NICHOLAS COPERNICUS' SKETCH OF HIS HYPOTHESES FOR THE HEAVENLY
MOTIONSOur ancestors assumed, I observe, a large number of
celestial spheres for this reason especially, to explain the apparent motion of
the planets by the principle of regularity. For they thought it altogether
absurd that a heavenly body, which is a perfect sphere, should not always move
uniformly. They saw that by connecting and combining regular motions in various
ways they could make any body appear to move to any position.
Callippus and Eudoxus, who endeavored to solve the problem by the use of
concentric spheres, were unable to account for all the planetary movements; they
had to explain not merely the apparent revolutions of the planets but also the
fact that these bodies appear to us sometimes to mount higher in the heavens,
sometimes to descend; and this fact is incompatible with the principle of
concentricity. Therefore it seemed better to employ eccentrics and epicycles, a
system which most scholars finally accepted.
Yet the planetary theories of Ptolemy and most other astronomers,
although consistent with the numerical data, seemed likewise to present no small
difficulty. For these theories were not adequate unless certain equants were
also conceived; it then appeared that a planet moved with uniform velocity
neither on its deferent nor about the center of its epicycle. Hence a system of
this sort seemed neither sufficiently absolute nor sufficiently pleasing to the
Having become aware of these defects, I often consideredwhether there could
perhaps be found a more reasonable arrangement of circles, from which every
apparent inequality would be derived and in which everything would move
uniformly about its proper center, as the rule of absolute motion requires.
After I had addressed myself to this very difficult and almost insoluble
problem, the suggestion at length came to me how it could be solved with fewer
and much simpler constructions than were formerly used, if some assumptions
(which are called axioms) were granted me. They follow in this order.
Having set forth these assumptions, I shall endeavor briefly to show
how uniformity of the motions can be saved in a systematic way. However, I have
thought it well, for the sake of brevity, to omit from this sketch mathematical
demonstrations, reserving these for my larger work. But in the explanation of
the circles I shall set down here the lengths of the radii; and from these the
reader who is not unacquainted with mathematics will readily perceive how
closely this arrangement of circles agrees with the numerical data and
- There is no one center of all the celestial circles or spheres.
- The center of the earth is not the center of the universe, but only
of gravity and of the lunar sphere.
- All the spheres revolve about the sun as their mid-point, and
therefore the sun is the center of the universe.
- The ratio of the earth's distance from the sun to the height of the
firmament is so much smaller than the ratio of the earth's radius to its
distance from the sun that the distance from the earth to the sun is
imperceptible in comparison with the height of the firmament.
- Whatever motion appears in the firmament arises not from any motion
of the firmament, but from the earth's motion. The earth together with its
circumjacent elements performs a complete rotation on its fixed poles in a
daily motion, while the firmament and highest heaven abide unchanged.
- What appear to us as motions of the sun arise not from its motion but from
the motion of the earth and our sphere, with which we revolve about the sun
like any other planet. The earth has, then, more than one motion.
- The apparent retrograde and direct motion of the planets arises not from
their motion but from the earth's. The motion of the earth alone, therefore,
suffices to explain so many apparent inequalities in the heavens.
Accordingly, let no one suppose that I have gratuitously asserted, with
the Pythagoreans,the motion of the earth; strong proof will be found in my
exposition of the circles. For the principal arguments by which the natural
philosophers attempt to establish the immobility of the earth rest for the most
part on the appearances; it is particularly such arguments that collapse here,
since I treat the earth's immobility as due to an appearance.
The Order of the SpheresThe celestial spheres are arranged in the
following order. The highest is the immovable sphere of the fixed stars, which
contains and gives position to all things. Beneath it is Saturn, which Jupiter
follows, then Mars. Below Mars is the sphere on which we revolve; then Venus;
last is Mercury. The lunar sphere revolves about the center of the earth and
moves with the earth like an epicycle. In the same order also, one planet
surpasses another in speed of revolution, according as they trace greater or
smaller circles. Thus Saturn completes its revolution in thirty years, Jupiter
in twelve, Mars in two and one-half, and the earth in one year; Venus in nine
months, Mercury in three.
The Apparent Motions of the SunThe earth has three motions. First, it
revolves annually in a great circle about the sun in the order of the signs,
always describing equal arcs in equal times; the distance from the center of the
circle to the center of the sun is 1/25 of the radius of the circle. The radius
is assumed to have a length imperceptible in comparison with the height of the
firmament; consequently the sun appears to revolve with this motion, as if the
earth lay in the center of the universe. However, this appearance is caused by
the motion not of the sun but of the earth, so that, for example, when the earth
is in the sign of Capricornus, the sun is seen diametrically opposite in Cancer,
and so on. On account of the previously mentioned distance of thesun from the
center of the circle, this apparent motion of the sun is not uniform, the
maximum inequality being 2 1/6ø. The line drawn from the sun through the center
of the circle is invariably directed toward a point of the firmament about 10ø
west of the more brilliant of the two bright stars in the head of Gemini,
therefore when the earth is opposite this point, and the center of the circle
lies between them, the sun is seen at is greatest distance from the earth. In
this circle, then, the earth revolves together with whatever else is included
within the lunar sphere.
The second motion, which is peculiar to the earth, is the daily rotation on
the poles in the order of the signs, that is, from west to east. On account of
this rotation the entire universe appears to revolve with enormous speed. Thus
does the earth rotate together with its circumjacent waters and encircling
The third is the motion in declination. For the axis of the daily
rotation is not parallel to the axis of the great circle, but is inclined to it
at an angle that intercepts a portion of a circumference, in our time about 23
1/2ø. Therefore, while the center of the earth always remains in the plane of
the ecliptic, that is, in the circumference of the great circle, the poles of
the earth rotate, both of them describing small circles about centers
equidistant from the axis of the great circle. The period of this motion is not
quite a year and is nearly equal to the annual revolution on the great circle.
But the axis of the great circle is invariably directed toward the points of the
firmament which are called the poles of the ecliptic. In like manner the motion
in declination, combined with the annual motion in their joint effect upon the
poles of the daily rotation, would keep these poles constantly fixed at the same
points of the heavens, if the periods of both motions were exactly equal. Now
with the long passage of time is has become clear that this inclination of the
earth to the firmament changes. Hence it is the common opinion that the
firmament has several motions in conformity with a law not yet sufficiently
understood. But the motion of the earth can explain all these changes in a less
surprising way. I am not concerned to state what the path of the poles is. I am
aware that, in lesser matters, a magnetized iron needle always points in the
same direction. It has nevertheless seemed a better view to ascribe the changes
to a sphere, whose motion governs the movements of the poles. This sphere must
doubtless be sublunar.