Transcript Uber Week 5

Phys 181-701
Astronomy
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“The danger to which the success of revolutions is most
exposed, is that of attempting them before the principles on
which they proceed, and the advantages to result from them,
are sufficiently seen and understood.”
Thomas Paine - American Revolutionary
“Anyone in a free society where the laws are unjust has an
obligation to break the law.”
Henry David Thoreau - American Philosopher
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“To command the professors of astronomy to confute their
own observations is to enjoin an impossibility, for it is to
command them to not see what they do see, and not to
understand what they do understand, and to find what they
do not discover.”
Galileo Galilei – In Science
“Numero pondere et mensura Deus omnia condidit.”
Sir Isaac Newton – Principia Mathematica
“If I have been able to see further, it was only because I stood
on the shoulders of giants.”
Newton, in a letter to Robert Hooke
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(rěv΄ə-lōō’shən))
1.
2.
n A drastic and far-reaching
change in ways of thinking and
behaving.
n Orbital motion about a point,
the planetary revolution about the
sun.
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The Copernican
Revolution
1473 - 1542
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There are problems with the
Ptolemaic Model
Problems with Ptolemy
The solar system according to the Ptolemaic Model from
100 A.D. to 1500
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Features…
•Deferent Circles
•Epicycles on the Deferents
•Inferior planets are never more than 47º from the sun
•Retrograde motion of mars is explained
Features
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•
As the precision of astronomical
measurements grew the need for
adjustments to the model called for
additional epicycles.
•
In 1252 King Alfonso X of Castile funded a
10 year project by Arab and Jewish
astronomers to calculate extensive tables.
•
Calculations became horrendously
complicated and even Alfonso suggested
that the model should by simpler if it was to
have any truth in it.
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“Multiplicity ought not be
posited without necessity.”
William Occam – English Scholar - 1340
“Keep it simple, stupid.”
Anonymous 20th Century Philosopher
This principle is known as Occam’s Razor…
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Copernican Theory…
The motions of the planets would be
more easily explained if the sun were
at the center.
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DeRevolutionibus, 1543…
“Venus and Mercury revolve around the sun and cannot
go nearer or further from it than the circles of their orbits
permit…If, acting upon this supposition, we connect
Saturn, Jupiter and Mars with the same center, keeping in
mind the greater extent of their orbits…we cannot fail to
see the explanation of the regular order of their motions.
This proves sufficiently that their center belongs to the
sun…”
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Going Further…
“The extent of the universe…is so great that…[the
earth] disappears when compared to the sphere of
the fixed stars.”
“Although this may appear incomprehensible and
contrary to the opinion of many, I shall, if God
wills, make it clearer than the sun, at least to those
who are not ignorant of mathematics.”
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“…that fool who would reverse the
entire art of astronomy…Joshua
bade the SUN and not the earth to
stand still.”
Martin Luther - 1539
Under very real threat of persecution,
Copernicus changed the title of his book
and its publication was finished only in the
final days of his life.
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•Royal Astronomer of Denmark
•UraniborgBrahe
Tycho
•Observations with the naked eye
•Measured parallax of planets
•Observed a supernova (1572)
•Realized that Ptolemy was not right but denied
Copernicus
1546-1601
•Proposed a model with the earth at the center
and the sun revolving around it, but all of the
other planets revolved around the sun
•Collected the best data available
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KEPLER!
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Johannes Kepler – 1571-1630
Kepler
Deeply religious believer in astrology
Mathematics was evidence of God
Subscriber to the Copernican theory
Hired by Tycho to prove the earth centered
model
Convinced that a mathematical “harmony”
existed for the planets
Inherited Tycho’s fine data
Analyzed data regarding mars
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Kepler’s Laws
1. Each planet moves in an ellipse, with the
sun at one focus.
2. The line between the sun and the planet
sweeps out equal areas in equal times.
3. The ratio of the cube of the average radius
of a planets orbit to the square of its
orbital period of revolution is the same for
each planet. (Harmonic Law)
Kepler’s laws
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Ellipses and Areas
This orbit is in the shape of an ellipse….
The area AAB= The Area ACD
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Law of Conservation of
Angular Momentum
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The Harmonic Law:
Harmonic Law
2
P
a3
k
P2
3
a
k
a = Average radius of planet’s orbit
P = The orbital period of the planet
k = A constant for all objects orbiting the sun
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Consider the earth…
Harmonic Constant

