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Phys 181-701
Astronomy
Galileo’s Apparatus – Deutches Museum, Munchen, Germany
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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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Programming Notes…..
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Astronomy 181 - Midterm Exam Results
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Number of Students
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The Results Are In…
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3
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0-49%
50-59%
60-69%
70-79%
80-89%
90-99%
100%
Exam Average = 74.2% = 44.52/60
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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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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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“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?
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8000 m/s!!!
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•Newton invents calculus
Summary
•Newton Proves Kepler’s Laws
•Universal Gravitation used to determine the mass
of the earth
•Tides understood
•Moon “lock” understood
•Satellite motion possible
•Solar system travel made possible
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Electromagnetic Radiation
Chapter 3 (3.3, 3.4, 3.5)
Chapter 4 (4.2, 4.4)
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The frequency is measured in Hertz (Hz) and is the number of
waves which pass a given point in one second.
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Time period of mars
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NEXT TIME:
Two Laws of
RADIATION
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