Students will learn about the historical evolution of models of the Solar System with particular emphasis on the attempt to solve the riddle of the apparent retrograde movement of Mars.

The film clips, set in ancient times, show the geocentric system of Ptolemy which held that the planets and the Sun move around the Earth. This demonstrates that the modern view of the Solar system took centuries to develop and introduces students to Hypatia, the greatest women of ancient Greek mathematics and philosophy. Animations from the Internet show how the motion of the planets (the “wanderers” in ancient Greek) are explained in both the geocentric and heliocentric models of the Solar system.

In clip # 1 Hypatia is shown teaching in fifth century Alexandria. She gives the ancient explanation for the tendency of objects to fall to earth, i.e., the assumption that the Earth is at the center of the Universe, to which all objects are attracted.

Clip #1 from Agora: From 0:00:48 to 0:04:26. This clip starts at the beginning of the film, just after opening credits, when the night sky is shown from outer space and the legend explaining the setting of the film comes onto the screen. It ends after the scene of the prayer to Sarapis. Explain to the class that Hypatia is teaching within the Library of Alexandria which was also a center for worship of the Pagan gods.

Clip #2 from Agora: From 0:12:00 to 0:15:34. This clip begins just after Hypatia has put salve on Davus’ back where he was whipped by her father. She sees his model of the Ptolemaic system. Orests then criticizes the Ptolemaic system because it is not straightforward, instinctively applying Occam’s Razor. He is criticized by a Christian who for not accepting the universe as God made it. The clip ends when Hypatia states that despite all that is going on in the streets, the scholars in the class are all brothers and asks for a round of applause for Davus’ model.

Animation # 1 shows the Ptolemaic system. This short animation made need to be allowed to run server al times.

Animation #2 explains the apparent retrograde motion of Mars in the heavens. Show this short animation several times, pointing out the difference in the speeds at which the Earth and Mars orbit the Sun. Point out the site lines that show when the animation is not moving.

An alternative suitable for 11th and 12th Grade Honors classes or for college-level students is to also use a clip in which Hypatia discovers that the Earth moves around the Sun in an eliptical orbit. This clip lasts for about 4.5 minutes from 1:41:18 to 1:45:42. There is no evidence in the historical record that this discovery was made until some 1200 years after Hypatia died when Copernicus, inspired by Aristarcus, demonstrated that the Sun was the center of the solar system and Kepler discovered that the Earth’s orbit around the Sun was eliptical in shape. Second, the scene does not accurately show the process by which such a discovery would have been made because it would have been based on precise astronomical measurements and testing and rejecting various hypotheses to arrive at a hypothesis which seemed to match observations. TWM recommends showing this scene only if, through class assignments or lectures, the class looks carefully at empricism in Ancient Greco-Roman science.

The geocentric model, not only of the Solar System, but of the Universe held sway from the time of the ancient Greeks hundreds of years before Christ and was only challenged in the 16th century C.E. after which it was gradually replaced by the heliocentric view of the Solar System and a view of the Universe that has no particular center. The main proponents of the geocentric system were Aristotle and Ptolemy. Geocentrism was endorsed by the early Christians and the Catholic church because it appeared to be consistent with certain Biblical passages. (Joshua 10:12 in which the Sun and Moon are said to stop in the sky, and Psalms 93:1 in which the world is described as immobile.) Even today, some adherents of Biblical fundamentalism claim that the Earth is the center of the Universe and that the Sun revolves around the Earth.

The Ptolemaic geocentric system posited that the circle was a perfect shape and that all movements in the heavens were circular.

The latter was first challenged by the apparent movement of the planets in the sky with respect to the stars, particularly that of Mars, in its recurrent retrograde motion. It appears to move backward and form a loop for a brief time before resuming its regular path across the star field.

Hypatia’s fictional slave Davus makes a model that illustrates the solution proposed by Ptolemy to explain the retrograde motion of the planets preserving the circle as the only possible orbit (clip #2). Ptolemy’s explanation involves the superposition of two circular motions which, together, are able to explain the retrograde motion of Mars together with the other observed paths of the planets across the sky while keeping the Earth at its center.

But adding circle upon circle only made the models more complicated and it is an accepted principle among scientists to think that nature tends toward the simple. This idea is behind Occam’s Razor, a principle of logic by which the simpler option is preferred between competing theories, all else being equal. So, the Ptolemaic model with its epicycles seemed a strained explanation of the observed motion of the planets. To move away from it, however, it would take two more gigantic leaps in understanding that would have to wait more than a thousand years after the time of Hypatia.

The first new concept was that the Earth is not the center of the Universe and the second was to let go of the notion that the circle was the only possible orbit in the Universe.

Polish astronomer Nikolas Copernicus hypothesized in 1543 that the Sun, and not the Earth, was at the center of the Solar System. A debate followed for many years. Shortly afterward the Danish astronomer Tycho Brahe tried to come up with a compromise between both models, placing the Earth in the center of the universe and placing the Moon and the Sun in (circular) orbits around it. All the planets also had a circular orbit around the Sun. The spell of circularity was difficult to shake off.

