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Renaissance
Astronomy
Nicholas Copernicus1473 - 1543
(Niklas Koppernigk)
Developed a mathematical model
for a Heliocentric solar system
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
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
Nicholas Copernicus
Planetary Configurations - Inferior Planets
Nicholas Copernicus
Planetary Configurations - Superior Planets
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
Tycho Brahe1546-1601
Danish Aristocrat Superb naked eye positions of planets Observations (experiment) can decide
between physical models
Kepler’s Laws
First LawPlanets orbit the Sun in ellipses
with the Sun at one focus of the ellipse
Sun
Planet
Ellipses
Focus Focus
d1 d2
d1 + d2 = constant for any point on ellipse
Ellipses
a = Semi-major axis
b = Semi-minor axis
Eccentricity
a
c
e = c/a
Kepler’s Laws
Second LawA line drawn from the planet
to the Sun sweeps out equal areas in equal intervals of time
The Search for Order
Perfect solids
The Search for Order
Music of the Spheres
Kepler’s Laws
Third LawThe orbital period of a planet
squared is proportional to the length of the semi-major axis cubed.
P2 a3
Using the Third Law
P2 a3
P2 constanta3
P2 a3
P measured in years, a in AU, object orbits Sun
Kepler’s Laws
Empirical Kepler could not explain why the
planets orbited the Sun (he thought it had something to do with magnetism)
Universal
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
Telescope Discoveries
Milky Way
Objects exist that Aristotle knew nothing about - the combined light of many faint stars can produce an observable result.
The Moonb Mountains, valleys (Earthlike) features
were observed.b But the Moon was in the Celestial Realm
Telescope Discoveries
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?
Telescope DiscoveriesPhases of Venus
The full range of phases cannot happen in the Geocentric Model.
The Phases of VenusGeocentric Model
The Phases of VenusHeliocentric Model
Telescope DiscoveriesSunspots
Showed they were really on the Sun
The Sun was the physical mani-festation of God
Board of Inquisition
The Trial of Galileo
Isaac Newton1642 - 1727
Newton’s Laws
A body continues to move as it has
been moving unless acted upon by an
external force.
The 1st Law
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
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
Newton’s Laws
For every action force there is an equal and opposite reaction force
(You cannot touch without being touched)
The 3rd Law
Newton’s Universal Gravitation
M m
d
Two masses separated by a distance
Newton’s Universal Gravitation
2d
GMmF
2d
MmF
Newton’s Universal Gravitation
Inverse Square Law
Separation Force
R F
2R ¼F
3R 1/9F
½R 4F
¼R 16F
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
The Apple
2
R
mGMF
m
M
mgR
mGM
2
2
R
GMg
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
Orbiting Falling without getting closer
to the ground.T Newton’s estimate of orbital velocity
Examples:T Space ShuttleT ElevatorT Amusement Park Rides
The Earth and Moon
F
2R
mGMF
Earth
Moon
Rma
R
mGM
2
G
aRM
2
Orbiting - the Complete Story
< vorb Ellipse
Circle
vorb Circle
Ellipse
vorb<v<vesc Ellipse
Velocity Shape
Parabola
vesc Parabola Hyperbola
> Vesc Hyperbola
Link
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)
The Principle of Elegance
Physicists look for symmetry
• Occam’s Razor
End of Renaissance Astronomy
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