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The Reign of Epicycles

Posted on July 23rd, 2007 by Admin.
Categories: Uncategorized.

After Ptolemy had published his book there seemed to be nothing more
to do for the solar system except to go on observing and finding more
and more accurate values for the constants involved–viz., the periods
of revolution, the diameter of the deferent,[1] and its ratio to that
of the epicycle,[2] the distance of the excentric[3] from the centre
of the deferent, and the position of the line of apses,[4] besides the
inclination and position of the plane of the planet’s orbit. The only
object ever aimed at in those days was to prepare tables for
predicting the places of the planets. It was not a mechanical problem;
there was no notion of a governing law of forces.

From this time onwards all interest in astronomy seemed, in Europe at
least, to sink to a low ebb. When the Caliph Omar, in the middle of
the seventh century, burnt the library of Alexandria, which had been
the centre of intellectual progress, that centre migrated to Baghdad,
and the Arabs became the leaders of science and philosophy. In
astronomy they made careful observations. In the middle of the ninth
century Albategnius, a Syrian prince, improved the value of
excentricity of the sun’s orbit, observed the motion of the moon’s
apse, and thought he detected a smaller progression of the sun’s
apse. His tables were much more accurate than Ptolemy’s. Abul Wefa, in
the tenth century, seems to have discovered the moon’s “variation.”
Meanwhile the Moors were leaders of science in the west, and Arzachel
of Toledo improved the solar tables very much. Ulugh Begh, grandson of
the great Tamerlane the Tartar, built a fine observatory at Samarcand
in the fifteenth century, and made a great catalogue of stars, the
first since the time of Hipparchus.

At the close of the fifteenth century King Alphonso of Spain employed
computers to produce the Alphonsine Tables (1488 A.D.), Purbach
translated Ptolemy’s book, and observations were carried out in
Germany by Muller, known as Regiomontanus, and Waltherus.

Nicolai Copernicus, a Sclav, was born in 1473 at Thorn, in Polish
Prussia. He studied at Cracow and in Italy. He was a priest, and
settled at Frauenberg. He did not undertake continuous observations,
but devoted himself to simplifying the planetary systems and devising
means for more accurately predicting the positions of the sun, moon,
and planets. He had no idea of framing a solar system on a dynamical
basis. His great object was to increase the accuracy of the
calculations and the tables. The results of his cogitations were
printed just before his death in an interesting book, _De
Revolutionibus Orbium Celestium_. It is only by careful reading of
this book that the true position of Copernicus can be realised. He
noticed that Nicetas and others had ascribed the apparent diurnal
rotation of the heavens to a real daily rotation of the earth about
its axis, in the opposite direction to the apparent motion of the
stars. Also in the writings of Martianus Capella he learnt that the
Egyptians had supposed Mercury and Venus to revolve round the sun, and
to be carried with him in his annual motion round the earth. He
noticed that the same supposition, if extended to Mars, Jupiter, and
Saturn, would explain easily why they, and especially Mars, seem so
much brighter in opposition. For Mars would then be a great deal
nearer to the earth than at other times. It would also explain the
retrograde motion of planets when in opposition.

We must here notice that at this stage Copernicus was actually
confronted with the system accepted later by Tycho Brahe, with the
earth fixed. But he now recalled and accepted the views of Pythagoras
and others, according to which the sun is fixed and the earth
revolves; and it must be noted that, geometrically, there is no
difference of any sort between the Egyptian or Tychonic system and
that of Pythagoras as revived by Copernicus, except that on the latter
theory the stars ought to seem to move when the earth changes its
position–a test which failed completely with the rough means of
observation then available. The radical defect of all solar systems
previous to the time of Kepler (1609 A.D.) was the slavish yielding to
Plato’s dictum demanding uniform circular motion for the planets, and
the consequent evolution of the epicycle, which was fatal to any
conception of a dynamical theory.

