Foundations-Copernican Revolution
Lecture 2:
Newton: Gravity and the Laws of Motion
Ancient Observatories
Ancient Peoples around the world made places to mark dates from the
celestial calendar and/or observe the sky
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Chaco Canyon, New
Mexicohttp://www.exploratorium.edu/ancientobs/
Chichen Itza
http://www.exploratorium.edu/ancientobs/
Angor Wat, Cambodia
Medicine Wheel, Saskatchewan, Canada
Stonehenge, England
Abu Simbel, Egypt
Science vs. Pseudo-science
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What makes science different?
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What do we know?
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How do we know it?
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Why do we believe it?
Is what we know supported by the evidence?
Kuhn Paradigm
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Thomas Kuhn: Structure of Scientific Revolution
Navigating the web of a 1000 lies
End of the world in 2012?
December 21, 2012
See National Geographic and NASA websites on this
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Mayan Calendar – long count calendar enters a new cycle
Each cycle is 5,125.37 years
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The sun will cross in front of the center of the Milky Way
But this has happened many times before
No significant increase in gravitational interaction
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Sun will be in solar maximum – more solar flares and storms
This has happened may times before
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A tenth planet known to the ancients that would hit us by end of
the year would be visible to astronomers for past decade
Why the hype?
Copernican model would have been a triumph of the Scientific Method
Except
It did not fit the data
Scientific Method:
a)
b)
c)
d)
e)
Make high quality observations of some natural phenomenon
Come up with a theory that explains the observations
Use the theory to predict future behavior
Make further observations to test the theory
Refine the theory, or if it no longer works, make a new one
- Occam’s Razor: Simpler Theories are better
-You can prove a theory WRONG but not
RIGHT
Prediction
Observation
Theory
Question 1
Mars, Jupiter, and
Saturn show retrograde
motion because
a) planets move on epicycles.
b) planets orbit the Sun in the same
direction.
c) Earth moves faster in its orbit.
d) they are closer than Uranus.
e) they rotate quickly on their axes.
Question 1
Mars, Jupiter, and
Saturn show retrograde
motion because
a) planets move on epicycles.
b) planets orbit the Sun in the same
direction.
c) Earth moves faster in its orbit.
d) they are closer than Uranus.
e) they rotate quickly on their axes.
As Earth overtakes and “passes”
the outer planets, they seem to
slow down and then reverse
direction.
Question 2
Epicycles were used
in Ptolemy’s model
to explain
a) why planets moved in the sky.
b) why Earth was at the center.
c) why retrograde motion occurred.
d) why Earth wobbled on its axis.
e) why inner planets were always seen
near the Sun.
Question 2
Epicycles were used
in Ptolemy’s model
to explain
a) why planets moved in the sky.
b) why Earth was at the center.
c) why retrograde motion occurred.
d) why Earth wobbled on its axis.
e) why inner planets were always seen
near the Sun.
.
Planets were assumed to move
uniformly on an epicycle, as it
moved uniformly around Earth.
Question 3
Which of Galileo’s initial
observations was most
challenging to established
geocentric beliefs?
a) craters on the Moon
b) sunspots
c) lunar maria
d) satellites of Jupiter
e) stars of the Milky Way
Question 3
Which of Galileo’s initial
observations was most
challenging to established
geocentric beliefs?
a) craters on the Moon
b) sunspots
c) lunar maria
d) satellites of Jupiter
e) stars of the Milky Way
Seeing four moons clearly move
around Jupiter disproved that
everything orbited Earth
and
showed Earth could orbit the Sun and
not lose its moon, too.
Question 4
Earth is closer to the Sun in
January. From this fact,
Kepler’s 2nd law tells us
a) Earth orbits slower in
January.
b) Earth orbits faster in January.
c) Earth’s orbital speed doesn’t
change.
Question 4
Earth is closer to the Sun in
January. From this fact,
Kepler’s 2nd law tells us
a) Earth orbits slower in
January.
b) Earth orbits faster in January.
c) Earth’s orbital speed doesn’t
change.
Kepler’s 2nd law means that a
planet moves faster when
closer to its star.
Faster
Slower
At this time, actual distances of planets from Sun were
unknown, but were later measured. One technique is "parallax"
"Earth-baseline parallax" uses
telescopes on either side of Earth to
measure planet distances.
Timelines of the Big Names
Galileo
Copernicus
1473-1543
1564-1642
Brahe
1546-1601
Kepler
1571-1630
Newton
1642-1727
Kepler's Third Law
The square of a planet's orbital period is proportional to the
cube of its semi-major axis.
P2
is proportional to
or
P2  a3
(for circular orbits, a=b=radius).
Translation: the larger a planet's orbit,
the longer the period.
a3
a
b
1.3 The Laws of Planetary Motion
Kepler’s laws:
3. Square of period of planet’s orbital motion is
proportional to cube of semimajor axis.
Newton (1642-1727)
Kepler's laws were basically playing with
mathematical shapes and equations and seeing
what worked.
