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Renaissance
Astronomy
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Nicholas Copernicus1473 - 1543
(Niklas Koppernigk)
Developed a mathematical model
for a Heliocentric solar system
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Nicholas Copernicus
Synodic PeriodThe orbital period of a planet as measured by a
moving observer
Sidereal Period The orbital period of a planet as measured by a
stationary observer
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Planet Approximate
Sidereal Period
Mercury 88 days
Venus 7.5 months
Earth 1 year
Mars 687 day
Jupiter 12 years
Saturn 30 years
Nicholas Copernicus
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Nicholas Copernicus
Planetary Configurations - Inferior Planets
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Nicholas Copernicus
Planetary Configurations - Superior Planets
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Planetary Distances
Planet Copernicus Modern
Mercury 0.38 0.387
Venus 0.72 0.723
Earth 1.00 1.000
Mars 1.52 1.520
Jupiter 5.22 5.200
Saturn 9.17 9.540
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Tycho Brahe1546-1601
Danish Aristocrat Superb naked eye positions of planets Observations (experiment) can decide
between physical models
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Kepler’s Laws
First LawPlanets orbit the Sun in ellipses
with the Sun at one focus of the ellipse
Sun
Planet
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Ellipses
Focus Focus
d1 d2
d1 + d2 = constant for any point on ellipse
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Ellipses
a = Semi-major axis
b = Semi-minor axis
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Eccentricity
a
c
e = c/a
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Kepler’s Laws
Second LawA line drawn from the planet
to the Sun sweeps out equal areas in equal intervals of time
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The Search for Order
Perfect solids
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The Search for Order
Music of the Spheres
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Kepler’s Laws
Third LawThe orbital period of a planet
squared is proportional to the length of the semi-major axis cubed.
P2 a3
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Using the Third Law
P2 a3
P2 constanta3
P2 a3
P measured in years, a in AU, object orbits Sun
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Kepler’s Laws
Empirical Kepler could not explain why the
planets orbited the Sun (he thought it had something to do with magnetism)
Universal
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Galileo Galilei1564-1642
Among the first to turn a telescope to the sky Developed the Scientific Method Believed in the popularization of science Developed the Law of Inertia
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Telescope Discoveries
Milky Way
Objects exist that Aristotle knew nothing about - the combined light of many faint stars can produce an observable result.
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The Moonb Mountains, valleys (Earthlike) features
were observed.b But the Moon was in the Celestial Realm
Telescope Discoveries
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Telescope DiscoveriesThe Moons of Jupiter
g Clear example of four objects that do not orbit the Earth.
g If Aristotle was wrong here, could he not also be wrong in other areas?
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Telescope DiscoveriesPhases of Venus
The full range of phases cannot happen in the Geocentric Model.
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The Phases of VenusGeocentric Model
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The Phases of VenusHeliocentric Model
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Telescope DiscoveriesSunspots
Showed they were really on the Sun
The Sun was the physical mani-festation of God
Board of Inquisition
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The Trial of Galileo
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Isaac Newton1642 - 1727
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Newton’s Laws
A body continues to move as it has
been moving unless acted upon by an
external force.
The 1st Law
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Newton’s First Law
No mention of chemical composition
No mention of terrestrial or celestial realms
Force required when object changes motion
Acceleration is the observable consequence of forces acting
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Newton’s Laws
The 2nd Law
The Sum of the Forces acting on a body is proportional to the acceleration that the body
experiences F a
F = (mass) a
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Newton’s Laws
For every action force there is an equal and opposite reaction force
(You cannot touch without being touched)
The 3rd Law
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Newton’s Universal Gravitation
M m
d
Two masses separated by a distance
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Newton’s Universal Gravitation
2d
GMmF
2d
MmF
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Newton’s Universal Gravitation
Inverse Square Law
Separation Force
R F
2R ¼F
3R 1/9F
½R 4F
¼R 16F
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Newton’s Universal Gravitation
The force of gravity cannot be made zero.
G is small
•6.67 X 10-11 N m2/kg2
Mass causes gravity
•Only one kind of mass
•Contrast with the electric force
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The Apple
2
R
mGMF
m
M
mgR
mGM
2
2
R
GMg
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Gravity at Work
All objects fall at the same rate in a gravitational field.T Leaning Tower of Pisa - GalileoT Galileo’s Experiment on the MoonT Apparent weightlessnessT Lack supporting force
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Orbiting Falling without getting closer
to the ground.T Newton’s estimate of orbital velocity
Examples:T Space ShuttleT ElevatorT Amusement Park Rides
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The Earth and Moon
F
2R
mGMF
Earth
Moon
Rma
R
mGM
2
G
aRM
2
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Orbiting - the Complete Story
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< vorb Ellipse
Circle
vorb Circle
Ellipse
vorb<v<vesc Ellipse
Velocity Shape
Parabola
vesc Parabola Hyperbola
> Vesc Hyperbola
Link
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Where was Newton Wrong?
Moving too fast Close to the speed of light Solution was Special Relativity (1905)
Too close to a large gravitational field Solution was General Relativity (1917)
On very small scales Inside the atom Solution was Quantum Mechanics (1927)
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The Principle of Elegance
Physicists look for symmetry
• Occam’s Razor
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End of Renaissance Astronomy