What is a scientific model?

9/1/09
Why does modern science trace its roots to
the Greeks?
•  Greeks were the first
people known to make
models of nature.
•  They used logic and
geometry to explain
patterns in nature
without resorting to
myth or the supernatural.
Greek geocentric model (400 BC)
•  Scientific model is a conceptual
representation whose purpose is to explain
and predict observed phenomena.
•  They sought to
understand the
architecture of the
Universe by constructing
models of nature.
How did the Greeks explain planetary motion?
Underpinnings of the Greek geocentric model: •  Earth is at the center of the
Universe and is not moving
(otherwise objects on Earth will be
left behind).
Plato (B.C. 427-347)
What is a scientific model?
But this geocentric view made it difficult to
explain the apparent retrograde motion of
some planets, like Mars.
•  Heavens must be “perfect:” objects
move on perfect spheres or in perfect
circles.
•  Heavens are unchanging.
Aristotle (B.C. 384-322)
Over a period of 10 weeks, Mars appears to stop, back up, then
go forward (west2east) again.
The most sophisticated (many
circles, off-set circles, etc.)
geocentric model was that of
Ptolemy — the Ptolemaic
model:
•  Sufficiently accurate (a few
degrees) to remain in use for
nearly 1,500 years!
•  Arabic translation of Ptolemy’s
work named Almagest (meaning
The greatest compilation).
How does the Ptolemaic model explain retrograde motion?
(Planets really do go backward in this model!)
deferent
epicycle
Ptolemy (A.D. 100-170)
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How was geocentric model turned
down?
•  Earlier models of planetary motion, such as the geocentric
Ptolemaic system and the heliocentric Copernican
system, allowed only perfect circles as orbits.
•  These models were therefore compelled to combine many
circular motions to reproduce the variations in the planets'
motions.
•  Kepler eliminated the epicycles and deferents that had
made each planet a special case.
•  His three laws apply generally to all orbiting bodies.
•  Mars was the planet whose motions were in greatest
disagreement with existing models, and its derived orbit
provided the critical test for Kepler’s hypotheses.
•  To obtain the precise orbit of Mars, Kepler relied on the
astronomical observations of his mentor, Tycho Brahe,
which were much more accurate than any earlier work!
How did Copernicus, Tycho, Kepler, and
Galileo challenge the Earth-centered idea
to explain the motions of planets?
Nicolas Copernicus (1473-1543)
•  He proposed Sun-centered model
presented in Concerning the Revolutions
of the Heavenly Spheres (published in
1543, a few weeks before he died).
•  He used the model to determine layout
of the solar system (planetary distances
in AUs and orbital periods)
But: •  This model was no more accurate than
Ptolemaic model in predicting planetary
positions, because still used perfect circles.
•  Kepler first tried to match Tycho’s
observations with circular orbits.
Tycho Brahe (1546-1601)
•  Tycho compiled the most accurate (one
arc-minute!) naked eye measurements
ever made of planetary positions!
•  He still could not detect the stellar
parallax, and thus thought that the Earth
must be at the center of solar system
(but recognized that other planets go
around Sun).
•  He hired a brilliant mathematician,
Kepler, who used his observations taken
over many years to discover the truth
about planetary motion.
What is an Ellipse?
•  But he found an 8 arc-minute
discrepancy, which eventually led him
conclude that the planetary orbits are
ellipses.
Johannes Kepler
(1571-1630)
“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’s First Law: The orbit of each planet around
the Sun is an ellipse with the Sun at one focus.
An ellipse looks like an elongated circle.
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Examples of Ellipse Eccentricity
Kepler’s Second Law: As a planet moves around its
orbit, it sweeps out equal areas in equal times.
Planetary orbit eccentricities
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
0.206
0.0068
0.0167
0.0934
0.0485
0.0556
0.0472
0.0086
0.25
Kepler was the first to calculate the elliptical orbit of
Mars. This was immensely laborious process, and
Kepler himself referred to this work as “My War with
Mars.”
Kepler’s Third Law: The square of the period of
any planet is proportional to the cube of the semi
-major axis of its orbit.
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T
s
=2.97 ×10−19 3
a3
m
€
T2 =
4π2 3
a
G MS
Summary of Kepler's Laws
I.  The Law of Ellipses: The shape of each planet's orbit is an
ellipse with the Sun at one focus.
II. The Law of Equal Areas: An imaginary line drawn from the
center of the Sun to the center of the planet will sweep out equal
areas in equal periods of time at all points in the orbit.
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This law results to the law
of gravitation discovered
by Newton later on!
⇒  This means that a planet travels faster when it is nearer to
the Sun and slower when it is farther from the Sun.
a3
T2
III. The Law of Harmonies: The ratio of the cube of the semimajor axis a to the square of the orbital period T is the same for
all the planets including the Earth, i.e., a3/T2=constant.
•  Kepler's first and second laws were published in 1609 in
Commentaries on the Motions of Mars.
•  The third law appeared in 1619 in Harmony of the Worlds.
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How did Galileo solidify the
heliocentric model?
Galileo (1564-1642)
He overcame the major objections
to the Copernican view. Three key
objections rooted in Aristotelian
view were:
1.  Earth could not be moving because
objects in air would be left behind.
2.  Non-circular orbits are not “perfect”
as heavens should be (well, heavens
are not perfect, look at the Moon!).
3.  If Earth were really orbiting Sun,
we would detect stellar parallax
(well, not if stars are far, far away!).
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).
