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Transcript
CHAPTER 2
From an Earth-Centered to a Sun-Centered System
CHAPTER OUTLINE
2-1 Science and Its Ways of Knowing
1. Science is about discovering the orderliness of nature and the rules that govern this
order. It is also the body of knowledge about nature that represents the collective efforts
of people throughout history. Science progresses through the interaction of observations
and experiments with theory.
2. It is especially important to recognize the different meanings of the words “fact” and
“theory” as they are used in science compared to their everyday meanings.
3. The scientific method is a never-ending cycle of hypothesis, prediction, data
gathering, and verification.
4. A scientific hypothesis is an educated guess made in describing the results of an
experiment or observation. A hypothesis can be wildly speculative but must make
testable predictions.
5. A scientific fact is generally a close agreement by competent observers of a series of
observations of the same phenomenon.
6. A scientific law or principle is a scientific hypothesis that has been repeatedly tested
and has not been contradicted.
7. A scientific model is a description of a phenomenon, based on observation,
experiment, and theoretical considerations. It is not necessarily the truth or reality, but a
description that allows prediction of future events.
8. A scientific theory is a synthesis of a large body of information that encompasses
well-tested (by repeatable experiments) and verified hypotheses about certain aspects of
the natural world. No theory can be proven to be true, but data can prove a theory to be
false.
9. In science a scheme is not usually called a theory until its ideas are shown to fit
observed data successfully. In every-day language, however, the word “theory” is often
used to refer to ideas that are much more fanciful and less secure.
Criteria for Scientific Models
1. The model must fit the data.
2. The model must make predictions that can be tested and be of such nature that it would
be possible to disprove the model.
3. The model should be as simple as possible. The principle that the best explanation is
the one that requires the fewest unverifiable assumptions is called Occam’s razor.
2-2 From an Earth-Centered to a Sun-Centered System
1. We examine these theories of the observed motions of stars and planets to answer the
question of where the Earth fits into the scheme of things, to see how well they match the
criteria for a good scientific theory.
2. To understand how astronomy—and science in general—works, we must look at how
it progresses with time.
2-3 The Greek Geocentric Model
1. There is a fundamental difference between the contributions to astronomy made by the
ancient Greeks and those made by other ancient civilizations. They were interested in
astronomy because of a pure philosophical desire to understand how the universe works.
They believed in, and looked for, a sense of symmetry, order, and unity in the cosmos.
They took the first steps in creating a unified model of the universe.
2. Aristotle argued that the absence of parallax for the stars in the sky implied that the
Earth must be at the center of the solar system. This is a valid scientific argument.
3. Parallax is the apparent shifting of nearby objects with respect to distant ones as the
position of the observer changes.
4. Stellar parallax is the apparent annual shifting of nearby stars with respect to
background stars, measured as the angle of shift. It was not observed until 1838; the
greatest annual shift observed for any star is only 1.5 arcseconds.
5. Even though Aristotle used a correct logical argument, the conclusion was wrong
because it was based on incomplete data. Parallax is hard to observe because stars are at
great distances from us.
6. Aristotle used very good arguments to conclude that the Moon and Earth are spherical
and that the Sun is farther away from earth than the Moon is.
7. Aristotle saw a difference in the “natural” behavior of Earthly objects compared to
heavenly objects. He believed that two different sets of rules existed, one for Earthly
objects and one for celestial objects.
8. The Greeks’ love of geometry led them to construct a model of the heavens based on
spheres, with the Earth at the center. In order to account for the Sun’s apparent motion in
the sky, the Sun was located on a sphere around the Earth, inside the celestial sphere of
the stars. The axes of the two spheres were tilted with respect to one another.
9. Ptolemy (150 AD) presented the most comprehensive geocentric model, called the
Ptolemaic model. Presented in his book called the Almagest, lasted for almost 1400
years after his death.
10. Because the heavens were viewed as perfect, the use in the Ptolemaic model of the
symmetrical circle to model the motions of celestial objects was thought to be the most
reasonable choice.
11. Any model for the planets must explain the various motions of all celestial objects,
such as the Sun, Moon, and planets.
A Model of Planetary Motion: Epicycles
1. Ptolemy’s geocentric model was able to explain the planetary motions using epicycles.
An epicycle is the circular orbit of a planet, the center of which revolves around the Earth
in another circle.
2. The model retained the idea of perfect heavenly circles and uniform speeds. (In an
effort to match the observations, Ptolemy actually did try models with varying speeds for
the planets and moved the Earth off-center among the planets’ paths.) The model
explained why the planets never move far from the ecliptic, but treated Mercury and
Venus as special cases in order to explain their small elongations.
3. Ptolemy’s model meets the first two criteria for a scientific model fairly well but it is
much less successful with the third.
4. The Ptolemaic model did fit the data and made testable predictions, so we must judge it
as an acceptable model even though it lacked that certain neatness we would like.