The finding that orbits of the planets were not circular, but were instead elliptical was made by Johannes Kepler. For a summary of their discoveries see Nikolaus Copernicus, Tycho Brahe, & Johannes Kepler

1. Be familiar with the location of the clips on the DVD, check for accuracy of the minute and second locations of the clips on the DVD, and practice getting quickly from one film clip to the other. Also review the animations and practice making them repeat.

2. Review the Helpful Background Section including the links cited to determine what information to present to the class.

3. Cue the DVD to the beginning of the first clip.

1. Introduce the geocentric model of the solar system, relating it to the obvious observation that the sun “moves” across the sky and the Earth appears solid and stationary. Tell students a little about Hypatia, perhaps the greatest female mathematician and philosopher, who had a school in Alexandria, Egypt, during the Fourth Century C.E.

2. Show Clip # 1 to illustrate this worldview as held by the Greeks in Hypatia´s time.

3. Introduce the concept of the planets, “the wanderers,” which move differently than the stars. Introduce the problem of the retrograde motions of the planets, particularly Mars.

4. Show Clip # 2 to illustrate how the Ptolemaic model could be tweaked to make it explain the retrograde motion of the planets. Introduce the discomfort of scientists with explanations that rely on convoluted models and relate this to the preference towards simple models and theories known as Occam’s Razor. Note that this is what the character Orestes was talking about when he complained that the Ptolemaic model was whimsical.

5. Show the animation of the Ptolemaic system (Animation 1). Show the animation several times so that students understand what is going on.

6. Explain the discoveries of Copernicus and Tycho Brahe and Kepler.

7. Have students explain, if they can, how these theories solve the problem of the apparent retrograde motion of Mars.

8. Show Animation #2: the retrograde motion of Mars. Show the animation several times so that students understand what is going on. Explain to them the sight lines when the animation is paused and then run the animation again.

two static depictions of the retrograde motion of the planets

The Ptolemaic Model from the Polaris Project with a simple animation that shows the operation of the Ptolemaic model.

1. Students can be asked to research and write an essay or a report to the class (or both) on the contributions to astronomy of one of each of the following: Hypatia, Aristotle, Ptolemy, Tycho Brahe, Johannes Kepler, Nikolas Copernicus, Galileo, and Isaac Newton.

2. Students can be asked to research Occam’s Razor and provide an example of its use in developing scientific theories.

Using the Third Clip – Hypatia Discovering a Heliocentric Solar System with Eliptical Orbits
An Assignment for Honors Level 11th and 12th Grades or for College

From 1:41:18 to 1:45:42 Hypatia, like a good Neoplatonist, reasons her way to a recognition that the Earth moves around the Sun in an eliptical orbit. The analysis of this fictitious scene will help students understand the difference between empiricist attitudes of modern science and the non-empiricist ideals of the Neoplatonists. For a full discussion of this, see Was Hypatia of Alexandria a Scientist? a film review by S. James Killings, on sceptic.com; this article challenges the credibility of the scene; be sure to read the comments to the article which support the credibility of the scene and strongly challenge the thesis of the main article. See also Richard Carrier’s Blog of August 1, 2010 which also challenges Killings’ hypothesis.

Have students prepare a research paper based on the following prompt:

The scene in which Hypatia, a Neoplatonist, reasons her way to a recognition that the Earth moves around the Sun in an eliptical orbit, a theory that will not be taken seriously until the discoveries of Copernicus and Kepler 1200 years after Hypatia’s death, has been criticized by many because there is no historical support for it. Others say that all of Hypatia’s writings were lost and that it is a logical jump to think that she could have made this discovery on her own. Note that Copernicus and Kepler made their discoveries by applying the scientific method which is an expression of the branch of philosophy called Empiricism. Write an essay evaluating this scene as a piece of historical fiction, i.e., whether there is a reasonable possibility that Hypatia could have made this discovery. In your essay describe and comment on Neoplatonist views about observations of physical phenomena as a means of ascertaining the truth, the strength of Empricism in Greco-Roman philosophy and, of course, the writings of Antarchus and Ptolemy on the subject of the Solar system.

SNIPPET MENU:

Learner Outcomes/Objectives
Rationale
Description of the Snippet
Helpful Background

Using the Snippet in Class:

Preparation
Step by Step
Other Helpful Resources
Assignments

LOCATION:

Minute and second calculations may differ from what is set out below. Check your disc for exact locations before using the film in class.

Clip #1 from Agora:

From 0:00:48 to 0:04:26.

Clip #2 from Agora:

From 0:12:00 to 0:15:34.

Animation #1:

detailed animation of The Ptolemaic System

Animation #2:

retrograde motion of Mars.

Possible Problems for the Clips Used in this Snippet Lesson Plan:

None.

What about using the whole movie?

The film has several substantial historical inaccuracies, particularly the discovery by the Hypatia character of the elliptical orbit of the Earth around the Sun. The understanding of those concepts would have to await the work of Copernicus, Brahe, and Kepler some 1200 years later.

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