# Math Tutorials and Moreby George

## Math Tutorials and Moreby George

### Problems Emerge for Aristotelian Viewpoint

A working telescope was first unveiled in the Netherlands in 1608. Initially it was used for military applications. In 1609 Galileo began using the telescope for astronomical observations. He refined the instrument and eventually achieved a magnification of 30x. His observations with the telescope challenged many of Aristotle's assumptions. His observations of the moon revealed an uneven (mountainous) surface much as we have on the earth. He also observed sun spots by projecting a telescopic image onto a piece of paper. These observations challenged the assumed perfection of the superlunar region. He also observed objects he correctly identified as moons revolving around the planet Jupiter. This challenged the view that everything revolved around a stationary earth. Here was an example of objects revolving around another object that was itself moving. He also observed that the planet Venus went through a complete set of phases like those of the moon. This was consistent with the sun-centered model of Copernicus (1473–1543), but was not consistent with Ptolemy's model. In Ptolemy's model Mercury and Venus had orbits between the earth and the sun. Since they always appear close to the sun, the centers of their epicycles must revolve around the earth at the same rate as the sun does. Thus, Ptolemy's model would never show a wide range of phases. There is always a significant portion of the dark side of Venus facing the earth. You can see this from Figure 6.

Figure 7 shows the phases of Venus in the Copernican model (without epicycles). Here an observer on the earth will see a wide range of phases. Galileo's observations were repeated by Jesuit astronomers, and they confirmed what he saw.

Galileo viewed his observations as a confirmation of the sun-centered Copernican model. Although his observations did pose a serious threat to the model of Aristotle and Ptolemy, there was another earth-centered model that produced accurate results and was also consistent with Galileo's observations. This was the model proposed by the Danish astronomer Tycho Brahe.