A100–Exploring the Universe: The beginnings of physical laws
Martin D. Weinberg
UMass Astronomy
[email protected]
January 28, 2016
Read: Chaps 3 & 4
01/28/16 – slide 1
Announcements
⊲ Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
Read: Chaps 3 & 4
New assignment available
MasteringAstronomy pointers (see Exercises)
01/28/16 – slide 2
Announcements
⊲ Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
Read: Chaps 3 & 4
New assignment available
MasteringAstronomy pointers (see Exercises)
Reading
01/28/16 – slide 2
Announcements
⊲ Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
New assignment available
MasteringAstronomy pointers (see Exercises)
Reading
Today’s topic: Discovery of Laws of Motion and Gravity
⊲
⊲
⊲
⊲
⊲
Read: Chaps 3 & 4
How did Copernicus, Tycho, and Kepler challenge
the Earth-centered idea?
What are Kepler’s three laws of planetary motion?
How did Galileo solidify the Copernican revolution?
How do we describe motion?
Isaac Newton . . .
01/28/16 – slide 2
Announcements
⊲ Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
New assignment available
MasteringAstronomy pointers (see Exercises)
Reading
Today’s topic: Discovery of Laws of Motion and Gravity
⊲
⊲
⊲
⊲
⊲
How did Copernicus, Tycho, and Kepler challenge
the Earth-centered idea?
What are Kepler’s three laws of planetary motion?
How did Galileo solidify the Copernican revolution?
How do we describe motion?
Isaac Newton . . .
Questions?
Read: Chaps 3 & 4
01/28/16 – slide 2
Kepler’s Three Laws
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
1. The orbit of a planet about the Sun is an ellipse with the
Sun at one focus
01/28/16 – slide 3
Kepler’s Three Laws
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
1. The orbit of a planet about the Sun is an ellipse with the
Sun at one focus
2. A line joining a planet and the Sun sweeps out equal
areas in equal intervals of time
01/28/16 – slide 3
Kepler’s Three Laws
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
1. The orbit of a planet about the Sun is an ellipse with the
Sun at one focus
2. A line joining a planet and the Sun sweeps out equal
areas in equal intervals of time
3. The squares of the periods of the planets are
proportional to the cubes of their semimajor axes
01/28/16 – slide 3
Kepler’s First Law
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
The orbit of each planet around the Sun is an ellipse with the
Sun at one focus.
01/28/16 – slide 4
Keplers Second Law
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
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.
[demo]
Read: Chaps 3 & 4
01/28/16 – slide 5
Kepler’s Third Law
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
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
01/28/16 – slide 6
Kepler’s Third Law
Graphical version of Keplers Third Law
Read: Chaps 3 & 4
[Planet X]
01/28/16 – slide 7
Thought Question
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
An asteroid orbits the Sun at an average distance a = 4 AU.
How long does it take to orbit the Sun?
A. 4 years
B. 8 years
C. 16 years
D. 64 years
Hint: Remember that p2 = a3
01/28/16 – slide 8
Thought Question
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
An asteroid orbits the Sun at an average distance a = 4 AU.
How long does it take to orbit the Sun?
A. 4 years
B. 8 years
C. 16 years
D. 64 years
We need to find p so that p2 = a3
Since a = 4 ⇒ a3 = 43 = 64
Therefore p2 = 82 = 64 ⇒ p = 8
Read: Chaps 3 & 4
01/28/16 – slide 8
Galileo
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
Galileo Galilei (1564-1642)
Telescope invented by Dutch optician in 1600s
First to use telescope for astronomical observations
Observed phases of Venus
Discovered moons of Jupiter
Tried to understand general laws of Nature
01/28/16 – slide 9
Galileo
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
Galileo Galilei (1564-1642)
Telescope invented by Dutch optician in 1600s
First to use telescope for astronomical observations
Observed phases of Venus
Discovered moons of Jupiter
Tried to understand general laws of Nature
Galileo: “the first scientist”
01/28/16 – slide 9
Galileo
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
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 the heavens should be
3. If Earth were really orbiting
Sun, we’d detect stellar parallax
Read: Chaps 3 & 4
01/28/16 – slide 10
Overcoming the first objection
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
Galileos 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).
01/28/16 – slide 11
Overcoming the first objection
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
Galileos 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).
01/28/16 – slide 11
Overcoming the second objection
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
“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)
01/28/16 – slide 12
Overcoming the third objection
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
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 lack of detectable
parallax was no longer so troubling.
