Transcript Chapter3 (with interactive links)

Lecture Slides
CHAPTER 3: Laws of Motion
Understanding Our Universe
SECOND EDITION
Stacy Palen, Laura Kay, Brad Smith, and George Blumenthal
Prepared by Lisa M. Will,
San Diego City College
Copyright © 2015, W. W. Norton & Company
Laws of Motion
 Describe planetary
orbits.
 Understand laws of
motion and gravity.
Planetary Orbits
 Copernicus realized the Solar System was
heliocentric—centered on the Sun.
 Planets exhibit apparent retrograde motion due to
their distances from Earth and orbits around the Sun.
Planetary Orbits: Ellipses
 Kepler’s 1st Law:
Planetary orbits are
ellipses.
 Each ellipse has two foci.
 The Sun is at one focus
of a planet’s elliptical
orbit.
Planetary Orbits: Semimajor Axis
 An ellipse has a size,
described by the
semimajor axis.
 The longest length (major
axis) is twice the length
of the semimajor axis.
Planetary Orbits: Eccentricity
 Each orbit has a shape
as well as a size.
 The eccentricity
describes the shape how elongated the
ellipse is and how far
the foci are separated.
Class Question
Does Kepler’s 1st Law allow for a circular
planetary orbit?
A. Yes
B. No
Planetary Orbits: Remember
 A circle is an ellipse with an
eccentricity of zero.
 Most planetary orbits are very
close to circular.
 The slight deviations from circular
are why Kepler’s Laws are needed
to explain orbits!
Planetary Orbits: Remember (Cont.)
Planetary Orbits: Remember (Cont.)
Planetary Orbits: Kepler’s 2nd Law
 Kepler’s 2nd Law: the
Law of Equal Areas.
 The line between the
Sun and the planet
“sweeps” out equal
areas in equal times.
Planetary Orbits: What is Kepler’s 2nd Law
 What does Kepler’s 2nd
law mean?
• A planet will go fastest
when closest to the
Sun.
• It will go slowest when
farthest from the Sun.
Class Question
The Earth is closest to the Sun in January and
furthest from the Sun in July. When is the Earth
moving the fastest In its orbit?
A. January
B. July
Planetary Orbits: Kepler’s 3rd Law
 Kepler’s 3rd Law:
 Distant planets
take longer to
orbit the Sun.
 Distant planets
travel at slower
speeds.
 For P = orbital
period in years
and a =
semimajor axis in
AU
P2 = a 3
Class Question
The semimajor axis of Earth’s orbit is 1 AU. The
semimajor axis of Saturn’s orbit is 9.5 AU. What
Saturn’s orbital period in Earth years?
Use Kepler’s 3rd law!
P2 = a 3
So P = a3/2
Answer: Ps/PE = (aS/aE)3/2 = (9.5/1)1.5= 29. So 1 year
on Saturn is about 29 Earth years!
Galileo
 Galileo Galilei was the first to use a telescope for
astronomical observations, around the year 1609.
 He made important discoveries (you could have,
too, if you were the first to look at the night sky with
the newly invented telescope!)
 Galileo discovered Jupiter’s four largest moons,
observing them to orbit Jupiter over several nights.
He also observed phases of Venus.
 Both discoveries were controversial. =>
Contradicted the widely held geocentric view of the
universe and were consistent with a heliocentric
view
Galileo: Model of Motion
 He experimented with falling and moving objects
and crafted a model of motion.
=>An object in motion will continue moving along a
straight line with a constant speed until an
unbalanced force acts on it.
He also came up with formulas for distance, velocity
and acceleration as a function of time. For
constant (uniform) acceleration, such as for falling
bodies, starting from rest, the distance travelled is
proportional to the time squared. (d ~ t2 )
Laws of Motion
 Sir Isaac Newton discovered laws that explain why
objects in the universe move the way they do.
 Newton’s Laws of Motion and Law of Gravity explain
why planets orbit the Sun, following Kepler’s
observationally-derived Laws.
Laws of Motion: Newton’s First Law of Motion
Newton’s First Law of Motion: Galileo’s result
(also called the law of Inertia)
 A moving object will stay in constant motion.
•
•
“Constant” motion means at a constant speed and in a
constant direction.
An object at rest stays at rest.
Laws of Motion: Newton’s Second Law
 Newton’s Second Law:
Net forces cause
changes in motion =>
acceleration.
Laws of Motion: Example
 In this example, the coffee cup is at rest with respect
to the car that it is in.
 As long as the car travels at a constant speed and
direction, the coffee will be level.
Laws of Motion: Acceleration
 A change in speed
and/or direction is called
acceleration.
 Acceleration measures
how quickly a change in
motion takes place.
 Acceleration = (change in
velocity)/time
 a = (vfinal- vinitial)/time
interval
Laws of Motion: Acceleration – Force Vs. Mass
 A net force causes acceleration.
 Mass resists changes in motion.
• More mass => less acceleration for a given force.
• Greater forces => greater accelerations.
• F = ma (or a = F/m)
Laws of Motion: Acceleration – Force Vs. Mass (Cont.)