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Overcoming the second objection: heavenly perfection
•  Tycho’s observations of a comet and
supernova already challenged this idea.
•  Using his telescope, Galileo saw:
  sunspots on Sun (“imperfections”)
  mountains and valleys on the
Moon (proving it is not a perfect
sphere!)
•  The Catholic Church
ordered Galileo to recant his
claim that Earth orbits the
Sun in 1633.
•  His book on the subject was
removed from the Church’s
index of banned books in
1824.
•  Galileo was formally
vindicated by the Church in
1992 (359 years later!).
Kepler's Foretelling of the
Law of Gravity
•  Kepler believed that the Sun did not sit passively at the center of the
solar system, but that through some mysterious power or “virtue”
actually compelled the planets to hold to their orbits.
•  Because the planets moved slower when they were farther from the
Sun, this power must diminish with increasing distance.
Overcoming the third objection: stellar 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
the Milky Way is countless individual stars.
If stars were much farther away, then the lack of
detectable stellar parallax was no longer so troubling!
Summary
•  How did Copernicus, Tycho and Kepler challenge the
Earth-centered idea?
•  Copernicus created a Sun-centered model; Tycho
provided the data needed to improve this model; Kepler
found a scientific model that fit Tycho’s data!
•  What was Galileo’s role in 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.
•  The idea that the planets were controlled by the Sun was developed by
Isaac Newton in his laws of motion and law of gravitation.
•  Newton assumed that the Sun continuously exerts a force on each
planet that pulls the planet toward the Sun.
•  He calculated that elliptical orbits would result if the force varied
inversely as the square of the distance from the Sun (i.e., when the
distance doubles, the force becomes four times weaker).
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Hallmarks of Science: #2
Science progresses through the
creation and testing of models of nature
that explain the observations as simply
as possible.
What is a scientific theory?
•  The word theory has a different meaning in science
than in everyday life.
•  In science, a theory is NOT the same as a
hypothesis, rather:
•  A scientific theory must:
  Explain a wide variety of observations with a few simple
principles, AND
  Must be supported by a large, compelling body of evidence.
  Must NOT have failed any crucial test of its validity.
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.
Nicolas Copernicus
(Astronomer/Mathematician)
Born: 19 February 1473
Birthplace: Torun, Poland
Death: 24 May 1543
Best Known As: Astronomer known for figuring out
that the Sun is the center of our solar system.
For years he worked on his theory that the planets
in our solar system revolved around the Sun
(Ptolemy of ancient Greece had explained that the
universe was a closed system revolving around the
Earth, and the Catholic church concurred). Hesitant
to publish his work for fear of being charged with
heresy, Copernicus summarized it in 1530 and
circulated it among Europe's scholars, where it was
greeted with enthusiasm. His work, titled De
Revolutionibus Orbium Coelestium was finally
published in 1543, apparently just a few weeks
before he died!
Because Copernicus' heliocentric theory of the
planets defied 1,500 years of tradition, some
historians mark the publication date of De
Revolutionibus as the beginning of the “scientific
revolution.” It was not until 1835 that his work was
taken off the list of books banned by the Vatican…
Other scientists who got in trouble for believing that
the Earth moved around the Sun were Johannes
Kepler and Galileo Galilei.
Tycho Brahe
Johannes Kepler
(Astronomer)
(Mathematician/Astronomer)
Born: 14 December 1546
Birthplace: Skane, Denmark (now Sweden)
Death: 24 October 1601 (gastrointestinal trouble)
Best Known As: Denmark's hottest stargazer
Brahe is not as famous as Galileo or Copernicus, but
in some circles he is considered the father of
modern astronomy. He spent much of his life
compiling the world's first truly accurate and
complete set of astronomical tables — all before the
invention of the telescope! Brahe's assistant,
Johannes Kepler, later used the tables to deduce
the laws of planetary motion.
In 1566 Brahe lost most of his nose in a duel, and
wore a metal replacement the rest of his life.
Born: 27 December 1571
Birthplace: Weil der Stadt, Württemberg
Death: 15 November 1630
Best Known As: The astronomer who explained planetary
motion
Johannes Kepler supported the heliocentric theory by Nicolas
Copernicus, defending it in his first major work, Mysterium
Cosmographicum (1596). In 1601 Kepler became the imperial
mathematician to Rudolf II (emperor of the Holy Roman
Empire), succeeding Tycho Brahe. Using Brahe's data, between
1609 and 1619 Kepler developed his three laws of planetary
motion in Astronomia Nova and Harmonices Mundi. In 1628
Kepler published the Rudolphine Tables, a list of remarkably
accurate logarithmic astronomical tables based on Brahe's
observations and Kepler's subsequent analysis. Thanks in part
to a telescope he received from Galileo (they knew each other
through correspondence only), Kepler also advanced the
science of optics. His achievements in astronomy and
mathematics shaped our current understanding of the solar
system.
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Galileo Galilei
(Astronomer/Mathematician)
Born: 15 February 1564
Birthplace: Pisa, Italy
Death: 8 January 1642
Best Known As: One of the greats of modern
science
Galileo's achievements include: demonstrating that
the velocities of falling bodies are not proportional
to their weights; showing that the path of a
projectile is a parabola; building the first
astronomical telescope; coming up with the ideas
behind Newton's laws of motion; and confirming the
Copernican theory of the solar system. He was
denounced for heretical views by the church in
Rome, tried by the Inquisition, and forced to
renounce his belief that the planets revolved around
the Sun.
The Vatican officially recognized the validity of
Galileo's work in 1993 — 351 years after his death!
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