Newton's work based on experiments of how
objects interact.
His three laws of motion and law of gravity
described how all objects interact with each other.
Newton's First Law of Motion
DEMO - Smash the HAND
Newton's First Law of Motion
Last time – Demo of objects at rest
Demo – nature of how objects move
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Hover disk
1.4 Newton’s Laws
Newton’s laws of motion explain how objects interact
with the world and with each other.
Newton’s first law:
An object at rest will remain at rest, and an object will
move in a straight line at constant speed if and only if
the sum of forces that act on it are balanced.
Newton's Second Law of Motion
When a force, F, acts on an object with a mass, m, it produces an
acceleration, a, equal to the force divided by the mass.
Fnet
a=
m
or Fnet = ma
acceleration is a change in velocity or a change in
direction of velocity.
Newton's Second Law of Motion
Demo - Force and Acceleration
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Fan Carts
Clicker Question:
Why didn’t my hand get crushed by the hammer?
A: My bones are actually stronger than steel.
B: The plate has a lot of inertia
C: The plate is very strong
D: The force of gravity kept the plate from moving
Newton's Third Law of Motion
To every action there is an equal and opposite reaction.
Or, when one object exerts a force on a second object, the
second exerts a force on first, that is:
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Equal in magnitude
Opposite in direction
Of the same type
Newton's Third Law of Motion
DEMO: CART
DEMO: Force Probes
A.
B.
C.
D.
Cart 1 will exert a larger force on Cart 2 than Cart 2
exerts on Cart 1
Cart 2 will exert a larger force on Cart 1 than Cart 1
exerts on Cart 2
The carts will exert forces of equal magnitude on each
other
Not possible to determine
Newton's Law of Gravity
For two objects of mass m1 and m2, separated by a
distance R, the force of their gravitational attraction is
given by:
F=
G m1 m2
R2
F is the gravitational force.
G is the "gravitational constant".
An example of an "inverse-square law".
Your "weight" is just the gravitational force
between the Earth and you.
1.4 Newton’s Laws
Gravity
For two massive objects,
the gravitational force is
proportional to the product
of their masses divided by
the square of the distance
between them.
1.4 Newton’s Laws
Gravity
On Earth’s surface,
the acceleration due
to the force of gravity
(Newton’s 2nd Law)
is approximately
constant, and
directed toward the
center of Earth.
Falling Objects
DEMO: paper and ball
Movie: Hammer and Feather
1.4 Newton’s Laws
Gravity
The gravitational pull
of the Sun keeps the
planets moving in their
orbits.
Newton’s Laws and Gravity
Massive objects actually orbit around their
common center of mass; if one object is much
more massive
than the other, the
center of mass is not far
from the center of the
more massive object.
For objects more equal
in mass, the center of
mass is between the two.
Throwing a ball into orbit
1.4 Newton’s Laws
Kepler’s laws are a
consequence of
Newton’s laws.
The orbit of a planet around the Sun
has the common center of mass
(instead of the Sun) at one focus.
Escape Velocity
Velocity needed to completely escape the gravity of a planet.
The stronger the gravity, the higher the escape velocity.
Examples:
Earth
Jupiter
Deimos (moon of Mars)
11.2 km/s
60 km/s
7 m/s = 15 miles/hour
Consider Helium Gas at room temperature (300 K)
E = kT = 4.1 x 10-14 erg
E = 0.5 m v2 = 4.1 x 10-14 erg
so v = 1 km/sec on average, but sometimes more
Newton's Laws of Motion
Newton’s Zeroeth Law of Motion
Objects are dumb. They do not know the past and they are not good predictors of the
future. They only know what forces act on them right now.
Newton’s First Law of Motion
Every object continues in a state of rest or a state of motion with a constant speed in a
straight line unless acted on by an unbalanced force.
Newton’s 2nd Law of Motion
When a force, F, acts on an object with a mass, m, it produces an acceleration, a, equal
to the force divided by the mass.
a=
Fnet
m
Newton’s Third Law of Motion
For every action there is an equal and opposite reaction.
Or, when one object exerts a force on a second object, the second object exerts
an equal and opposite force on the first.
Newton's Law of Gravity
For two objects of mass m1 and m2, separated by a
distance R, the force of their gravitational attraction is
given by:
F=
G m1 m2
R2
F is the gravitational force.
G is the universal "gravitational constant".
An example of an "inverse-square law".
Your "weight" is just the gravitational force
between the Earth and you.
M=
r v2
G
What happens if ball is thrown harder than
what is needed to go into circular orbit?
Escape Velocity
Velocity needed to completely escape the gravity of a planet.
The stronger the gravity, the higher the escape velocity.
Examples:
Earth
Jupiter
Deimos (moon of Mars)
11.2 km/s
60 km/s
7 m/s = 15 miles/hour
Consider Helium Gas at room temperature (300 K)
E = kT = 4.1 x 10-14 erg
E = 0.5 m v2 = 4.1 x 10-14 erg
so v = 1 km/sec on average, but sometimes more