•Blue arrow is applied
force , green arrow is
acceleration
Laws of Motion: Acceleration – Force Vs. Mass (Cont.)
Laws of Motion: Acceleration – Force Vs. Mass (Cont.)
Laws of Motion: Summary
 Newton’s Third Law: forces occur in action-reaction
pairs.
 The two forces are equal in strength.
 The two forces have opposite directions.
 Note that the strengths of the forces between the Earth
and Moon are equal, but the accelerations are not!
Law of Gravity
 All objects on Earth have been experimentally shown
to fall with the same acceleration, g = 9.8 m/s2.
 Experiments on the Moon have shown the same
phenomenon but with a different value of the
acceleration (about 1/6 of Earth’s) due to the Moon’s
different mass and radius.
Law of Gravity: Weight
 Weight is the product of your mass and the
acceleration due to gravity:
Fweight  m  g
 Because different worlds have different gravitational
accelerations, you would weigh a different amount
elsewhere!
Class Question
The acceleration due to gravity on the Moon is 1/6 g.
The acceleration due to gravity on Mars is 1/3 g. On
which of these worlds would you weigh more?
A. Mars
B. Moon
Law of Gravity: Definition
 Gravity is an attractive, mutual force between any two
objects with mass.
 It depends on the objects’ masses.
 It depends on the distance between them.
Law of Gravity: Mass Vs. Force
 The greater the mass, the greater the gravitational
force they experience.
 The force of gravity includes the product of both
masses.
Law of Gravity: Distance Vs. Force
 The greater the distance between the objects, the
weaker the gravitational force.
 The gravitational force is dependent on the inverse
square of the distance between the two objects.
Law of Gravity: Inverse Square Law
 Putting the pieces together:
• G is the universal gravitational constant.
• The m terms are the two masses.
• The r is the separation distance.
 This form is known as an inverse square law.
Fgrav
m1  m2
 G
2
r
Class Question
Object A and Object B initially have the same mass.
If Object A’s mass increased, what would happen to
the gravitational force between the two masses?
A. The force would decrease.
B. The force would increase.
Class Question
Object A and Object B have the same mass. If the
distance between the two objects increased, what
would happen to the gravitational force between the
two masses?
A. The force would decrease.
B. The force would increase.
Law of Gravity: Orbits and Satellite
 Orbits are one body falling
around another.
 The less massive object is
considered a satellite of the more
massive object.
Law of Gravity: Orbits and Satellite (Cont.)
Law of Gravity: Orbits and Satellite (Cont.)
Law of Gravity: Orbits and Satellite (Cont.)
Law of Gravity: Orbits and Satellite (Cont.)
Law of Gravity: Centripetal Force
 Gravity provides the centripetal force that holds a
satellite in its orbit.
 If moving too fast or too slow, orbit will not be circular.
Law of Gravity: Centripetal Force (Cont.)
Law of Gravity: Centripetal Force (Cont.)
Law of Gravity: Astronauts
 Astronauts float freely in the space station because
they and the station are both falling at the same rate
around Earth.
 Gravity is acting on the astronauts!
Law of Gravity: Relation to Planetary Orbits
How does this relate
to planetary orbits?
 Gravity changes both the direction
and the speed of the planet.
 Explains Kepler’s
Second Law.
Law of Gravity: Relation to Planetary Orbits (Cont.)
Law of Gravity: Relation to Planetary Orbits (Cont.)
Law of Gravity: Bound or Unbound Orbit
 An object’s speed at its closest approach will
determine the shape of the orbit and if the orbit will be
bound or unbound.
 For example, an comet with an unbound orbit will
orbit the Sun once and never return.
Newton and Kepler
 Newton derived Kepler’s Laws from his law of gravity.
• Physical laws explain Kepler’s results!
 Newton’s laws were tested by Kepler’s observations.
• Their agreement showed that Newton’s law of gravitation
was correct.
Chapter Summary
 Kepler’s Laws describe planetary orbits.
• Planetary orbits are ellipses.
• Planets sweep out equal areas in their orbits in equal
times.
• The larger the orbit of a planet, the longer the orbital
period of the planet.
 Newton’s Laws of Motion and Gravitation explain why
Kepler’s Laws work.
Astronomy in Action
Velocity, Force and Acceleration
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AstroTour
Elliptical Orbits
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AstroTour
Newton’s Laws and Universal Gravitation
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AstroTour
Velocity, Acceleration, Inertia
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Ptolemaic Orbit of Mars
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Ptolemaic Phases of Venus
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Retrograde Motion
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Eccentricity Demonstrator
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Planetary Configurations Simulator
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Planetary Orbit Simulator
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Synodic Period Calculator
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Kepler’s Third Law
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Phases of Venus
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Newton’s Law of Gravity Calculator
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Gravity Algebra
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Planetary Orbit Simulator
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Earth Orbit Plot
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Understanding Our Universe
SECOND EDITION
Stacy Palen, Laura Kay, Brad Smith, and George Blumenthal
Prepared by Lisa M. Will,
San Diego City College
This concludes the Lecture slides for
CHAPTER 3: Laws of Motion
wwnpag.es/uou2
Copyright © 2015, W. W. Norton & Company