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Chapter 04 - Renaissance Astronomy
CHAPTER 4
RENAISSANCE ASTRONOMY
CHAPTER OUTLINE AND LECTURE NOTES
1. Astronomy After Ptolemy
In an earlier edition of the book I mistakenly referred to the Islamic astronomers as Arabic
astronomers. It was pointed out to me that although the Islamic astronomers were required
to publish their work in Arabic, they often resented this requirement and would have
preferred to write in their native languages.
2. The Rebirth of Astronomy in Europe
I think it is important to emphasize the slow growth of scientific thought in the centuries
before Copernicus in order to show that his ideas developed from those of his predecessors
rather than appearing from nowhere to confront a previously unquestioned Ptolemaic
model.
3. Copernicus
Nothing seems to work like a mechanical model of the solar system (an orrery) to convince
the students that the heliocentric model can produce retrograde motion. At Iowa we built a
geared device that has two arms with balls, representing planets, that sweep out circles in
different periods of time. A rod with an arrowhead on one end connects the two balls and
points in the direction in which one planet is viewed from the other as they orbit. If you
have such a device, be sure to emphasize that it is the direction in which the arrow points,
rather than the position of the arrowhead that is important and shows retrograde motion
whenever the two planets pass each other. If there is an arrowhead on each end of the rod,
you can show that each planet sees the other in retrograde motion when they pass. Another
idea is to ask the students to imagine how we would see Mars move first if the Earth were
stationary and Mars moved (steady prograde motion) and then if Mars were stationary and
the Earth moved (back and forth motion, or parallax). The actual motion of Mars is the
combination of these two motions. This is shown in Figure 4.4.
4. Tycho Brahe—The Great Observer
Tycho actually used what we would recognize as the scientific method to reject the model
of Copernicus. On the basis of the heliocentric model, he predicted that parallax should be
detectable. He then tested this prediction, found no parallax, and modified the Copernican
model accordingly. Tycho’s model is a coordinate transformation of the model of
Copernicus but, with the Earth stationary, doesn’t produce parallax.
5. Kepler and Planetary Orbits
Kepler’s laws come up repeatedly throughout the rest of the book, so it’s important for the
students to get a good grip on them now. Figures 4.15 may help students understand
Kepler’s 2nd Law.
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Chapter 04 - Renaissance Astronomy
6. Galileo and the Telescope
Although Galileo made many significant observations, some of the most important were
that Venus shows a full range of phases from crescent to gibbous. This clearly showed that
the Ptolemaic model was wrong, although the Earth-centered model of Tycho was still
possible.
KEY TERMS
aphelion — The point in the orbit of a solar system where it is farthest from the Sun.
astronomical unit (AU) — The average distance between the Earth and the Sun.
eccentricity — A measure of the extent to which an orbit departs from circularity. Eccentricity
ranges from 0.0 for a circle to 1.0 for a parabola.
ellipse — A closed, elongated curve describing the shape of the orbit that one body follows
about another.
focus — One of two points from which an ellipse is generated. For all points on the ellipse, the
sum of the distances to the two foci is the same.
greatest elongation — The position of Mercury or Venus when it has the greatest angular
distance from the Sun.
impetus — A theory of motion, developed in the fourteenth and fifteenth centuries, that motion
could continue only so long as a force was at work.
inferior planet — A planet whose orbit lies inside the Earth’s orbit.
Kepler’s laws of planetary motion — Three laws, discovered by Kepler, that describe the
motions of the planets around the Sun.
major axis — The axis of an ellipse that passes through both foci. The major axis is the longest
straight line that can be drawn inside an ellipse.
perihelion — The point in the orbit of a body when it is closest to the Sun.
semimajor axis — Half of the major axis of an ellipse. Also equal to the average distance from
the focus of a body moving on an elliptical orbit.
sidereal period — The time it takes for a planet or satellite to complete one full orbit about the
Sun or its parent planet.
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Chapter 04 - Renaissance Astronomy
stellar parallax — The shift in the direction of a star caused by the change in the position of the
Earth as it moves about the Sun.
superior planet — A planet whose orbit lies outside the Earth’s orbit.
transverse velocity — The part of the orbital speed of a body perpendicular to the line between
the body and the Sun.
ANSWERS TO QUESTIONS AND PROBLEMS
Conceptual Questions
1. As seen from Mars, the Earth undergoes retrograde motion when the Earth passes Mars.
2. They have very long orbital periods, so the Earth requires only a little more than a year to
catch up with and pass them again.
3. Both systems predicted that Mars, Jupiter, and Saturn could be seen only at gibbous and full
phases. Thus, the phases of the outer planets could not be used as a way to test the
superiority of either system.
Problems
1. 1.5 years, 1.5 years
2. 0.59 years
3. 3.5 years
4. either 3 years or 0.6 years
5. 19.8 years
6. 0.4 years
7. 0.94 AU
8. 41°
9. The star’s diameter would be 2 AU, much larger than the Sun.
10. eccentricity = 0.5, perihelion = 5 cm, aphelion = 15 cm
11. 0 cm, this is a circle.
12. 29.6 AU, 49.4 AU, 1.67
13. 0.59 years
14. 6.5 years
15. 0.79 AU
16. 8.5 AU
Figure-Based Questions
1. 0.47 AU, 1 AU, the angle is 28°, the sine of 28° is 0.47
2. 0.47, 0.09, 0.67
3. About 52
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