Copernicus

The big change began with a Polish scientist named Nicolaus Copernicus (1473–1543). Copernicus was not the first person to suggest that Earth orbits the Sun; recall that this idea had been proposed by Aristarchus some 1,800 years earlier [Section 3.1.2]. Indeed, in his writings, Copernicus acknowledged that he was aware of Aristarchus’s proposal.

Why did Copernicus decide to try a Sun-centered model? If you think back to what we’ve discussed, you’ll realize that there were almost certainly two main reasons:

Once he started down the path of using a Sun-centered model, Copernicus spent a lot of time working out its mathematical details so that he could use it to predict planetary positions. In that process, he also discovered that he could use the geometry of his model to calculate how long it took each planet to orbit the Sun and how far (compared to Earth) each planet was from the Sun. The fact that his model led to a mathematically simple layout for the solar system gave him added confidence that he was on the right track in putting the Sun at the center.

Copernicus ultimately wrote a book describing his model in depth (Figure 3.7). The book was titled De Revolutionibus Orbium Coelestium, which translates to “On the Revolutions of the Heavenly Spheres.” It was published in 1543 — the same year in which Copernicus died; in fact, he apparently received the first printed copy of his book on the very day that he died.

Copernicus’s book spread quickly among European scholars and scientists, drawing wide interest. It did not immediately convince everyone, for reasons we’ll discuss next. However, the fact that Copernicus began the process with a book title that included the word “revolution” explains why we refer to the dramatic change that overturned the Earth-centered view of the universe as the Copernican revolution.

Why Copernicus’s Idea Was Not Immediately Accepted

What went wrong? The answer is that while Copernicus had been willing to overturn the ancient idea of an Earth-centered universe, he still believed that “heavenly perfection” required that all heavenly motion had to occur in perfect circles. Because planetary orbits are not perfect circles (they are ellipses, as we’ll discuss shortly), his model made inaccurate predictions. He tried to improve the predictions of his model by adding additional complexity to it (including using “circles upon circles” like those in Ptolemy’s model), but it still didn’t work very well.

In the end, Copernicus’s complete model was no more accurate and no less complex than Ptolemy’s model. Given that fact, few people were willing to throw out thousands of years of traditional belief in an Earth-centered universe when the new model worked just as poorly as the old one.

Nevertheless, many scholars and scientists of the time liked Copernicus’s idea. We don’t know for sure what drew these people to the Sun-centered model, but its much simpler explanation for apparent retrograde motion probably played a major role. Copernicus himself had died, but others picked up where he left off.

Data and Modeling

In very general terms, doing science always requires two things: data and modeling. The data come from observations and experiments. The models seek to explain why we find that data that we do. We test the models by comparing their predictions to the data.

After Copernicus published his book in 1543, scholars and scientists were faced with a key problem: Neither the old (Ptolemy’s) nor the new (Copernican) models agreed well with the data (observed planetary positions). It was therefore obvious to them that they needed a better model. They also recognized a need for better data against which to test any new model. The problem was that all existing data had been obtained by naked eye using hand-held instruments, and this did not provide enough precision for careful tests of how model predictions compared to actual planetary positions.

Two people ended up playing particularly important roles in developing better data and better models: a man named Tycho Brahe provided the data, and Johannes Kepler provided the models. We’ll talk about them in a moment, but first we need to talk about angle measurement so that you’ll be able to appreciate their work.

Arcminutes and Arcseconds

You are already familiar with angle measurement in degrees, which is defined by the fact that there are 360° in a full circle. Sometimes, however, we need to measure angles that are much smaller than 1°, and for that we divide degrees into smaller units as shown in Figure 3.8:

• We subdivide each degree into 60 arcminutes (symbolized by ‘ ).
• Then we further subdivide each arcminute into 60 arcseconds (symbolized by ” ).

Tycho’s Data

Tycho Brahe (1546–1601), usually known simply as Tycho (pronounced “tie-koe”), was an eccentric Danish nobleman. When he was 20 years old, he lost much of his nose in a sword fight with another student over who was the better mathematician. He then spent the rest of his life wearing a replacement nose that he made himself out of silver and gold.

Tycho recognized the need for better observations. The telescope still had not yet been invented, so Tycho set out to find a way to make more precise observations by naked eye. He developed numerous new instruments and built an observatory that worked much like a giant protractor (Figure 3.9).

Tycho was convinced that his data held the key to coming up with a correct model for the heavens, but he himself struggled to come up with one. He therefore sought help. In the year 1600, he hired a man named Johannes Kepler (1571-1630) for this purpose. As Tycho lay dying just over a year later, he handed over all his data to Kepler. Kepler later wrote that while Tycho lay on his death bed, he kept repeating over and over the words “Let me not seem to have lived in vain.”

Kepler’s Model

When Kepler began work on creating a new model, he shared Copernicus’s beliefs that the model should be Sun-centered and that it should use only perfect circles for planetary orbits. After years of effort, he succeeded in creating a model with perfect circles that matched most of Tycho’s observations quite well. The match was not perfect, but even in the worst cases (which were for the planet Mars), this model with circular orbits predicted planetary positions that were within 8 arcminutes of Tycho’s observed positions. This is quite close, since 8 arcminutes is barely one-fourth the angular diameter of the full moon.

Kepler surely was tempted to attribute such small discrepancies to errors by Tycho. But he was convinced that Tycho’s observations had been made and recorded very carefully. He therefore concluded that it must be the circular orbits of his model, not Tycho’s data, that were wrong. About this fact, Kepler wrote:

If I had believed that we could ignore these eight arcminutes, I would have patched up my hypothesis accordingly. But, since it was not permissible to ignore, those eight arcminutes pointed the road to a complete reformation in astronomy.

With his decision to abandon perfect circles, Kepler began to try other shapes for orbits, and ultimately found the correct answer: Earth and other planets do indeed orbit the Sun, but their orbits take the shapes of the special ovals known as ellipses . Moreover, Kepler found that planets move faster in the portions of their elliptical orbits in which they are close to the Sun and slower when they are farther away (Figure 3.10).

Kepler summarized his discoveries with three precisely stated mathematical laws that we now call Kepler’s laws of planetary motion . He published the first two of these laws, which were the ones needed to match Tycho’s data, in the year 1609. (The third law, which he published a decade later, describes how the time it takes each planet to orbit the Sun — called the orbital period — depends on its distance from the Sun.)

Kepler’s laws represent a model of planetary motion that can be used to predict the locations of planets in our sky at any time. Just as with the earlier models of Ptolemy and Copernicus, the process works basically like this:

• Start by observing the current positions of planets in the sky.
• Then use the mathematics of the model to predict future (or past) locations for the planets.

The critical difference is that while the models of both Ptolemy and Copernicus made noticeably inaccurate predictions, Kepler’s model gave essentially perfect predictions. Kepler’s model also had a second important advantage over the earlier ones: It was much simpler. Recall that calculations with Ptolemy’s model were extremely tedious and complex, and the same was true for Copernicus’s model with the complexity he was forced to add in his attempt to keep circular orbits.

In contrast, Kepler’s model is so simple that it is possible to build clockwork-like mechanisms that can reproduce planetary motion. Figure 3.11 shows one such device, in which each planet moves along an elliptical track, driven by clockwork built to follow Kepler’s laws. Of course, today it is much easier to program Kepler’s laws into a computer than to build a mechanical device. This is essentially how modern software can make perfect predictions of past and future planetary positions.

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