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Renaissance Astronomy

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Nicholas Copernicus 1473 - 1543 (Niklas Koppernigk) Developed a mathematical model for a Heliocentric solar system

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Nicholas Copernicus Synodic Period The 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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Planetary Configurations - Inferior Planets

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Nicholas Copernicus Planetary Configurations - Superior Planets

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Planetary Distances PlanetCopernicusModern Mercury0.380.387 Venus0.720.723 Earth1.001.000 Mars1.521.520 Jupiter5.225.200 Saturn9.179.540

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Tycho Brahe 1546-1601 Danish Aristocrat Superb naked eye positions of planets Observations (experiment) can decide between physical models

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Kepler’s Laws First Law Planets orbit the Sun in ellipses with the Sun at one focus of the ellipse Sun Planet

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Ellipses Focus d1d1 d2d2 d 1 + d 2 = constant for any point on ellipse

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Ellipses b a 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 Law A 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 Law The orbital period of a planet squared is proportional to the length of the semi-major axis cubed. P 2 a 3

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Using the Third Law P 2 a 3 P 2 constant a 3 P 2 a 3 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 Galilei 1564-1642 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 Moon b Mountains, valleys (Earthlike) features were observed. b But the Moon was in the Celestial Realm Telescope Discoveries

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Telescope Discoveries The 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 Discoveries Phases of Venus The full range of phases cannot happen in the Geocentric Model.

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The Phases of Venus Geocentric Model

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The Phases of Venus Heliocentric Model

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Telescope Discoveries Sunspots 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 Newton 1642 - 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 1 st 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 2 nd 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 3 rd 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

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Inverse Square Law Separation Force R F 2R ¼F 3R 1/9 F 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 m 2 /kg 2 Mass causes gravity Only one kind of mass Contrast with the electric force

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The Apple m M

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Gravity at Work All objects fall at the same rate in a gravitational field. T Leaning Tower of Pisa - Galileo T Galileo’s Experiment on the MoonExperiment T Apparent weightlessness T 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 Shuttle T Elevator T Amusement Park Rides

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The Earth and Moon F Earth Moon R

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Orbiting - the Complete Story

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< v orb Ellipse Circle v orb Circle Ellipse v orb <v<v esc Ellipse Velocity Shape Parabola v esc Parabola Hyperbola > V esc 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

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