01/28/16 – slide 13
Overcoming the third objection
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
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 lack of detectable
parallax was no longer so troubling.
Parallax not measured until 1830s by Friedrich Bessel (0.3
seconds of arc!)
Read: Chaps 3 & 4
01/28/16 – slide 13
Predictions
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
The heliocentric models makes predictions that can be tested
using telescopic observations!
Read: Chaps 3 & 4
01/28/16 – slide 14
Phases of Venus
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Venus has phases, just like the Moon
Full Venus is behind the Sun
Read: Chaps 3 & 4
01/28/16 – slide 15
Phases of Venus
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
Photographs through a telescope over part of a Venusian
year
01/28/16 – slide 16
Phases of Venus
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
Venus’ deferent must revolve at the same rate as
Sun’s deferent
Earth observer would
never see Venus more
than half illuminated
Inconsistent
with
Galileo’s observations
⊲
Ptolemaic model must be
wrong!
[demo]
Read: Chaps 3 & 4
01/28/16 – slide 17
Moons of Jupiter
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
01/28/16 – slide 18
Moons of Jupiter
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
Jupiter has four moons
easily seen with a telescope or binoculars
Appear to move back and
forth relative to Jupiter
⊲
Read: Chaps 3 & 4
01/28/16 – slide 18
Moons of Jupiter
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
Jupiter has four moons
easily seen with a telescope or binoculars
Appear to move back and
forth relative to Jupiter
Largest orbits, longest
periods
A miniature Copernican
solar system!
01/28/16 – slide 18
Scientific theory
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
The Copernican Heliocentric Theory
The word theory has a different meaning in science than
in everyday usage
In science, a theory is NOT the same as a hypothesis
A scientific theory must:
⊲
⊲
⊲
⊲
Read: Chaps 3 & 4
Explain a wide variety of observations with a few
simple principles
Must be supported by a large, compelling body of
evidence.
Must NOT have failed any crucial test of its validity.
01/28/16 – slide 19
Scientific theory
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
A flowchart describing
the scientific process
01/28/16 – slide 20
Back to Galileo
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
Similarity of Earth–Moon–Sun and Jupiter–moons–Sun
Rolled balls down inclined planes
Found that objects increased their speed independently
of weight
Uniform, straight-line motion is the natural state for
motion of objects
⊲
Read: Chaps 3 & 4
01/28/16 – slide 21
Back to Galileo
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
Similarity of Earth–Moon–Sun and Jupiter–moons–Sun
Rolled balls down inclined planes
Found that objects increased their speed independently
of weight
Uniform, straight-line motion is the natural state for
motion of objects
Galilean relativity
The mechanical laws of physics are the same
for every inertial observer. By observing the
outcome of mechanical experiments, one
cannot distinguish a state of rest from a state of
constant velocity.
01/28/16 – slide 21
Back to Galileo
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
Example: centripetal motion
⊲
State of motion called inertia
Objects preserve their inertia unless acted on by a force
Read: Chaps 3 & 4
01/28/16 – slide 22
Acceleration by Gravity
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
Galileo showed that g is
the same for all falling
objects, regardless of their
mass.
Probably
used
balls
rolling on inclined planes,
not the Leaning Tower of
Pisa . . .
01/28/16 – slide 23
Acceleration by Gravity
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
⊲
Read: Chaps 3 & 4
Galileo showed that g is
the same for all falling
objects, regardless of their
mass.
Probably
used
balls
rolling on inclined planes,
not the Leaning Tower of
Pisa . . .
01/28/16 – slide 23
Acceleration by Gravity
All falling objects accelerate at
the same rate (not counting friction of air resistance)
On Earth, g ≈ 10 m/s2 : speed
increases 10 m/s with each second of falling
Note: ≈ means approximately equal
Read: Chaps 3 & 4
01/28/16 – slide 24
Acceleration by Gravity
Announcements
Kepler’s laws
First Law
Second Law
Third Law
Thought Question
Galileo
...Objection 1
...Objection 2
...Objection 3
Predictions
Phases of Venus
Moons of Jupiter
Scientific theory
Back to Galileo
Acceleration by
Gravity
Galileo’s thought experiment
Earth is sphere
Shoot a cannonball fast
enough and rate of falling
will balance curvature
⊲
[demos]
Read: Chaps 3 & 4
01/28/16 – slide 25