In what respects were Ptolemy's and Copernicus' models similar? The Earth was at the center of the Ptolemy model, and all planets circled around it. The sun was at the center of Copernicus' cosmology, and all planets circled around it.
These two great astronomers built upon the work of Plato and Aristotle by discussing how the universe worked with mathematical proofs. They also used mathematics to help them predict future events such as eclipses.
Furthermore, both Ptolemy and Copernicus had lived their entire lives in Greece. This means that they were familiar with the works of Plato and Aristotle and knew how important it was for scientists to understand our planet and the stars surrounding it.
Finally, both Ptolemy and Copernicus died before reaching old age. They passed away in AD 148 and 1473 respectively.
Why is it important that Ptolemy and Copernicus were alike? Science has shown that planets do not orbit the sun but rather rotate around themselves. In other words, the earth revolves around its axis instead. This fact shows that people needed new ideas about how the universe worked in order to explain this phenomenon. Mathematicians can now use Copernicus' theory as a basis for further research.
What distinguished Ptolemy's model from the prior Greek one? According to Ptolemy, the Earth was at the center of a system of planets and stars. Ptolemy's hypothesis, on the other hand, was unique in that he believed planets traveled in small circles within larger circles. Venus, like the moon, passes through phases. It is this fact which led Ptolemy to believe that it too moved around the earth in an annual cycle.
Greek philosophers including Aristotle had proposed models of the universe that were very similar to Ptolemy's. In contrast to these predecessors, however, Ptolemy claimed his model was supported by better evidence. For example, he argued that since no motion is observed in the orbits of the planets except for the apparent movement of their centers around the Earth, then they must be surrounded by empty space. This idea was not new - it can be found in the work of Plato and Cicero - but its presentation in terms of a mathematical model helped to make it more acceptable.
It was also because of his use of mathematics that Ptolemy's model became so influential. No longer did scholars have to rely on their subjective beliefs about the universe when constructing models of it. They could instead use reason and logic to arrive at conclusions about what might happen based on known facts.
Mathematics plays an important role in Ptolemaic astronomy.
The Sun, rather than the Earth, was at the heart of Ptolemy's conception. The planets in Ptolemy's conception moved in smaller circles tied to bigger spheres. Ptolemy's model featured a different sphere arrangement than Aristotle's. They had unmistakable proof that the Earth-centered model was right. But they couldn't prove which model was correct for the heavens.
Aristotle believed that the fixed stars were fixed because they were perfect, shapely objects that could not move. They could only be seen moving against the background of the night sky because their brightness always kept them on the horizon. He also believed that they were very far away from the Earth, beyond the orbit of Mercury.
Ptolemy believed that the fixed stars were fixed because they were physical bodies that could not travel across space. Thus, they could not leave their celestial spheres. Their location was perfectly fixed because there were no other stars that could interfere with their movement across the sky. Also, like us, they were located within the limits of the Earth's atmosphere so they could never reach infinite distances since their distance can only be estimated by measuring the time it takes light to reach us from them.
Both models were correct but they served two different purposes. Aristotle's model was used to explain certain astronomical observations while Ptolemy's model was used to predict future events.
What was the distinction between Copernicus' and his own viewpoint? According to Ptolemy, the earth was at the center of the cosmos, but Copernicus stated that the sun was at the center and that the planets circled around it. This difference in opinion resulted in a conflict between the two men which led to Copernicus leaving his job as dean of the university in 1543.
Why did Copernicus come up with his own idea about the solar system instead of following Ptolemy's instructions? According to historians, Copernicus decided to create his own model of the universe because he wanted to prove that the Earth moved around the Sun. By using mathematics, he was able to show that all the planets except Mercury moved around the Sun as it traveled through the galaxy. This explanation was contrary to what Ptolemy had said so it made sense why Copernicus would want to prove him wrong.
Through his work on astronomy, Copernicus helped scientists understand the movement of the planets better than anyone before him. He also showed them that they could use math to learn more about our universe. These are just some examples of how Copernicus' contribution to science was far-reaching. After publishing his book "On the Revolutions of the Celestial Spheres" in 1543, he went back to teaching at the University of Krakow until his death in 1572.
Copernicus' approach employed only uniform circular movements, addressing what many saw as Ptolemy's system's main flaw. Ptolemy's equant circles were replaced by extra epicycles in the Copernican paradigm. Ptolemy's model's 1500-year lifespan aided Copernicus in developing a more precise estimate of the planets' movements. However, it also meant that he had to modify several aspects of the model to keep it working correctly.
One problem with Ptolemy's system was that it required very large orbits for the planets if one wanted their positions to remain accurate over long periods of time. For example, if Mercury moved in an orbit twice as wide as its actual distance from the Sun then its average distance from the Earth would be about half its actual distance, meaning that on average it would appear half as far away from the Earth as it does now. Because of this, people needed to use approximations when calculating distances across large intervals of time (for example when plotting the positions of planets against each other in order to identify patterns).
Another problem was that Ptolemy's model required heavy use of fudge factors in order to make the planets' orbits fit together correctly. For example, if you calculated the angle between Mars and Jupiter at one point in time and then repeated the calculation a few days later you might get different results because the angles they occupied relative to the Earth had changed slightly due to the effects of gravity.
In essence, Copernicus' solar system model has almost the same amount of epicycles as Ptolemy's, with the sole difference being that Copernicus' epicycles are significantly smaller. This changes how we view the planets' movements: whereas for Ptolemy a planet moves in an epicycle whose radius is equal to half its orbit, for Copernicus a planet moves in an epicycle whose radius is one-fifth its orbit.
Here is how Copernicus describes his model of the solar system in De Revolutionibus Orbium Coelestium (On the Revolutions of the Celestial Spheres):
"But surely some other arrangement could be found which would keep all the planets moving in circles but with different sizes for their epicycles. I decided to make the circles not equal in size but rather in proportion to the distances of the planets from the Sun. For example, the circle for Mercury should be about four hundredth part of the circle describing the orbits of the Moon and Earth; Venus', about seven hundredth part of the same circle; and so on."
This method was not new at the time it was proposed by Copernicus. It had been suggested before by others, including Aristarchus of Samos and Eratosthenes of Cyrene.