Philosophy and Cosmology: A Revolution
(PHIL 20612)
Dr K Brading
4. Kepler and the Copernican System
Kepler’s teacher, Michael Maestlin, taught him about Copernicus’s astronomical system. Kepler sought
to address three questions within the context of the Copernican system:
Why are there exactly six planets?
Why is are the planets spaced as they are?
What are the speeds of the planets?
How did Kepler seek to answer these questions? Was he successful? What arguments did Kepler offer in
support of the Copernican system? How strong are these arguments?
Study questions
What is Kepler’s “platonic solids model” of the cosmos, and how is it constructed?
Which of his three questions is Kepler able to address using his “platonic solids model”?
How important is the position of the Sun in Kepler’s system?
What role does the Sun play in Kepler’s system?
Given the kinematic equivalence of Copernicus’s and Ptolemaic astronomy, how does Kepler propose
that we decide between the two systems?
What role do physical arguments play in Kepler’s support for heliocentrism?
What role do considerations of harmony play in Kepler’s arguments for heliocentrism?
In the light of Kepler’s laws of motion we can understand why Ptolemaic astronomy was so successful
predictively, even though it was so wrong about the structure of the cosmos. In the light of Kepler’s
laws, explain (a) the predictive success of Ptolemaic astronomy, and (b) the remaining sources of error
in Ptolemaic predictions.
Why were Tycho Brahe’s observations important for Kepler’s astronomy?
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Extract from James R. Voelkel, Johannes Kepler, OUP, 1999, pp. 29-32 and p. 24.
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Kepler’s Laws of Planetary Motion
1. The orbits of the planets are ellipses with the Sun at one focus.
2. The radial segment from the Sun to the planet sweeps out equal areas in equal times.
3. The ratio of the cube of the semi-major axis of the planetary orbit to the square of its period is a fixed
constant, the same for all the planets orbiting the Sun.
Kepler, New Astronomy, 1609, Chapter 33 (Translated by William H. Donahue, CUP, 1992.)
But which body is it that is at the centre? Is there none, as for Copernicus when he is computing,
and for Tycho in part? Is it the earth, as for Ptolemy and for Tycho in part? Or finally, is it the sun
itself, as I, and Copernicus when he is speculating, would have it? This question I began to discuss in
physical terms in Part I. I there supposed as one of the principles what has now been expressly and
geometrically proved in chapter 32: that a planet is moved less vigorously when it recedes from the
point whence the eccentricity is computed.
From this principle I presented a probable argument that the sun is at that point and at the centre of
the world (or the earth for Ptolemy) rather than its being some other point occupied by no body. Allow
me, then, to recall that same probable argument, its principles now demonstrated, in the present chapter.
Then, as you may remember, I demonstrated in the second part, that the phenomena at either end of the
night follow beautifully if the oppositions of Mars are reckoned according to the sun’s apparent position.
If this is done, then we likewise set up the eccentricity and the distances from the very centre of the
sun’s body, so that the sun itself again comes to be at the centre of the world (for Copernicus), or at least
at the centre of the planetary system (for Tycho). But of these two arguments, one depends upon
physical probability, and the other proceeds from possibility to actuality. And so in the third place I have
demonstrated from the observations (in a proof which, because of its conceptual difficulty, I have
postponed until chapter 52) that we cannot avoid referring Mars to the apparent position of the sun, and
drawing the line of apsides, which bisects the eccentric, directly through the sun’s body, unless perhaps
we wish to allow an eccentric such as will by no means be in accord with the parallax of the annual orb.
Anyone who cannot tolerate the delay may read about this in chapter 52, and then may carry on here
afterwards. For there nothing is assumed but the bare observations. You will find a similar proof in Part
V, from considerations of latitudes.
Therefore, with the sun belonging in the centre of the system, the source of motive power, from what
has now been demonstrated, belongs in the sun, since it too has now been located in the centre of the
world.
But indeed, if this very thing which I have just demonstrated a posteriori (from the observations) by
a rather long deduction, if, I say, I had taken this as something to be demonstrated a priori (from the
worthiness and eminence of the sun), so that the source of the world’s life (which is visible in the
motion of the heavens) is the same as the source of the light which forms the adornment of the entire
machine, and which is also the source of the heat by which everything grows, I think I would deserve
an equal hearing.
Tycho Brahe himself, or anyone who prefers to follow his general hypothesis of the second
inequality, should consider by how close a likeness to the truth this physically elegant combination has
for the most part been accepted (since for him, too, this substitution of the apparent position of the sun
brings the sun back to the centre of the planetary system) yet to some extent recoils from his hypothesis.
For it is obvious from what has been said that only one of the following can be true: either the power
residing in the sun, which moves all the planets, by the same action moves the earth as well; or the
sun, together with the planets linked to it through its motive force, is borne about the earth by some
power which is seated in the earth.
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Extract from Julian Barbour, ‘Science and History’, Contemporary Physics (1999)
The achievements of Ptolemy and Kepler are seriously underrated, while Copernicus is credited ... with
the doctrine of heliocentricity (instead of terrestrial mobility, which is what he actually proposed). In
fact, as far as Copernicus was concerned the Sun simply happened to be near the centre of his universe.
It played so little role in his system that it does not even appear in the diagrams in which he explains the
motions of the planets. ... when Copernicus had his brilliant insight that the epicyclic motions of the five
naked-eye planets could all be explained by the motion of the earth alone, he unfortunately had no
further deep insights. He attempted to construct a new model of the solar system simply by taking
Ptolemy’s models and converting them unchanged. He got into an unholy muddle ... He made the Sun a
mere lantern to illuminate the dance of the planets, which had to perform some very odd movements
indeed.. .
Many historians of science have completely failed to understand the nature and manner of the next great
advance in theoretical astronomy, which was Kepler’s. ... Kepler started with one brilliant heuristic idea
- that the Sun is not just accidentally near but precisely at the true centre of the planetary system because
it actually controls the motions of the planets by physical forces. No one had dreamed of such a thing
before. The notion at the heart of modem physics - that matter interacts with matter through forces - was
born when Kepler had this idea.
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J. T. Cushing, Philosophical Concepts in Physics, CUP, 1998; pp. 66-71 (section 5.4).
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