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“… the shuttle blasts off … Then comes the
tremendous pressure of three G’s and the
sudden release into weightlessness as the ship
leaves the gravitational field behind…”
-from The Arizona Republic
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Monday, October 3, 2011
Quiz #3:
Wednesday
Chp. 2-4
Next homework (due Wednesday)
Chp. 5
Problems: 1, 2
Learning to look: 1, 2
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Monday, October 3, 2011
Chapter 5
Newton, Einstein,
and Gravity
Monday, October 3, 2011
Outline
I. Galileo and Newton
A. Galileo and Motion
B. Newton and the Laws of Motion
C. Mutual Gravitation
II. Orbital Motion and Tides
A. Orbits
B. Orbital Velocity
C. Calculating Escape Velocity
D. Kepler's Laws Re-examined
E. Newton's Version of Kepler's Third Law
F. Tides and Tidal Forces
G. Astronomy After Newton
III. Einstein and Relativity
A. Special Relativity
B. The General Theory of Relativity
C. Confirmation of the Curvature of Space-Time
Monday, October 3, 2011
A New Era of Science
Mathematics as a tool for
understanding physics
Monday, October 3, 2011
Isaac Newton (1643 - 1727)
• Building on the results of Galileo and Kepler
• Adding physics interpretations to the
mathematical descriptions of astronomy by
Copernicus, Galileo and Kepler
Major achievements:
1. Invented Calculus as a necessary tool to solve
mathematical problems related to motion
2. Discovered the three laws of motion
3. Discovered the universal law of mutual gravitation
Monday, October 3, 2011
Newton’s 1st Law of Motion
An object continues in a state of rest or
in a state of uniform motion at a
constant speed along a straight line
unless compelled to change that state
by a net force.
Why? Because objects have “inertia”
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Monday, October 3, 2011
Uniform Motion
Uniform Motion: same speed, same direction
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Monday, October 3, 2011
Inertia
The “tendency” that Newton observed
for objects at rest to stay at rest and
objects in motion to stay in uniform
motion in a straight line.
How do we measure inertia?
MASS
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Monday, October 3, 2011
Force
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Monday, October 3, 2011
Force
Net force = sum of all forces:
Here, we say that the NET force is zero!
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Monday, October 3, 2011
Force
Net force = sum of all forces:
Here, we say that the NET force is zero!
The box stays at rest. There is no change in its
state of motion – no net force is acting on it.
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Monday, October 3, 2011
The ball moves over
my head at a
constant speed as
shown. Is the ball
changing its state of
motion? Is there a
net force acting on
the ball?
a.
b.
c.
d.
e.
Monday, October 3, 2011
Yes. Yes.
No. No.
Yes. No.
No. Yes
Yes/Yes if I am moving
my hand back and forth.
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Force and Inertia
Natural state of motion
is at a constant speed,
in a straight line.
Ball wants to travel in a
straight line, but the
string continuously pulls
it back toward the center
of the circle.
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Monday, October 3, 2011
Acceleration
A change in velocity (state of motion)
Refers to an increase in velocity OR a
decrease in velocity OR a change in the
direction of velocity.
A net force acting on an object will cause
that object to accelerate.
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Monday, October 3, 2011
Acceleration
Acceleration: can be a change in speed,
either increasing or decreasing.
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Monday, October 3, 2011
Acceleration
Acceleration: can be a change in
direction
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Monday, October 3, 2011
Newton’s 2nd Law of Motion
The amount of acceleration (a) produced by a
force(F) depends on the mass (m) of the
object being
accelerated.
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Monday, October 3, 2011
Newton’s 2nd Law of Motion
The amount of acceleration (a) produced by a
force(F) depends on the mass (m) of the
object being
accelerated.
Mathematically:
F = m×a
Alternatively:
a = F/m
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Monday, October 3, 2011
Newton’s 2nd Law of Motion
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Monday, October 3, 2011
Which of the objects are NOT accelerating?
a) a car traveling at a constant speed around
a bend.
b) a ball that has been thrown up into the air
just before it begins falling back down.
c) a car traveling at 65 mph down a straight
highway.
d) a car getting off the freeway on a straight
off-ramp.
e) an electron circling around an atomic
nucleus.
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Monday, October 3, 2011
Law of Gravitation
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Monday, October 3, 2011
Law of Gravitation
G=6.67×10-11
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Monday, October 3, 2011
Question:
A linebacker and a kitten are put into space far from
any other object. How do the gravitational forces
each feels compare? How do their accelerations
compare?
a. Linebacker feels larger force,
but accelerates less.
b. Kitten feels larger force and
accelerates more.
c. Both feel same force, but kitten
accelerates more.
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Monday, October 3, 2011
Example
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Monday, October 3, 2011
Example
The linebacker and the kitten
on Earth:
How do the forces that they feel
(due to the Earth’s gravity)
compare? How do their
accelerations compare if
they both jump off a table?
a. Forces equal, kitten
accelerates more.
b. Larger force on
linebacker, accelerations
equal.
c. Forces equal,
accelerations equal.
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Monday, October 3, 2011
Acceleration of Gravity
http://video.google.com/videoplay?docid=6926891572259784994
Monday, October 3, 2011
Acceleration of Gravity
Acceleration of
gravity is
independent of the
mass (weight) of
the falling object!
http://video.google.com/videoplay?docid=6926891572259784994
Monday, October 3, 2011
Acceleration of Gravity
Iron ball
Acceleration of
gravity is
independent of the
mass (weight) of
the falling object!
http://video.google.com/videoplay?docid=6926891572259784994
Monday, October 3, 2011
Acceleration of Gravity
Iron ball
Wood ball
Acceleration of
gravity is
independent of the
mass (weight) of
the falling object!
http://video.google.com/videoplay?docid=6926891572259784994
Monday, October 3, 2011
Weight
Weight:
Weight is NOT the same as “mass”.
