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The sun, moon, and planets sweep out a beautiful and complex dance across the heavens. Previous chapters have described that dance; this chapter describes how astronomers learned to understand what they saw in the sky and how that changed humanity’s understanding of what we are.
In learning to interpret what they saw, Renaissance astronomers invented a new way of knowing about nature, a way of knowing that we recognize today as modern science.
This chapter tells the story of heavenly motion from a cultural perspective. In the next chapter, we will give meaning to the motions in the sky by adding the ingredient
Renaissance astronomers were missing —gravity.

I. The Roots of Astronomy
A. Archaeoastronomy
B. The Astronomy of Greece
C. The Ptolemaic Universe
II. The Copernican Revolution
A. Copernicus the Revolutionary
B. Galileo the Defender
III. The Puzzle of Planetary Motion
A. Tycho the Observer
B. Tycho Brahe's Legacy
C. Kepler the Analyst
D. Kepler's Three Laws of Planetary Motion
E. The Rudolphine Tables
IV. Modern Astronomy

• Already in the stone and bronze ages, human cultures realized the cyclic nature of motions in the sky.
• Monuments dating back to ~ 3000 B.C. show alignments with astronomical significance.
• Those monuments were probably used as calendars or even to predict eclipses.

Summer solstice
• Constructed: 3000
– 1800 B.C.
Heelstone
• Alignments with locations of sunset, sunrise, moonset and moonrise at summer and winter solstices
• Probably used as calendar.

Big Horn Medicine Wheel (Wyoming)

Caracol (Maya culture, approx. A.D. 1000)

Ancient Greek Astronomers (1)
• Unfortunately, there are no written documents about the significance of stone and bronze age monuments.
• First preserved written documents about ancient astronomy are from ancient Greek philosophy.
• Greeks tried to understand the motions of the sky and describe them in terms of mathematical (not physical!) models.

Ancient Greek Astronomers (2)
Models were generally wrong because they were based on wrong “first principles”, believed to be “obvious” and not questioned:
1. Geocentric Universe: Earth at the
Center of the Universe.
2.
“Perfect Heavens”: Motions of all celestial bodies described by motions involving objects of “perfect” shape, i.e., spheres or circles.

Ancient Greek Astronomers (3)
• Eudoxus (409 – 356 B.C.):
Model of 27 nested spheres
• Aristotle (384 – 322 B.C.), major authority of philosophy until the late middle ages:
Universe can be divided in 2 parts:
1. Imperfect, changeable Earth,
2. Perfect Heavens (described by spheres)
• He expanded Eudoxus’ Model to use 55 spheres.

Angular distance between
Syene and Alexandria:
~ 7 0
Linear distance between
Syene and Alexandria:
~ 5,000 stadia
 Earth Radius ~ 40,000 stadia (probably ~ 14 % too large) – better than any previous radius estimate.

(SLIDESHOW MODE ONLY)

• Hipparchus: Placing the Earth away from the centers of the
“perfect spheres”
• Ptolemy: Further refinements, including epicycles

Introduced to explain retrograde
(westward) motion of planets

(SLIDESHOW MODE ONLY)

Nicolaus Copernicus (1473 – 1543):
Heliocentric Universe (Sun in the Center)

Copernicus’ new (and correct) explanation for retrograde motion of the planets
Retrograde
(westward) motion of a planet occurs when the
Earth passes the planet.
This made Ptolemy’s epicycles unnecessary.

• Invented the modern view of science:
Transition from a faithbased “science” to an observation-based science.
• Greatly improved on the newly invented telescope technology. (But Galileo did
NOT invent the telescope!)
• Was the first to meticulously report telescope observations of the sky to support the Copernican Model of the
Universe.

Major Discoveries of Galileo
• Moons of Jupiter
(4 Galilean moons)
(What he really saw)
• Rings of Saturn
(What he really saw)

• Surface structures on the moon; first estimates of the height of mountains on the moon

• Sun spots (proving that the sun is not perfect!)

• Phases of Venus (including “full Venus”), proving that Venus orbits the sun, not the Earth!

