Chapter 3
What are Kepler's three laws of planetary motion?
1.) The orbit of each planet is an ellipse with the Sun at one focus. 2.) As a planet moves around its orbit it sweeps out equal areas in equal times. 3.) More distant planets orbit the Sun at slower average speeds: p2 = a3.
An asteroid orbits the Sun at an average distance a = 4 AU. How long does it take to orbit the Sun?
8 years We need to find p so that p2 = a3. Because a = 4, a3 = 43 = 64. Therefore, p = 8, p2 = 82 = 64.
Hallmarks of Science: #3
A scientific model must make testable predictions about natural phenomena that would force us to revise or abandon the model if the predictions do not agree with observations.
Darwin's theory of evolution meets all the criteria of a scientific theory. This means:
After more than 100 years of testing, Darwin's theory stands stronger than ever, having successfully met every scientific challenge to its validity.
What is an ellipse?
An ellipse looks like an elongated circle.
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.
How is modern science rooted in ancient astronomy?
Astronomy is the oldest of the sciences. It was often practiced for practical reasons. In keeping track of time and seasons for practical purposes, including agriculture for religious and ceremonial purposes In aiding navigation
The idealized scientific method:
Based on proposing and testing hypotheses Hypothesis = educated guess
Tycho Brahe
Brahe compiled the most accurate (1 arcminute) naked eye measurements ever made of planetary positions. He still could not detect stellar parallax, and thus still thought Earth must be at the center of the solar system (but recognized that other planets go around the Sun). He hired Kepler, who used Tycho's observations to discover the truth about planetary motion.
How did Copernicus, Tycho, and Kepler challenge the Earth-centered model?
Copernicus created a Sun-centered model Tycho provided the data needed to improve this model Kepler found a model that fit Tycho's data.
How did Copernicus, Tycho, and Kepler challenge the Earth-centered model?
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.
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...
A scientific theory must:
Explain a wide variety of observations with a few simple principles Be supported by a large, compelling body of evidence NOT have failed any crucial test of its validity
How did Galileo solidify the Copernican revolution?
Galileo (1564-1642) overcame major objections to the Copernican view. Three key objections rooted in the Aristotelian view were the following: Earth could not be moving because objects in air would be left behind. Noncircular orbits are not "perfect" as heavens should be. If Earth were really orbiting Sun, we'd detect stellar parallax.
Overcoming the first objection (nature of motion):
Galileo's experiments showed that objects in air would stay with a moving Earth. Aristotle thought that all objects naturally come to rest. Galileo showed that objects will stay in motion unless a force acts to slow them down (Newton's first law of motion).
Why does modern science trace its roots to the Greeks?
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.
How did Galileo solidify the Copernican revolution? .
His experiments and observations overcame the remaining objections to the Sun-centered solar system
Hallmarks of Science: #1
Modern science seeks explanations for observed phenomena that rely solely on natural causes. (A scientific model cannot include divine intervention.)
Kepler's Third Law
More distant planets orbit the Sun at slower average speeds, obeying the relationship p2 = a3 p = orbital period in years a = average distance from Sun in AU
So how does the Ptolemaic model explain retrograde motion?
Planets really do go backward in this model
In what ways do all humans employ scientific thinking?
Scientific thinking is based on everyday ideas of observation and trial-and-error experiments.
How did the Greeks explain planetary motion?
The Ptolemaic model had each planet move on a small circle whose center moves around Earth on a larger circle.
Why does modern science trace its roots to the Greeks?
They developed models of nature and emphasized that the predictions of models should agree with observations.
the Ptolemaic model:
The most sophisticated geocentric model was that of Ptolemy Sufficiently accurate to remain in use for 1500 years
Kepler's First Law:
The orbit of each planet around the Sun is an ellipse with the Sun at one focus.
Overcoming the third objection (parallax):
Tycho thought he had measured stellar distances, so lack of parallax seemed to rule out an orbiting Earth. Galileo showed stars must be much farther than Tycho thought—in part by using his telescope to see that the Milky Way is countless individual stars. If stars were much farther away, then lack of detectable parallax was no longer so troubling Galileo also saw four moons orbiting Jupiter, proving that not all objects orbit Earth.
Overcoming the second objection (heavenly perfection):
Tycho's observations of comet and supernova already challenged this idea. Using his telescope, Galileo saw: Sunspots on the Sun ("imperfections") Mountains and valleys on the Moon (proving it is not a perfect sphere)
