1. What are the similarities and differences between the Aristotelian cosmos and the Ptolemaic cosmos? Why did Ptolemy make changes to the Aristotelian model?

There are various similarities between the Aristotelian and Ptolemaic cosmoses. The first similarity is that both cosmoses are geocentric and are restricted by the sphere of fixed stars. Secondly, planet motions in both cosmoses are circular. Third, heavenly bodies in both cosmoses are perfect spheres. Lastly, both have dissimilar physics for both supralunar and sublunar realms. The differences between the cosmoses are the additions made by Ptolemy to his model of the cosmos to match the real observations of the planets such as retrograde movement. Ptolemy added eccentrics and equants, and epicycles and deferents.

2. What happened to Ancient Greek thought during the Arab Empire? Give one example of a great Islamic thinker and state his contribution. How did Aristotelian thinking make its way back into Europe after the Dark Ages, and where was it developed?

One of the most significant events involving ancient Greek thought during the Arabic empire is the translation and copying of texts containing ancient Greek thought to Arabic. Wide-ranging observations and developments to ancient Greek thinking were added to scientific literature.

Several Islamic thinkers contributed to scientific though. An example is Ibn Rushd (Averoes) who made commentaries to Aristotelian ideas that were utilized extensively in medieval and renaissance institutions of learning.

Aristotelian thinking was not transmitted directly from ancient Greece to Europe, but was introduced from the Arabic empire via Sicily and Spain. These regions had been part of the Arabic empire for many centuries, but were conquered by European powers in the 11th century. Aristotelian thinking was first introduced in cathedral schools created by Charlemagne, which later developed into the first universities.

3. Describe the model of the universe proposed by Tycho Brahe and explain why he developed this model. What changes did Kepler make to the Copernican model, and why? Describe 2 telescope observations of Galileo and explain how these posed a threat to the Aristotelian worldview.

The model of the universe put forward by Tycho Brahe is geoheliocentric. The motion of the sun and moon around the earth is circular. The earth is located at the centre of the cosmos, while the planets move around the sun in circles.

Brahe created the model since he recognized the strong points of the Copernican model in calculating the positions of the planets that was founded on accurate observational data. Brahe's model maintains these strong points, but he lacked sufficient evidence to prove that the earth was in motion; therefore the earth is stationary in his model.

Galileo made various telescope observations that threatened the Aristotelian worldview. One of the observations is the phases of the planet Venus. The only model that can clarify these phases is heliocentric due to the relationship between the sun and observer on earth. For instance, Venus would not be complete in the geocentric model, while Galileo observations show it is complete.
The other observation is mountains on the moon's surface. These irregularities illustrate that the moon's surface is not perfectly smooth and posses some earth-like characteristics.