Copernicus could not sever himself from this obnoxious tradition.[5]
It is true that neither the Pythagorean nor the Egypto-Tychonic system
required epicycles for explaining retrograde motion, as the Ptolemaic
theory did. Furthermore, either system could use the excentric of
Hipparchus to explain the irregular motion known as the equation of
the centre. But Copernicus remarked that he could also use an
epicycle for this purpose, or that he could use both an excentric and
an epicycle for each planet, and so bring theory still closer into
accord with observation. And this he proceeded to do.[6] Moreover,
observers had found irregularities in the moon’s motion, due, as we
now know, to the disturbing attraction of the sun. To correct for
these irregularities Copernicus introduced epicycle on epicycle in the
lunar orbit.

This is in its main features the system propounded by Copernicus. But
attention must, to state the case fully, be drawn to two points to be
found in his first and sixth books respectively. The first point
relates to the seasons, and it shows a strange ignorance of the laws
of rotating bodies. To use the words of Delambre,[7] in drawing
attention to the strange conception,

  he imagined that the earth, revolving round the sun, ought always to
  show to it the same face; the contrary phenomena surprised him: to
  explain them he invented a third motion, and added it to the two
  real motions (rotation and orbital revolution). By this third motion
  the earth, he held, made a revolution on itself and on the poles of
  the ecliptic once a year…. Copernicus did not know that motion in
  a straight line is the natural motion, and that motion in a curve is
  the resultant of several movements. He believed, with Aristotle,
  that circular motion was the natural one.

Copernicus made this rotation of the earth’s axis about the pole of
the ecliptic retrograde (i.e., opposite to the orbital revolution),
and by making it perform more than one complete revolution in a year,
the added part being 1/26000 of the whole, he was able to include the
precession of the equinoxes in his explanation of the seasons. His
explanation of the seasons is given on leaf 10 of his book (the pages
of this book are not all numbered, only alternate pages, or leaves).

In his sixth book he discusses the inclination of the planetary orbits
to the ecliptic. In regard to this the theory of Copernicus is unique;
and it will be best to explain this in the words of Grant in his great
work.[8] He says:–

  Copernicus, as we have already remarked, did not attack the
  principle of the epicyclical theory: he merely sought to make it
  more simple by placing the centre of the earth’s orbit in the centre
  of the universe. This was the point to which the motions of the
  planets were referred, for the planes of their orbits were made to
  pass through it, and their points of least and greatest velocities
  were also determined with reference to it.  By this arrangement the
  sun was situate mathematically near the centre of the planetary
  system, but he did not appear to have any physical connexion with
  the planets as the centre of their motions.

According to Copernicus’ sixth book, the planes of the planetary
orbits do not pass through the sun, and the lines of apses do not pass
through to the sun.

Such was the theory advanced by Copernicus: The earth moves in an
epicycle, on a deferent whose centre is a little distance from the
sun. The planets move in a similar way on epicycles, but their
deferents have no geometrical or physical relation to the sun. The
moon moves on an epicycle centred on a second epicycle, itself centred
on a deferent, excentric to the earth. The earth’s axis rotates about
the pole of the ecliptic, making one revolution and a twenty-six
thousandth part of a revolution in the sidereal year, in the opposite
direction to its orbital motion.

In view of this fanciful structure it must be noted, in fairness to
Copernicus, that he repeatedly states that the reader is not obliged
to accept his system as showing the real motions; that it does not
matter whether they be true, even approximately, or not, so long as
they enable us to compute tables from which the places of the planets
among the stars can be predicted.[9] He says that whoever is not
satisfied with this explanation must be contented by being told that
“mathematics are for mathematicians” (Mathematicis mathematica
scribuntur).

At the same time he expresses his conviction over and over again that
the earth is in motion. It is with him a pious belief, just as it was
with Pythagoras and his school and with Aristarchus. “But” (as Dreyer
says in his most interesting book, _Tycho Brahe_) “proofs of the
physical truth of his system Copernicus had given none, and could give
none,” any more than Pythagoras or Aristarchus.

