## Simple Copernican Theory

Copernicus, following Aristarchus's suggestions, proposed that the Sun and the fixed stars should be regarded as stationary, and that the Earth be regarded as a planet that circled about the Sun in the same manner and direction as the other five planets. The Moon alone should be regarded as circling about the Earth. The length of time for any planet to complete one round trip around the Sun should be greater the further away the planet from the Sun. Retrograde motion and all the slowing down and speeding up of the planets is simply an "optical illusion," which occurs because the direction in which one of the other planets is seen from the Earth depends on the relative positions of the Earth and the planet in their respective orbits. These relative positions will change over time in the same way as the relative positions of racing cars in a long-distance race around an oval track. A fast planet will increase its lead over a slow planet until it gains a whole "lap" and will pass the slower planet again and again. Therefore as viewed from the Earth the other planets will sometimes seem to be ahead and sometimes behind the Earth. A conjunction is nothing more special than the observation that one planet is about to "lap" another planet.

Figure 2.7a shows schematically how retrograde motion is seen from the Earth. Figure 2.7b shows the relative positions of the Sun, Earth, and Mars at seven different times. The arrows show the directions (compared to the direction of a distant star) in which an observer on Earth would have to look to see Mars at those times. In Fig. 2.7c, the corresponding directions are superimposed on each other, as they would appear to astronomers (or anyone else) looking from Earth toward Mars. In addition, the lengths of the arrows are adjusted to correspond to the changing distances from Earth to Mars in the seven different positions. The result is a very simple and "natural" explanation of retrograde motion.

To explain the daily rotation (diurnal motion), Copernicus also proposed that the Earth is spinning on its own axis once in 23 hours and 56 minutes.6 The spin

6Note the time of rotation is not 24 hours. The other 4 minutes to make up the time for an apparent complete rotation of the heavens is needed because the Earth has moved to a different position in its orbit about the Sun.

Figure 2.7. Copernicus's heliocentric model, (a) Schematic perspective of Earth and Mars orbiting the Sun, showing the Earth spinning on its axis, (b) Relative positions of Earth and Mars showing different angles of sight from Earth to Mars, (c) Superposition of angles of sight as seen from the Earth itself.

Figure 2.7. Copernicus's heliocentric model, (a) Schematic perspective of Earth and Mars orbiting the Sun, showing the Earth spinning on its axis, (b) Relative positions of Earth and Mars showing different angles of sight from Earth to Mars, (c) Superposition of angles of sight as seen from the Earth itself.

axis is tilted with respect to the axis of the orbit by an amount equal to the angle (about 23^°) that the ecliptic makes with the celestial equator. (Copernicus also asserted that this tilt axis is rotating very slowly about the orbital axis, but maintaining the same tilt angle, thereby explaining a very slow change in the overall appearances of the fixed stars, which had been observed since the time of Ptolemy.)

In effect, Copernicus found that by shifting the point of view of the planetary motions from the Earth to the Sun, motions that had theretofore seemed very complicated became very simple. If one could stand on the Sun, then it would appear that all the planets are simply traveling in circular paths, with the planets closest to the Sun traveling the fastest. He then deduced from the astronomical measurements the correct order of the planets from the Sun, starting with the closest: Mercury, Venus, Earth, Mars, Jupiter, Saturn. He also calculated the ratios of their distances from the Sun fairly accurately, although his values for the actual distances were quite wrong. The Earth, for example, is actually 93 million miles from the Sun, whereas Copernicus took this distance to be about 4.8 million miles.

Having set up his general scheme, Copernicus then proceeded to make calculations as to exactly how the heavens would appear to astronomers on Earth. In particular, he calculated the appearances of the planets, time and place, for comparison with the astronomical measurements. He found, however, that his calculated positions gave much poorer results than the Ptolemaic theory! In other words, his beautiful and elegant conception, which worked so well qualitatively, had failed quantitatively.