2-4 Aristarchus’s Heliocentric Model
1. 400 years before Ptolemy, around 280 BC, the Greek philosopher Aristarchus
proposed a moving-Earth solution to explain celestial motions. He introduced the concept
of a spinning Earth and the first heliocentric model, meaning centered on the Sun, 1800
years before Copernicus.
2. Even though Aristarchus could not explain the lack of observable parallax at his time
(Aristotle’s argument), he believed that the Sun was at the center of the solar system
because it was much bigger in size than the Earth.
3. With powerful and simple arguments based on observations he concluded that the Sun
was about 20 times farther from the Earth than the Moon is (the correct value is about
390). He showed that the Earth is 3 times larger than the Moon in diameter, and that the
Sun is about 20 times larger than the Moon in diameter. This implies that the Sun is about
7 times larger than the Earth in diameter.
4. Aristarchus was the first to create a map of the solar system. He simply did not have
the scale for it.
Measuring the Size of the Earth
1. Eratosthenes (276–195 BC) was the first person to clearly understand the shape and
approximate size of the Earth.
2. By comparing shadows at noon during summer solstice at two different locations he
understood that the Sun must be directly overhead (at the zenith) in Syene but that the
Sun’s direction was off the vertical by 7 in Alexandria.
3. He realized that the 7 difference was due to the Earth’s curvature and therefore the
Earth’s circumference was about 360/7  50 times the distance between the two cities.
Knowing this distance he was able to find the Earth’s diameter. His calculation was very
close to the correct value.
4. Combining the calculations of Aristarchus and Eratosthenes, the ancient Greeks had
for the first time measurements of the radii of Earth, Moon, and Sun and their relative
distances. We had to wait until 1769 AD to observe the actual value of the astronomical
unit and thus the true dimensions of the solar system.
5. The important point here is not the accuracy of the measurements but the power of
simple logical arguments that allowed the ancient Greeks to have a very good sense of
the solar system more than 2200 years ago.
Advancing the Model: Astrology and Science
1. Astrology is the belief that the relative positions of the Sun, planets, and Moon affect
the destiny of humans. Casting a horoscope involves determining the positions of
significant heavenly objects at the moment of the person’s birth
Scientific Criteria Applied to Astrology
1. Does astrology fit the observations? It has been tested many times, but invariably the
tests show that astrologers are unable to identify the personality traits of people or to
predict future events.
2. Does it make verifiable predictions that could possibly prove the theory wrong?
Because it is claimed that horoscopes predict tendencies and people don't necessarily
follow those tendencies, an incorrect horoscope would still not contradict the predictions.
There is no way that astrology can be proved incorrect.
3. Simplicity and aesthetics; astrology it is not a single, unified theory, but instead is a
group of arbitrary rules as to the effect of heavenly objects on people.
4. Scientists do not accept astrology as a valid theory.
2-5 The Marriage of Aristotle and Christianity
1. In the 13th century St. Thomas Aquinas blended the natural philosophy of Aristotle
and Ptolemy’s work with Christian beliefs.
2. A central, unmoving Earth fit perfectly with Christian thinking and a literal
interpretation of the Bible.
3. People during the Middle Ages placed a great reliance on authority, especially
authorities of the past.
2-6 Nicolaus Copernicus and the Heliocentric Model
1. Copernicus, a contemporary of Columbus, worked for 40 years on a heliocentric—
Sun-centered—model for two main reasons. The Ptolemaic model predicted positions for
celestial objects had become less accurate over time, and the model was not aesthetically
pleasing enough.
The Copernican System
1. Copernicus’ system revived many of the ideas of Aristarchus. To explain why a
rotating Earth doesn’t produce a great wind, he assumed the air around the Earth simply
follows the Earth around.
2. Copernicus’ system is heliocentric with the Earth being just another one of the planets,
all of them revolving around a stationary Sun.
3. As seen from high above the Earth’s North Pole, all planets move in a
counterclockwise direction, with the planets closer to the Sun moving faster than those
farther away.
4. In order to explain the apparent motion of the Sun in the sky, Copernicus’ model had
the plane of the Earth’s equator tilted with respect to the plane of its orbit around the Sun.
5. Copernicus accounted for the Moon’s motion by having it on a sphere that revolves
around the Earth each month.
5. Copernicus’ model explains the generally west to east motion of the planets, as does
Ptolemy’s. However, the observed retrograde motion of planets such as Mars is explained
more simply in the Copernican system. Retrograde motion is a natural result in a
heliocentric system.
6. Using his model, Copernicus was able to calculate the relative distances of the planets
from the Sun.
7. In the Copernican system neither Mercury nor Venus can get very far from the Sun as
seen from Earth simply because they orbit the Sun at a distance less than the Earth’s
distance.
2-7 Comparing the Two Models
1. Accuracy in Fitting the Data
(a) Copernicus’ model was not accurate enough to account for all observed planetary
motions. Because of his assumption of uniform motion (like Ptolemy), Copernicus was
forced to add small epicycles of his own to improve accuracy.
