The idealized scientific method
•
Based on proposing and
testing hypotheses
•
hypothesis = educated guess
Hallmarks of Science: #1
Modern science seeks explanations for
observed phenomena that rely solely on
natural causes.
(A scientific model cannot include divine intervention)
Hallmarks of Science: #2
Science progresses through the
creation and testing of models of nature
that explain the observations as simply
as possible.
(Simplicity = “Occam’s razor”)
Hallmarks of Science: #3
A scientific model must make testable
predictions about natural phenomena.
The world view of Aristotle (384-322
B.C.)
Adopted as a part of Western tradition, and by the Catholic
Church
• The Earth is stationary
• The planets Mercury, Venus, Mars, Jupiter,
and Saturn, as well as the Sun and Moon,
move in circular orbits around the Earth
• The stars are fixed on the celestial sphere
• The stars aren’t much farther away than
the orbit of Saturn.
Special Topic: Eratosthenes measures the Earth (c. 240 BC)
Measurements:
Syene to Alexandria
distance ≈ 5000 stadia
angle = 7°
Calculate circumference of Earth:
7/360  (circum. Earth) = 5000 stadia
 circum. Earth = 5000  360/7 stadia ≈ 250,000 stadia
Compare to modern value (≈ 40,100 km):
Greek stadium ≈ 1/6 km  250,000 stadia ≈ 42,000 km
How did the Greeks explain planetary motion?
Underpinnings of the Greek geocentric model:
• Earth at the center of the universe
• Heavens must be “perfect”: Objects
moving on perfect spheres or in
perfect circles.
Plato
Aristotle
But this made it difficult to explain
apparent retrograde motion of
planets…
Review: Over a period of 10 weeks, Mars appears to stop, back
up, then go forward again.
The most sophisticated
geocentric model was that of
Ptolemy (A.D. 100-170) —
the Ptolemaic model:
• Sufficiently accurate to
remain in use for 1,500 years.
• Arabic translation of
Ptolemy’s work named
Almagest (“the greatest
compilation”)
Ptolemy
Claudius Ptolemaeus [Ptolemy]
(87-150 A.D.)
• Embraced Aristotle’s view of Earth-centered Universe
• And endorsed the idea of perfect circles
• But, he improved predictions of the positions of the
planets by introducing additional perfect circles to
Aristotle’s model.
• These additional circles are known as epicycles.
Fig 1-13, p.31
Nicolaus
Copernicus
(1473-1543)
Copernicus found the old model
of Ptolemy gave incorrect positions
of the planets.
He developed the Sun-centered
(heliocentric) view of the Universe,
which improved the predictions
of planetary positions.
How did Copernicus, Tycho, and Kepler
challenge the Earth-centered idea?
Copernicus (1473-1543):
• Proposed Sun-centered model
(published 1543)
• Used model to determine layout of
solar system (planetary distances
in AU)
But . . .
• Model was no more accurate than
Ptolemaic model in predicting
planetary positions, because it still used
perfect circles.
Fig 1-15, p.34
Johannes
Kepler
and Tycho
Brahe
Tycho made many observations
of the positions of the planets
and stars, before the invention
of the telescope.
Kepler used those observations,
particular those of Mars, to
develop his three laws of
planetary motion.
What are Kepler’s three laws of planetary motion?
Kepler’s First Law: The orbit of each planet around
the Sun is an ellipse with the Sun at one focus.
Kepler’s Second Law: As a planet moves around its
orbit, it sweeps out equal areas in equal times.
 means that a planet travels faster when it is nearer to the Sun and
slower when it is farther from the Sun.
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 = avg. distance from Sun in AU
Galileo
Galilei
(1564-1642)
A contemporary
of Kepler
Galileo was one of the
very first scientists to
do experiments to
understand Nature
He was the first
astronomer to use a
telescope (in 1610)
to study the sky.
Galileo’s most
important discovery
Galileo saw four little “stars”
Moving with Jupiter across
The sky, and changing their
Positions every night.
He quickly and correctly
concluded that they are in
orbit around Jupiter.
This confirmed the Copernican
view that the Earth is NOT
the center of all motion in the
Universe.
How did Galileo solidify the Copernican
revolution?
Galileo (1564-1642) overcame major
objections to 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.
3. If Earth were really orbiting Sun,
we’d detect stellar parallax.
Overcoming the second objection (heavenly perfection):
• Tycho’s observations of 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 Galilei
Galileo was formally
vindicated by the Church in
1992
Why do the planets move in the ways described by Kepler?
Isaac Newton (1643-1717)
Escape velocity
Throw the ball hard enough
and it will escape the
gravity pull of the Earth
How fast do you have to
throw it?
It depends on which planet
you live on …
Escape Velocity for the planets
The velocity of escape, V, from a planet is
given by
V  2Gm / r
G is the universal gravitational constant
m is the mass of the planet
r is the radius of the planet
The escape velocity of Earth is 11 km/sec, or
About 25,000 miles per hour.
Escape Velocities for the planets, the Sun, and the Moon
Object
Sun
Jupiter
Saturn
Neptune
Uranus
Venus
Mars
Mercury
Moon
Mass
(Earth = 1)
330,000
318
95
17
15
0.8
0.11
0.05
0.012
Radius
(Earth = 1)
109
11.2
9.5
3.4
3.7
0.96
0.52
0.38
0.27
Escape
Velocity
620 km/sec
60.0
35.6
25.4
22.4
10.4
5.2
4.3
2.4