand, the mere knowledge that a problem is soluble means
that half the game is already won.
The episode of the eight minutes arc had convinced Kepler that his problem
-- the orbit of Mars -- was insoluble so long as he felt bound by the
traditional rules of sky-geometry. Implied in those rules was the dogma
of 'uniform motion in perfect circles'. Uniform motion he had already
discarded before the crisis; now he felt that the even more sacred one
of
circular
motion must also go. The impossibility of constructing
a circular orbit which would satisfy all existing observations suggested
to him that the circle must be replaced by some other curve.
The conclusion is quite simply that the planet's path is not a circle --
it curves inward on both sides and outward again at opposite ends. Such a
curve is called an oval. The orbit is not a circle but an oval figure. [8]
This oval orbit was a wild, frightening new departure for him. To be fed
up with cycles and epicycles, to mock the slavish imitators of Aristotle
was one thing; to assign an entirely new, lopsided, implausible path
for the heavenly bodies was quite another. Why indeed an oval? There is
something in the perfect symmetry of spheres and circles which has a deep,
reassuring appeal to the unconscious mind -- otherwise it could not have
survived two millennia. The oval lacks that archetypal appeal. It has
an arbitrary, distorted form. It destroyed the dream of the 'harmony
of the spheres', which lay at the origin of the whole quest. At times
he felt like a criminal, or worse: a fool. All he had to say in his own
defence was: 'I have cleared the Augean stables of astronomy of cycles
and spirals, and left behind me only a single cartful of dung.' [9]
That cartful of dung -- non-uniform motion in non-circular orbits -- could
only be justified and explained by arguments derived not from geometry,
but from physics. A phrase kept humming in his ear like a catchy tune,
and crops up in his writings over and again: there is a force in the sun
which moves the planets, there is a force in the sun. . . . And since
there is a force in the sun, there must exist some simple relationship
between the planet's distance from the sun, and its speed. A light shines
the brighter the nearer one is to its source, and the same must apply
to the force of the sun: the closer the planet to it, the quicker it
will move. This had been his instinctive conviction; but now he thought
that he had found the proof for it. 'Ye physicists, prick your ears, for
now we are going to invade your territory.' The next six chapters in the
Astronomia Nova
are a report on that invasion into celestial physics,
which had been out of bounds for astronomy since Plato. He had found
the second matrix which would unblock his problem.
That excursion was something of a comedy of errors -- which nevertheless
ended with finding the truth. Since he had no notion of the principle of
inertia, which makes a planet persist in its tangential motion under
its own momentum, and had only a vague intuition of gravity, he had
to invent a force which, emanating from the sun, sweeps the planet
round its path like a broom. In the second place, to account for the
eccentricity of the orbits he had to postulate that the planets were
'huge round magnets' whose poles pointed always in the same direction so
that they would alternately be drawn closer to and be repelled by the
sun. But although today the whole thing seems cockeyed, his intuition
that there are