Download First exam next Wednesday Today in class Review

Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
First exam next Wednesday
Newton’s Law
Equivalence Principle
Orbits
Today in class
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Review: Motion, Gravity
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Gravity and Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Orbits
Review: Motion
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Newton’s laws of motion
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Orbits
1. Momentum (qualitative)
2. Force and Acceleration (quantitative)
3. Equal and opposite forces (structure of theory)
These are actually all aspects of conservation of momentum
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Newton’s first law
Review: Motion
Newton’s Laws of
Motion
Newton’s 1st law:
Objects at rest stay at rest
Objects in motion stay in motion
Unless acted upon by a force
Velocities are
unchanged without
force
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Contradicts Aristotle’s physics
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the earth can move through
space at high speed (around
the sun) and we would never
know it
Gravity and Orbits
Newton’s Law
Equivalence Principle
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Newton’s second law
higher mass
Newton’s second law:
Force = mass × acceleration
F = ma
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velocity
force
acceleration
same force
magnitude,
lower mass
Establishes mass as the
property of matter that defines
inertia (difficulty of changing
velocity)
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More mass requires larger force
to follow same path
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More acceleration requires
larger force for same mass
Often ”fixed” objects just have
mass so large that acceleration is
not perceptible. (The Earth)
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Newton’s third law
Review: Motion
Newton’s third law:
Every action has an equal and opposite reaction
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For an isolated system, all forces sum to zero
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Throwing something from a wheeled cart makes the
cart move
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In order to change velocity in space, must have reaction
mass (exhaust) to throw away
Conservation of momentum:
In a ”sticky” collision the object with a higher product of
mass and velocity ”wins.”
More massive objects are more ”stubborn” about changing
their motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Newton’s Laws of Motion
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Notable features of Newton’s laws of Motion
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Universal - apply the same to both heavenly and earthly
bodies
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Essential milestone in astronomy - broke division
between heavenly and earthly realm
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Principles discovered in the lab can be applied to the
cosmos
More on this as we discuss gravitation
Newton’s Law
Equivalence Principle
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Newton’s Law of Gravity
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Force = G
( Mass 1) × (Mass 2)
( distance separated )2
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The two forces are equal and opposite
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Force doubles if either mass is doubled
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Force decreases if distance increases
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Force is 4 times if distance is half
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Force is 1/4 if distance is double
Equivalence Principle
Review: Motion
Gravitational mass and inertial mass are the same!
gravity
large mass
small mass
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Orbits
Force
Acceleration
F1 = M1 a = M1 G
M2
M2
=⇒ a = G 2
2
d
d
Accelleration due to gravity does not depend on object’s mass
Depends on mass of other body
Two objects of different mass fall at same rate
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
orbiting objects
Review: Motion
equal forces
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Orbits
Different accelerations
Common mistake:
Forces are equal and opposite even with different masses
only accelerations are different
Thus, for example, the earth and moon feel the same force,
but the Earth only moves a small amount compared to the
Moon.
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Kepler’s Laws
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Orbits
All of Kepler’s laws of planetary motion are derivable from
Newton’s laws of motion and gravity
Newton’s laws can also describe
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Orbits of moons around planets
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Non-bound orbits (passing encounters)
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Orbital changes due to gravitational encounters or other
forces
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and more!
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Kepler’s 1st and 2nd Laws
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Orbits
Kepler:
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1. Planets move on ellipses
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2. Planets sweep out equal area in equal time
(thus moving faster when close to sun)
Newton:
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Objects closer to central object experience larger
acceleration and have larger velocity
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Laws give both shape of orbit (ellipse)
and variation in orbital speed per Kepler’s 2nd law
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Kepler’s 3rd Law
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Orbits
Kepler: only works for planets (proportionality more general)
(period)2 = (avg. distance from sun)3
where period and distance are measured in Earth years and
Earth’s orbital distance.
Newton: for any system (Earth-moon, Jupiter, etc)
(period)2 =
4π 2
(avg. distance from sun)3
G (M1 + M2 )
period is now related to masses of objects.
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Kepler’s 3rd Law
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
You should know:
Newton’s Law
Equivalence Principle
Orbits
4π 2
p =
a3
G (M1 + M2 )
2
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larger orbits have longer periods
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objects in larger orbits have
lower speeds
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same size orbit around larger
mass has shorter period
And the contrary of each
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version