(b) Copernicus did not abandon the circle as the preferred planetary orbit because he
thought circles are the best representative of the repetitive motions of the heavens.
(c) Using the evidence available in the 1500s, both models had about the same errors.
(3) Once parallax was observed (in 1838), it provided obvious evidence that the
heliocentric model is the better one. Stellar parallaxes prove the Earth moves. Parallax
also provided evidence that stars are not all at the same distance from Earth, which was
assumed in both the Copernican model and the Ptolemaic model.
2. Predictive Power
(a) A good theory (or model) must make testable predictions that might allow the theory
(or model) to be disproved.
(b) Both the Copernican and Prolemaic models made predictions about parallax. When
parallax was finally observed, it proved that the Ptolemaic model was wrong.
(c) The Copernican model also made predictions about relative distances of the then
known planets from the Sun; these predictions were (much) later confirmed.
3. Simplicity: Mercury and Venus
(a) Copernicus liked his model because it was aesthetically more pleasing than the
Ptolemaic model. A good model is nearly always simple and elegant in its power to
explain and predict.
(b) The Copernican model could explain the motions of Mercury and Venus without
resorting to special rules needed by the Ptolemaic model. (Recall that Mercury and Venus
never appear far from the Sun in the sky.)
(c) Copernicus offered a simpler explanation for retrograde motion that required no use
of epicycles. He did use epicycles, however, in order to make his model fit as accurate as
possible.
(d) Copernicus, who died in 1543 just as his book De Revolutionibus was published,
started such an upheaval in people’s thinking that the word “revolution” took on a second
meaning that is so familiar to us today.
2-8 Tycho Brahe: The Importance of Accurate Observations
1. Tycho (1546–1601) was born 3 years after Copernicus died. After developing an
interest in astronomy and learning that both the Ptolemaic and Copernican models were
based on inaccurate recorded data, he decided to obtain more accurate observations of
planetary positions.
2. Tycho built the largest and most accurate naked-eye instruments yet constructed. (The
telescope had not yet been invented.) They allowed him to measure angles to within 0.1º,
close to the limit the human eye can observe.
3. He not only made careful measurements, but he recorded the accuracy of each
measurement. The inclusion of an error in a measurement is now a common practice in
science.
Tycho’s Model
1. The quality of his observations led Tycho to reject the Copernican model because he
could not observe parallax for the distant stars. The irony here is that his observations of
a “new” star (a supernova) and a bright comet led him to conclude that these objects were
far away from the Earth because he could not measure their parallax.
2. Tycho’s model of the heavens was a mix between the Ptolemaic and Copernican
models. He positioned the Earth at the center with the Sun revolving around it, but he
argued that the other planets were revolving around the Sun.
2-9 Johannes Kepler and the Laws of Planetary Motion
1. In 1600, a year before Tycho died, he hired Johaness Kepler as his assistant. Tycho’s
accurate measurements of planetary positions (especially for Mars) proved invaluable for
Kepler.
2. After 4 years and 70 combinations of circles and epicycles, Kepler devised a
combination that would predict Mars’ position when compared to Tycho’s data to within
0.13º. Knowing the quality of Tycho’s work, Kepler decided to abandon the circle as the
basic motion of the planets.
3. The shape that worked not only for Mars but for every planet Kepler had data was the
ellipse.
The Ellipse
1. The ellipse is a geometrical shape of which every point is the same total distance from
two fixed points (the foci).
2. Eccentricity is the ratio of the distance between the foci divided by the longest
distance across the ellipse (major axis). The eccentricity tells us how “flat” the ellipse is.
Kepler’s First Two Laws of Planetary Motion
1. First Law: Each planet’s path around the Sun is an ellipse, with the Sun at one focus
of the ellipse (there is nothing at the other focus).
2. Second Law: A planet moves along its elliptical path with a speed that changes in
such a way that a line from the planet to the Sun sweeps out equal areas in equal intervals
of time.
The second law implies that a planet moves fastest when it is at the nearest point to the
Sun (the perihelion) while it moves most slowly at its farthest point from the Sun (the
aphelion).
Kepler’s Third Law
1. Kepler hypothesized that forces kept the planets near the Sun and caused them to move
around it, and that this force decreased with distance causing the more distant planets
move around the Sun more slowly. He did not know the origin of this force however.
2. Third Law: The ratio of the cube of a planet’s semimajor axis (the average distance a
from the Sun) to the square of its sidereal period P is the same for each planet: a3 / P2 =
constant.
3. A planet’s sidereal period is the time the planet takes to complete a full orbit around
the Sun, relative to the stars. This differs from the synodic period, which is the time
between two successive identical configurations between a planet and the Sun, as seen
from Earth.
2-10 Kepler’s Contribution
1. Kepler’s modification to the Copernican model brought it into conformity with the
data. Finally, the heliocentric theory worked better than the old geocentric theory.
2. Kepler’s breakthrough choice of ellipses to explain planetary motion was empirical —
ellipses worked but he did not know why they worked.