Weight is equivalent to the gravitational
force the Earth exerts on your body.
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Monday, October 3, 2011
Are you weightless
on the Moon?
a) yes
b) no
c) depends
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Monday, October 3, 2011
Are you weightless
on the Moon?
a) yes
b) no
c) depends
Is there “gravity” on
the Moon?
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Monday, October 3, 2011
Weight on other planets
Weight on Earth, Mars, and Saturn:
Mmars = 0.1 Mearth
Rmars = 0.5 Rearth
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Monday, October 3, 2011
Weight on other planets
Weight on Earth, Mars, and Saturn:
Mmars = 0.1 Mearth
Rmars = 0.5 Rearth
Msaturn = 95 Mearth
Rsaturn = 9.4 Rearth
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Monday, October 3, 2011
Are the astronauts orbiting the Earth weightless?
a) yes
b) no
c) depends
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Monday, October 3, 2011
Understanding Orbital Motion
The universal law of gravity allows us to
understand orbital motion of planets and
moons:
Example:
• Earth and moon attract each other through gravitation.
• Since Earth is much more
massive than the moon, the moon’s
effect on Earth is small.
• Earth’s gravitational force
constantly accelerates the moon
towards Earth.
• This acceleration is constantly
changing the moon’s direction of
motion, holding it on its almost
circular orbit.
Monday, October 3, 2011
v
v’
Moon
F
Earth
Orbital Motion (2)
In order to stay on a
closed orbit, an object
has to be within a
certain range of
velocities:
Too slow => Object falls
back down to Earth
Too fast => Object escapes
Earth’s gravity
Monday, October 3, 2011
Geosynchronous Orbits
Monday, October 3, 2011
What’s wrong with this….
“… the shuttle blasts off … Then comes the
tremendous pressure of three G’s and the
sudden release into weightlessness as the ship
leaves the gravitational field behind…”
-from The Arizona Republic
30
Monday, October 3, 2011
Kepler’s Third Law
Explained by Newton
Monday, October 3, 2011
Kepler’s Third Law
Explained by Newton
Balancing the force (called
“centripetal force”) necessary to
keep an object in circular motion
with the gravitational force →
expression equivalent to
Kepler’s third law
Monday, October 3, 2011
Kepler’s Third Law
Explained by Newton
Balancing the force (called
“centripetal force”) necessary to
keep an object in circular motion
with the gravitational force →
expression equivalent to
Kepler’s third law
Py2 = aAU3
Monday, October 3, 2011
The following questions are offered for additional practice.
They are not meant to represent the exact content or type of
questions that will be on the quiz. They are also not meant to
represent the totality of the information that will be on the
quiz.
The lecture notes and their embedded class participation
questions should give you a good idea of the content covered
in class.
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Monday, October 3, 2011
1. The period of Jupiter's orbit around the
sun is approximately 12 years. What is the
approximate distance from the sun to
Jupiter?
a. 144 AU
b. 1728 AU
c. 42 AU
d. 5.2 AU
e. 2.3
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Monday, October 3, 2011
2. In pre-Copernican astronomy, it was
almost universally believed that
a. the planets traveled in elliptical orbits
about the Earth.
b. the center of the universe was the Sun
with the Milky Way representing other
distant planets.
c. the Sun was at the center of the universe.
d. the Earth was at the center of the
universe.
e. None of the above was believed.
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Monday, October 3, 2011
3. An apparent westward motion of a planet in
the sky compared to the background stars (as
viewed from the Earth) when observed on
successive nights is referred to as
a. epicycle
b. retrograde motion
c. prograde motion
d. heliocentric motion
e. deferent
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Monday, October 3, 2011
4. The purpose of using epicycles and
deferents to explain the motion of the planets
in the night sky was to account for
a. prograde motion.
b. Mercury and Venus' limited angular
distance from the Sun.
c. retrograde motion.
d. non-uniform speed of the planets in their
orbits.
e. precession of the equinoxes.
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Monday, October 3, 2011
5. The greatest inaccuracy in Copernicus'
model of the solar system was that the planets
a. travel in circular orbits with uniform
motion.
b. traveled on epicycles whose centers
followed orbits around the Sun.
c. traveled in elliptical orbits.
d. were allowed to travel backwards in their
orbits.
e. the planets orbited the Sun.
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Monday, October 3, 2011
6. The orbit of the planet Jupiter is ellipse
with the Sun at one focus. What is located
at the other focus?
a. The asteroid belt
b. Earth
c. Saturn
d. Jupiter
e. Nothing
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Monday, October 3, 2011
7. Which of the following statements best
describes Kelper's 3rd law of planetary
motion?
a. The smaller the diameter of a planet, the
faster its rotational period.
b. The orbital period of a planet is directly
proportional to the diameter of the planet.
c. The smaller the orbit, the longer its orbital
period.
d. The larger the orbit, the longer its orbital
period.
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Monday, October 3, 2011
8. Why did Galileo's observations of moons
orbiting Jupiter disagree with the geocentric
model of the universe of his time?
a. The moons moved in non-circular orbits about
Jupiter.
b. The moons did not appear to orbit the Sun.
c. The moons did not appear to orbit the Earth.
d. The moons appeared to be too small, and
therefore too far away, to be considered part of
the solar system.
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Monday, October 3, 2011
1.d
2.d
3.b
4.c
5.a
6.e
7.d
8.c
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Monday, October 3, 2011