Planetary (Art Hobson)

How do we know that Earth is round? Science is based on
observable evidence. So scientists are always skeptical, always asking, "How do we know?" We will frequently ask this question.
How do we know that Earth is spherical rather than flat? The evidence is fairly direct today (Figure 1.7), but what evidence might the ancient Greeks have had? Take a minute, to think about this.
(This is a minute, for thinking.)
The Greek philosopher Aristotle, living two centuries after Pythagoras, stressed the importance of evidence. He gave many good observational reasons to believe that Earth is spherical rather than flat. For one thing, ships sink little by little below the horizon as they go out to sea (Figure 1.8). For a second thing, Greek travelers reported that in northern lands, the noontime sun is lower in the sky. For a third, the shadow cast by Earth on the moon, as observed during an eclipse of the moon, is the shape that would be expected if both Earth and the moon were spherical. -0
But there was a problem. Because the spheres rotated uniformly, the transparent spheres theory predicted that each planet moved at a uniform rate around Earth. But careful observation showed that they do not. Instead, their rate of rotation, as seen from Earth, changes. Figure 1.9 diagrams this effect for a single planet such as Mars. The diagram is drawn relative to the background stars, and so it does not show the nightly rotation of Mars and the stars. Relative to the stars, Mars generally moves from west to east, but at a variable rate. Occasionally, Mars even changes directions and moves east to west relative to the stars, a phenomenon known as retrograde motion.
The Greek philosopher Plato, convinced that an elegant mathematical reality lay behind the heavenly motions, challenged his students with the problem of finding a geometric scheme that would explain the observed motions. They constructed a theory similar to Pythagoras's but far more elaborate, involving multiple transparent spheres for each planet.
One Greek thinker, Aristarchus, proposed that the sun and not Earth was at rest at the center of the universe, that Earth and the five planets circled the sun, and that Earth spun on its axis. It was a radical idea, and few astronomers took it seriously because it seemed absurd for several reasons: Earth seems nothing like the heavens, so how could Earth be a planet like the heavenly planets? It seems
absurd to believe that Earth moves. It's too big! What immense force could be pushing it to keep it moving? If it does move, it seems that objects such as birds and clouds that are not attached to the ground should be left behind. If Earth spins on its axis, objects should be hurled off, just as a stone is hurled from a rotating sling. These things were not observed, and so for reasons that made sense at the time, Greeks rejected Aristarchus's theory. It would be 2000 years before a sun-centered theory would again be considered.
Another problem arose. The Greeks noticed that during a planet's retrograde motion, it appeared brighter than at other times, as though it were closer to Earth during this time. Yet Plato's theory, with each planet on an Earth-centered sphere, implied that each planet maintained a fixed distance from Earth.
To explain the varying brightness of the planets, the Greeks tried something rather different. Instead of moving on multiple spheres, each planet now moved around Earth in a circle within a circle. As shown in Figure 1.10, a planet such as Mars moved uniformly around a circle whose center was on another circle that was centered on Earth. The small outer circle was called the planet's "epicycle," and the inner circle centered on Earth was called the planet's "deferent." The center of the epicycle moved uniformly along the deferent, so that Mars moved in two circles at the same time. This produced a loop-the-loop orbit for each planet (Figure 1.10). In agreement with observation, the theory predicted that there would be occasional periods of retrograde motion (on the inside of the loops) and that the planet would be closest to Earth during retrograde motion and so should appear brightest. It was a satisfying picture, and it explained the observations. It was a good theory.
Figure 1.11 pictures this theory, greatly simplified. This theory was finally refined and summarized around A.D. 100 by Ptolemy, antiquity's greatest astronomer (Figure 1.12). In order to agree with the known observations, Ptolemy introduced two new ideas: the displacement or "eccentricity" of the centers and
the "equant point" from which the motion appears uniform. s The details of these are not crucial here. To agree with the observations, each planet needed lots of epicycles-more than 80. T'hirteenth-century Spanish King Alfonso X commented that "if the Lord Almighty had consulted me before embarking upon the creation, I should have recommended something simpler."