There was nothing so startlingly simple in his system as to lead the
cautious astronomer to accept it, as there was in the later Keplerian
system; and the absence of parallax in the stars seemed to condemn his
system, which had no physical basis to recommend it, and no
simplification at all over the Egypto-Tychonic system, to which
Copernicus himself drew attention. It has been necessary to devote
perhaps undue space to the interesting work of Copernicus, because by
a curious chance his name has become so widely known. He has been
spoken of very generally as the founder of the solar system that is
now accepted. This seems unfair, and on reading over what has been
written about him at different times it will be noticed that the
astronomers–those who have evidently read his great book–are very
cautious in the words with which they eulogise him, and refrain from
attributing to him the foundation of our solar system, which is
entirely due to Kepler. It is only the more popular writers who give
the idea that a revolution had been effected when Pythagoras’ system
was revived, and when Copernicus supported his view that the earth
moves and is not fixed.

It may be easy to explain the association of the name of Copernicus
with the Keplerian system. But the time has long passed when the
historian can support in any way this popular error, which was started
not by astronomers acquainted with Kepler’s work, but by those who
desired to put the Church in the wrong by extolling Copernicus.

Copernicus dreaded much the abuse he expected to receive from
philosophers for opposing the authority of Aristotle, who had declared
that the earth was fixed. So he sought and obtained the support of
the Church, dedicating his great work to Pope Paul III. in a lengthy
explanatory epistle. The Bishop of Cracow set up a memorial tablet in
his honour.

Copernicus was the most refined exponent, and almost the last
representative, of the Epicyclical School. As has been already
stated, his successor, Tycho Brahe, supported the same use of
epicycles and excentrics as Copernicus, though he held the earth to be
fixed. But Tycho Brahe was eminently a practical observer, and took
little part in theory; and his observations formed so essential a
portion of the system of Kepler that it is only fair to include his
name among these who laid the foundations of the solar system which we
accept to-day.

In now taking leave of the system of epicycles let it be remarked that
it has been held up to ridicule more than it deserves. On reading
Airy’s account of epicycles, in the beautifully clear language of his
_Six Lectures on Astronomy_, the impression is made that the
jointed bars there spoken of for describing the circles were supposed
to be real. This is no more the case than that the spheres of Eudoxus
and Callippus were supposed to be real. Both were introduced only to
illustrate the mathematical conception upon which the solar,
planetary, and lunar tables were constructed. The epicycles
represented nothing more nor less than the first terms in the Fourier
series, which in the last century has become a basis of such
calculations, both in astronomy and physics generally.

[Illustration: “QUADRANS MURALIS SIVE TICHONICUS.” With portrait of
Tycho Brahe, instruments, etc., painted on the wall; showing
assistants using the sight, watching the clock, and recording. (From
the author’s copy of the _Astronomiae Instauratae Mechanica._)]

FOOTNOTES:

[1] For definition see p. 22.

[2] _Ibid_.

[3] For definition see p. 18.

[4] For definition see p. 18.

[5] In his great book Copernicus says: “The movement of the heavenly
bodies is uniform, circular, perpetual, or else composed of circular
movements.” In this he proclaimed himself a follower of Pythagoras
(see p. 14), as also when he says: “The world is spherical because the
sphere is, of all figures, the most perfect” (Delambre,
_Ast. Mod. Hist_., pp. 86, 87).

[6] Kepler tells us that Tycho Brahe was pleased with this
device, and adapted it to his own system.

[7] _Hist. Ast._, vol. i., p. 354.

[8] _Hist. of Phys. Ast._, p. vii.

[9] “Est enim Astronomi proprium, historiam motuum coelestium
diligenti et artificiosa observatione colligere. Deinde causas
earundem, seu hypotheses, cum veras assequi nulla ratione possit
… Neque enim necesse est, eas hypotheses esse veras, imo ne
verisimiles quidem, sed sufficit hoc usum, si calculum observationibus
congruentem exhibeant.”