• Used the precise observational tables of
Tycho Brahe (1546 – 1601) to study planetary motion mathematically.
• Found a consistent description by abandoning both
1. Circular motion and
2. Uniform motion.
• Planets move around the sun on elliptical paths, with non-uniform velocities.

1. The orbits of the planets are ellipses with the sun at one focus.
c
Eccentricity e = c/a

1) 2) 3) e = 0.02
e = 0.1
e = 0.2
4) e = 0.4
5) e = 0.6

Orbits of planets are virtually indistinguishable from circles:
Earth: e = 0.0167
Most extreme example:
Pluto: e = 0.248

• A line from a planet to the sun sweeps over equal areas in equal intervals of time.
• A planet’s orbital period (P) squared is proportional to its average distance from the sun (a) cubed:
P y
2 = a
AU
3
(P y
= period in years; a
AU
= distance in AU)

archaeoastronomy eccentric uniform circular motion geocentric universe parallax retrograde motion epicycle deferent equant heliocentric universe paradigm ellipse semimajor axis, a eccentricity, e hypothesis theory natural law

1. Historian of science Thomas Kuhn has said that De
Revolutionibus was a revolution-making book but not a revolutionary book. How was it an old-fashioned, classical book?
2. Why might Tycho Brahe have hesitated to hire
Kepler? Why do you suppose he appointed Kepler his scientific heir?
3. How does the modern controversy over creationism and evolution reflect two ways of knowing about the physical world?

Quiz Questions
1. Why are Stonehenge and The Big Horn Medicine Wheel thought to be ancient astronomical observatories?
a. Petroglyphs at each site describe how they were used to make observations.
b. Ancient Greek writings list the important discoveries made at each of these two sites.
c. Stones at each site aligned with significant rising and setting positions.
d. Both a and c above.
e. All of the above.

Quiz Questions
2. Plato proposed that all heavenly motion is a. constantly changing b. circular c. uniform d. Answers a and b above.
e. Answers b and c above.

Quiz Questions
3. How did Claudius Ptolemaeus account for the retrograde motion of the planets?
a. Planets slow down, stop, and then reverse their orbital direction around the Sun. b. Inner planets orbit the Sun faster and pass outer planets as they orbit around the Sun.
c. Each planet moves on an epicycle, that in turn moves on a deferent that circles around Earth.
d. The Sun and Moon orbit Earth, whereas all the other planets orbit the Sun.
e. None of the above.

Quiz Questions
4. Who accurately determined the size of Earth by considering
Sun angles at Syene and Alexandria?
a. Thales of Miletus (c. 624-547 BC) b. Pythagoras (c. 570-500 BC) c. Eudoxus (409-356 BC) d. Aristotle (384-322 BC) e. Eratosthenes (c. 200 BC)

Quiz Questions
5. One of the first principles of ancient astronomy is that the heavens beyond _____ are perfect, and the Earth is corrupt.
a. the atmosphere b. the Sun c. the Moon d. Saturn e. Pluto

Quiz Questions
6. Who taught that the Earth is stationary and at the center of the universe with the Sun, the Moon, and the planets moving around Earth in perfect circles?
a. Thales of Miletus (c. 624-547 BC) b. Pythagoras (c. 570-500 BC) c. Eudoxus (409-356 BC) d. Aristotle (384-322 BC) e. Eratosthenes (c. 200 BC)

Quiz Questions
7. How did Nicolaus Copernicus account for the retrograde motion of the planets?
a. Planets slow down, stop, and then reverse their orbital direction around the Earth. b. Inner planets orbit the Sun faster and pass outer planets as they orbit around the Sun.
c. Each planet moves on an epicycle, that in turn moves on a deferent that circles around Earth.
d. The Sun and Moon orbit Earth, whereas all the other planets orbit the Sun.
e. None of the above.

Quiz Questions
8. What feature of Aristotle's model of the universe was included in the model proposed by Copernicus?
a. Earth is stationary and at the center.
b. Mercury and Venus move around the Sun.
c. Mars, Jupiter, and Saturn move around Earth.
d. Uniform circular motion.
e. Elliptical orbits.

