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