Planetary Motions

How did astronomical observations benefit ancient societies? In keeping track of time and seasons for practical purposes, including agriculture for religious and ceremonial purposes In aiding navigation

Ancient people of central Africa (6500 B. C Ancient people of central Africa (6500 B.C.) could predict seasons from the orientation of the crescent moon. Here’s an example of the practical application of observations: Africans could determine where they were in the rainy season or dry season from observations of the crescent moon.

Days of the week were named for the Sun, Moon, and visible planets. And here’s an example that we still live with today… Days of the week were named for the Sun, Moon, and visible planets.

What did ancient civilizations achieve in astronomy? Daily timekeeping Tracking the seasons and calendar Monitoring lunar cycles Monitoring planets and stars Predicting eclipses And more… Here we list a few examples of what ancient civilizations learned to do. The next several slides are a brief “slide show” of ancient structures.

Egyptian obelisk: Shadows tell time of day.

SW United States: “Sun Dagger” marks summer solstice

Scotland: 4000-year-old stone circle; Moon rises as shown here every 18.6 years.

Machu Picchu, Peru: Structures aligned with solstices Note: fun to discuss the claims that these had to have been made by “ancient astronauts”… Machu Picchu, Peru: Structures aligned with solstices

South Pacific: Polynesians were very skilled in the art of celestial navigation.

This picture is not in the text, but very cool—possible evidence of astronomical observations by cave dwellers. France: Cave paintings from 18,000 B.C. may suggest knowledge of lunar phases (29 dots).

This map is not in the book, but may be useful for giving students some context on the locations of ancient civilizations and the way the Greek empire was able to be a crossroads at which the knowledge of many cultures was combined. Point out location of Alexandria for context on the library... Our mathematical and scientific heritage originated with the civilizations of the Middle East.

The Geocentric Model Greek geocentric model (c. 400 B.C.) Greeks were the first people known to make models of nature. They tried to explain patterns in nature without resorting to myth or the supernatural. The ’Geocentric Model’, is a model that states that the Earth is the center of the universe and all objects in the heaven rotate about the Earth. This model lasted for about 2000 years. Greek geocentric model (c. 400 B.C.)

The Greeks measured the radius of the Earth Used shadows at noon to measure the radius of the Earth (c. 240 B.C.) This slide is based on the Special Topic box showing Eratosthenes’s calculation. Measured Radius ≈ 42,000 km (how good is this answer)?

Problems with the geocentric model Problems with the geocentric model. It could not explain the apparent retrograde motion of planets. You may wish to review what we mean by apparent retrograde motion before showing the Greek explanation… Example. Mars orbits the Sun more slowly than Earth. Over a period of 10 weeks as the Earth catches up with and eventually overtakes Mars, Mars appears to stop, back up, then go forward again.

The most sophisticated geocentric model was that of Ptolemy (A. D The most sophisticated geocentric model was that of Ptolemy (A.D. 100–170)— the Ptolemaic model: Sufficiently accurate to remain in use for 1500 years Arabic translation of Ptolemy’s work named Almagest (“the greatest compilation”) Ptolemy

So how does the Ptolemaic model explain retrograde motion So how does the Ptolemaic model explain retrograde motion? Planets really do go backward in this model. Note that we describe “circle upon circle” motion, avoiding use of “epicycle” and “deferent” in order to keep jargon to a minimum. You might wish to discuss the complexity of this model to help set stage for Copernican revolution.

Thought Question Which of the following is NOT a fundamental difference between the geocentric and Sun-centered models of the solar system? Earth is stationary in the geocentric model but moves around the Sun in Sun-centered model. Retrograde motion is real (planets really go backward) in the geocentric model but only apparent (planets don’t really turn around) in the Sun-centered model. Stellar parallax is expected in the Sun-centered model but not in the Earth-centered model. The geocentric model is useless for predicting planetary positions in the sky, whereas even the earliest Sun-centered models worked almost perfectly. Optional thought question to check student understanding…

How did Islamic scientists preserve and extend Greek science? The Muslim world preserved and enhanced the knowledge they received from the Greeks while Europe was in its Dark Ages. Al-Mamun’s House of Wisdom in Baghdad was a great center of learning around A.D. 800. With the fall of Constantinople (Istanbul) in 1453, Eastern scholars headed west to Europe, carrying knowledge that helped ignite the European Renaissance.

How did Copernicus, and Kepler challenge the Earth-centered idea? Copernicus proposed the Sun-centered model (published 1543). He used the model to determine the layout of the solar system (planetary distances in AU). But . . . The model was no more accurate than the Ptolemaic model in predicting planetary positions, because it still used perfect circles. It did explain apparent retrograde motion. Model was also nearly as complex as the Ptolemaic model because he still used circles upon circles (epicycles) to try to get better matches to data.

But an 8-arcminute discrepancy led him eventually to ellipses. Kepler first tried to match observed planetary motions with circular orbits. But an 8-arcminute discrepancy led him eventually to ellipses. “If I had believed that we could ignore these eight minutes [of arc], I would have patched up my hypothesis accordingly. But, since it was not permissible to ignore, those eight minutes pointed the road to a complete reformation in astronomy.” Kepler quote offers a good opportunity to talk about the nature of science, and how failure to match observations should force a change in our hypotheses… Johannes Kepler (1571–1630)

An ellipse looks like an elongated circle. What is an ellipse? Use this slide to review ellipses and the definition of eccentricity. An ellipse looks like an elongated circle.

Eccentricity of an Ellipse You can also use this tool to explain eccentricity (from the tutorial on Orbits and Kepler’s Laws). Eccentricity and Semimajor Axis of an Ellipse

What are Kepler’s three laws of planetary motion? Kepler’s First Law: The orbit of each planet around the Sun is an ellipse with the Sun at one focus.

Kepler’s Second Law: As a planet moves around its orbit, it sweeps out equal areas in equal times. This means that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun.

You can use this tool to demonstrate Kepler’s first two laws. Kepler's 2nd Law

Now work on the lecture tutorial for Kepler’s Second Law – Page 21-24