After Galileo
The Sun and the Earth
• Ptolemy c. AD 90 – c. AD 168 had said
planets travel in circles which traveled in
circles around the earth.
• Copernicus 1473 – 1543 said it would
require less circles if the sun were the
center. De Revolutionibus 1543.
• Galileo wrote a book in Italian defending
Copernicus’ views. Tried by the
Inquisition.
• Many scientists did not support Galileo
– Difficult to see through primitive telescope
– Earth obviously not moving
• No overwhelming evidence
Kepler 1571-1630
• Astronomer and Mathematician
• Assistant to Tycho Brahe
• Astrologer to
Holy Roman Emperor
• Mystic - Greek Geometry
– 5 Regular Solids
– 5 Planets
• Tycho’s Data
• Modern Science
• Einstein - “God does not play dice.”
Kepler
Three Laws:
• The orbit of a planet is an
ellipse with the Sun at one of
the two foci.
• A line segment joining a planet
and the Sun sweeps out equal
areas during equal intervals of
time.
• The square of the orbital
period of a planet is
proportional to the cube of
the semi-major axis of its orbit.
Prob Set 10C
Newton 1642-1727
• Mathematical Genius
• Manic-Depressive
No Social Life
• Invented Calculus
• Professor at Cambridge
• At the Royal Society rumor of a
mathematician at …
• “What path would a planet
follow if the sun attracted it with
an inverse square force?”
• Newton Answered: “An ellipse”
Inverse Square
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Legend has it that Newton was looking at an apple
aapple = 9.8 m/s2
amoon = .0027 m/s2
Ratio = 9.8 / .0027
≈ 3600
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Radius of earth = 6.38 * 106 m
Radius of moon’s orbit = 3.84 *108 m
Ratio = 3.84x108 / 6.38x106 = 60.2
60 x 60 = 3600
The moon is 60 times farther away
It’s acceleration is 3600 times less
a ~ 1 / r2
F ~ 1 / r2
• 10 times farther away, the earth’s gravity is 100 times
weaker
• Here we are 4,000 miles from the center of the earth.
• If you weight 200 pounds here, 40,000 miles into
space you will weigh 2 pounds
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a = k / r2
a∙r2 = k
a1 ∙ r12 = a2 ∙ r22
a1 / a2 = r22 / r12
a1 / a2 = (r2 /r1) 2
Prob Set 15G