a
1AU  1



1
2
2
P
1yr  1
3
3
This is true for all planets no matter
what the radius of their orbit.
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RetrogradeRetrograde
motion explainedMotion
at long last…
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How does Kepler know the time periods of planets other than the earth?
Consider…
•You can’t go to mars
•You can’t watch mars ‘go round’
•Every so often, mars exhibits
retrograde motion
•Retrograde motion is caused by the
passing of mars by the earth at
various points in their orbits.
How does Kepler know times?
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Working late on this lecture, the clock strikes midnight…
And the hands line up.
A little while later…
And they aren’t lined up at all.
I notice that they line up again sometime around
1:05 am. Is there some sort of a math rule that can
predict when the hands will align?
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A little scratch work and some calculations…
Big deal…
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If I use the hands of the clock as an
Time
mars
analogy
for period
the motionof
of the
planets…
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Radius of mars’ orbit
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Measurement
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IMPORTANT
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Occam’s Razor
Copernicus
Law of Ellipses
Law of Areas
Harmonic Law
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REVIEW:
Kepler Develops Three Laws:
•Law of Ellipses
•Law of Areas
•Harmonic Law
P2
 k  constant
a3
We now understand HOW the planets move…
but not WHY they move.
Review
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Galileo: The Death of the Earth
Centered Universe
•Contemporary of Kepler
•Demonstrated that all objects are accelerated by
gravity by the same amount
•Moving objects remain in motion
•Built a telescope in 1609* and observed the Sun,
Moon, Milky Way, Moons of Jupiter and the phases
of Venus.
1564-1642
*Hans
Lippershey invented the telescope in 1608
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If we assume (incorrectly) that the Tower of Pisa is
20m tall, the ball will take 2s to hit the ground.
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Even if the ball is thrown horizontally from the tower,
the acceleration toward the earth is still 10m/s2.
As a result, the ball that is dropped and the ball that is
thrown both hit the ground after 2 seconds!!!
We will return to this essential idea in a few slides…
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Sir Isaac Newton
1642-1727
Newton’s Laws:
1.
All objects at rest shall remain at rest and all objects
in motion shall remain in motion in a straight line,
unless compelled by a FORCE to do otherwise.
2.
The ACCELERATION of any object is directly
proportional to the FORCE applied to it and
inversely proportional to its MASS.
3.
For every force applied to an object, there is an
equal and opposite force applied by the object on the
actor.
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N
e
w
t
o
n
v
.
s
Newton’s Laws Relative to Galileo’s Experiment:
1.
When the ball is dropped it ceases to be at rest.
Therefore there must be a force, directed downward,
to cause the acceleration.
2.
The acceleration will be equal to the force that gravity
exerts on the ball divided by the mass of the ball, that
is, the acceleration is equal to the force per unit mass.
3.
If the Earth exerts a gravitational force on the ball, the
ball must exert an equal and opposite force on the
Earth!!!!
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Law of Universal Gravitation
Newton knows that the more mass an object has, the greater
the force of Gravity on it.
FG= m g
Where “g” is the special name given to the acceleration that
is caused by gravity. 10 m/s2
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The inverse square law…
Inverse square
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The Law
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Example:
Example
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Assumptions
Mass of baby
Mass of doctor
Distance between baby
and doctor
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“Knowns”
Mass of Mars
Mars-Baby Distance
Universal Gravitational
Constant
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“Weighing” the Earth…
A & B have equal masses and therefore equal weights.
The rod is balanced.
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The very small mass is needed to
balance the gravitational force of
the very large mass.
“G” can be calculated!
Knowing G and Kepler’s Law’s allows us to calculate the mass of the Earth,
Sun and all of the planets moons and asteroids in the solar system
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Return to Pisa…The earth is not flat…
Return to Pisa
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Curved Earth
After one second the projectile has fallen five meters…
But the earth has curved away.
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Question…
If the earth is curved such that it “curves away” 5 meters
for every 8000 meters traveled, how fast would the
projectile need to be going so that, after falling 5 meters, it
was still 5 meters above the earth?
Q
u
e
s
t
a3
k
P2
8000 m/s!!!
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Summary
WE NOW UNDERSTAND…
•Universal Gravitation used to determine the mass of the Earth
•Satellite motion possible
•Solar system travel made possible
WE ARE UNCLEAR ON…
•Newton invents calculus
•Newton Proves Kepler’s Laws
•Tides understood
•Moon “lock” understood
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Calculus and Planetary Motion…
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vt
h
R
R
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WHICH IS NOT THE RIGHT ANSWER….
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This does not represent the true motion….
The true motion is revealed when we
Make the time very, very, very small…
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Newton Tells us that…
An that, for gravity in particular…
We have just discovered that…
We may deduce then that…
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Determine the mass of the SUN….
R = 1.496 x 1011 m
T = 3.156 x 107 s
G = 6.673 x 10-11 Nm2/kg2
M = 1.99 x 1030 kg
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Forces are Balanced on a
Spherical Moon
Forces in Competition
on a Prolate Moon
Forces are Balanced
when Collinear on a
Prolate Moon
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S
u
m
m
a
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IMPORTANT
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Objects fall at the same rate.
Newton’s Laws
Inverse Square Law of Gravity
Nature of Orbits
Renaissance Astronomers
Occam’s Razor
Copernicus
Law of Ellipses
Law of Areas
Harmonic Law
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IMPORTANT
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•
•
•
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Occam’s Razor
Copernicus
Law of Ellipses
Law of Areas
Harmonic Law
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Electromagnetic Radiation
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