Quiz Questions
9. Why did the model of the universe proposed by Copernicus gain support soon after its publication? a. It more accurately predicted the position of planets.
b. It gave a better explanation for the phases of the Moon.
c. It was a more elegant explanation of retrograde motion.
d. The old system of Ptolemy was never very popular.
e. It displaced Earth from the center of the universe.

Quiz Questions
10. When Tycho observed the new star of 1572, he could detect no parallax. Why did that result undermine belief in the
Ptolemaic system?
a. This star is closer than the Moon, and thus stars are not all at the same distance.
b. This star is closer than the Moon, and thus smaller than other stars.
c. This star is farther away than the Moon, and thus the heavens are perfect and unchanging.
d. This star is farther away than the Moon, and thus the heavens are not perfect and unchanging.
e. This star is planet-like.

Quiz Questions
11. What was the most important contribution of Tycho Brahe to modern astronomy?
a. The invention of the optical telescope.
b. The discovery of four moons orbiting Jupiter.
c. A model of the universe that was part Aristotelian and part
Copernican.
d. The study of the Supernova of 1572. e. Twenty years of accurate measurements of planetary positions.

Quiz Questions
12. How was Tycho Brahe able to make more accurate astronomical measurements than had been made before his time?
a. He used a telescope to magnify the image and spacing of celestial objects.
b. He designed and used large devices to measure small angles. c. His island observatory was hundreds of miles offshore, under very dark skies.
d. His observatory was at high elevation and thus above much of Earth's atmosphere.
e. All of the above.

Quiz Questions
13. How did Kepler's first law of planetary motion alter the
Copernican system?
a. It changed the perfect circles to ellipses.
b. It added epicycles to the perfect circles.
c. It placed the Sun at one focus of each orbit.
d. Answers a and c above.
e. Answers b and c above.

Quiz Questions
14. Which of the "First Principles of Ancient Astronomy" did
Kepler's laws contradict?
a. Earth is at the center of the universe.
b. The heavens are perfect and Earth is imperfect.
c. All heavenly motion is uniform and circular.
d. Both a and b above.
e. Both a and c above.

Quiz Questions
15. What does Kepler's second law indicate about the orbital speed of a planet?
a. The orbital speed of each planet is constant.
b. A planet moves at its slowest when it is closest to the Sun.
c. A planet moves at its fastest when it is closest to the Sun.
d. The orbital speed of a planet varies in no predictable way.
e. None of the above.

Quiz Questions
16. If the semimajor axis of a planet is 4 AU, what is its orbital period?
a. 4 years.
b. 8 years.
c. 16 years.
d. 64 years.
e. It cannot be determined from the given information.

Quiz Questions
17. Galileo's discovery of four moons orbiting Jupiter showed that planetary bodies could move and carry moons. This supports the model of the universe presented by a. Aristotle b. Claudius Ptolemaeus c. Nicolaus Copernicus d. Both a and b above.
e. All of the above.

Quiz Questions
18. What phases of Venus are predicted by the Ptolemaic system?
a. New and Crescent phases only.
b. Quarter and Gibbous phases only.
c. Gibbous and Full phases only.
d. Crescent and Gibbous phases only.
e. New, Crescent, Quarter, Gibbous, and Full phases.

Quiz Questions
19. What phases of Venus were observed by Galileo?
a. New and Crescent phases only.
b. Quarter and Gibbous phases only.
c. Gibbous and Full phases only.
d. Crescent and Gibbous phases only.
e. New, Crescent, Quarter, Gibbous, and Full phases.

Quiz Questions
20. The phases of Venus observed by Galileo support the model of the universe presented by a. Aristotle b. Claudius Ptolemaeus c. Nicolaus Copernicus d. Both a and b above.
e. All of the above.

Answers
1.
c
2.
e
3.
c
4.
e
5.
c
6.
d
7.
b
8.
d
9.
c
10.
d
11.
e
12.
b
13.
d
14.
e
15.
c
16.
b
17.
c
18.
a
19.
e
20.
c