Assignment Problem: The Phases of Venus
Course Learning Objectives:
1. Use the Ptolemaic model to predict the phases of Venus.
2. Use the Copernican model to predict the phases of Venus.
3. Understand how Galileo's observation of the phases of Venus helps to select between these two models.
Introduction: As the first scientist to undertake detailed astronomical study with the aid of a telescope, Galileo Galilei (1564-1642) was able to make a number of important discoveries that greatly influenced our understanding of the universe. These observations were published in 1610 in his book The Starry Messenger, which was written in a style that made it accessible to a wide audience. One of his observations was that Venus exhibits phases much like our Moon.
Part I: Venus in the Ptolemaic Model
In the Ptolemaic model, Venus moves on an epicycle whose center is always directly between Earth and the Sun. The figure on page 163 shows Venus in a series of locations around its epicycle. Your task is to sketch the appearance of Venus (as observed through a telescope from Earth), when Venus is at each of the five indicated positions. Use the following procedure:
For each of the five positions along the epicycle (i.e., the top half of the page) shade in the dark half of Venus.
For each of these positions, sketch (in the spaces at the bottom of the page) what Venus would look like as seen from Earth. In your sketches, shade the portion that would appear dark and leave alone the part that would appear bright.
1. Is there any location along the epicycle at which Venus would appear as a nearly full lit disk? (If there is, indicate which one.)
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