Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
First exam next Wednesday
Newton’s Law
Equivalence Principle
Questions
Today in class
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Review: Motion, Gravity
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Gravity and Orbits
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Questions
Review: Motion
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
Question concepts
Question #1: Speed is related to the distance an object
moves in a given time, independent of direction. Velocity is
both the speed and the direction of motion. An object’s
velocity can change, due to acceleration, without its speed
changing.
Question #2: The ”feeling” of weightlessness is actually due
to the lack of a supporting force, not the lack of gravity.
Question #3: The force applied to an object is the product
of its mass and the resulting acceleration. Thus if similar
forces are applied to two objects, the one with more mass
experiences less ecceleration in an amount proportional to its
mass, (accel.) = (Force)/(mass).
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Questions
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Today
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Newton’s Laws of Motion
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Newton’s Law of Gravity
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Orbits - Keplers Laws
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Orbits - Newton’s version of Kepler’s Law
Newton’s Law
Equivalence Principle
Questions
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
Newton’s laws of motion
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
1. A force is required for velocity to change
Questions
2. Acceleration is a response to a force, reduced by mass
Orbits
3. Forces are always in equal pairs (structure of theory)
These are actually all aspects of conservation of momentum
Basically the rules for motion, acceleration and mass that I
described last lecture
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
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
Essential milestone in astronomy - broke division
between heavenly and earthly realm
Principles discovered in the lab can be applied to the
cosmos
Newton’s Law
Equivalence Principle
Questions
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
Newton’s Law of Gravity
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Questions
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
Questions
Question concepts
Question #4: The gravitational force between two objects
increses with each objects mass. The change in the velocity
of an object is proportional to the force applied to it.
Question #5: Newton’s law of gravity, F = GM1 M2 /d 2
expresses, for example, each of the following: Force increases
proportional to the mass of either object. Force is 4 times if
distance between the objects is half or 1/4 if distance is
double.
Question #6: From a typical planetary orbit, a black hole’s
gravitational field is no different than that of a star with the
same mass. The difference is that a black hole is very small,
so that very close to it gravity is quite strong.
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Questions
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
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
Questions
Force
Acceleration
M2
M2
F1 = M1 a = M1 G 2 =⇒ a = G 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
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
orbiting objects
Review: Motion
equal forces
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Questions
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.
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Questions
Questions
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
Question concepts
Review: Motion
Question #7: Two bodies of different masses still each
experience equal and opposite gravitational force due to
each other.
Newton’s Laws of
Motion
Question #8: In a binary star, both stars experience equal
and opposite forces. An object of greater mass subject to
the same force as an object of lesser mass will have a smaller
acceleration. Conversely, a less massive object will have a
larger acceleration.
Questions
Question #9: In a binary star system, the two stars
experience equal forces. Thus the less massive star
experiences a greater acceleration (change in velocity), and
therefore a larger orbital motion. Conversely for the star
with more mass.
Gravity and Orbits
Newton’s Law
Equivalence Principle
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
Kepler’s Laws
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Questions
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
Questions
Kepler’s 1st and 2nd Laws
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Questions
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
Questions
Review: Motion
Newton’s Laws of
Motion
Question concepts
Question #10: A planet in an elliptical (non-circular) orbit
does not move at constant speed during its orbit. It moves
fastest at the point in the orbit nearest the star, and slowest
at the point in the orbit farthest from the star. This motion
sweeps out equal area in equal time.
Gravity and Orbits
Newton’s Law
Equivalence Principle
Questions
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
Kepler’s 3rd Law
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Newton’s Law
Equivalence Principle
Questions
Orbits
Kepler: only works for planets (proportionality more general)
(period)2 = (avg. distance from sun)3
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
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 between)3
G (M1 + M2 )
period is now related to masses of objects.
Kepler’s 3rd Law
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
You should know:
Newton’s Law
Equivalence Principle
Questions
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
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions
Review: Motion
Newton’s Laws of
Motion
Gravity and Orbits
Question concepts
Newton’s Law
Equivalence Principle
Questions
Question #11: For an orbit a fixed distance from a central
object, orbital period is shorter for a more massive central
object.
Orbits
Kepler vs. Newton
Kepler’s Laws 1& 2
Kepler’s Laws 3
Newton’s version
Questions