Renaissance Astronomy
Nicholas Copernicus (Niklas Koppernigk) Developed a mathematical model for a Heliocentric solar system
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
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
Planetary Configurations - Inferior Planets
Nicholas Copernicus Planetary Configurations - Superior Planets
Planetary Distances PlanetCopernicusModern Mercury Venus Earth Mars Jupiter Saturn
Tycho Brahe Danish Aristocrat Superb naked eye positions of planets Observations (experiment) can decide between physical models
Kepler’s Laws First Law Planets orbit the Sun in ellipses with the Sun at one focus of the ellipse Sun Planet
Ellipses Focus d1d1 d2d2 d 1 + d 2 = constant for any point on ellipse
Ellipses b a a = Semi-major axis b = Semi-minor axis
Eccentricity a c e = c/a
Kepler’s Laws Second Law A 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 Law The orbital period of a planet squared is proportional to the length of the semi-major axis cubed. P 2 a 3
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
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 Galilei 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 Moon b Mountains, valleys (Earthlike) features were observed. b But the Moon was in the Celestial Realm Telescope Discoveries
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?
Telescope Discoveries Phases of Venus The full range of phases cannot happen in the Geocentric Model.
The Phases of Venus Geocentric Model
The Phases of Venus Heliocentric Model
Telescope Discoveries Sunspots Showed they were really on the Sun The Sun was the physical mani- festation of God Board of Inquisition
The Trial of Galileo
Isaac Newton
Newton’s Laws A body continues to move as it has been moving unless acted upon by an external force. The 1 st 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 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
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
Newton’s Universal Gravitation M m d Two masses separated by a distance
Newton’s Universal Gravitation
Inverse Square Law Separation Force R F 2R ¼F 3R 1/9 F ½R 4F ¼R 16F
Newton’s Universal Gravitation The force of gravity cannot be made zero. G is small 6.67 X N m 2 /kg 2 Mass causes gravity Only one kind of mass Contrast with the electric force
The Apple m M
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
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
The Earth and Moon F Earth Moon R
Orbiting - the Complete Story
< 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
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