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## Astronomy in the Renaissance

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**Astronomy in the Renaissance**• Nicolaus Copernicus (1473-1543) • Could not reconcile centuries of data with Ptolemy’s geocentric model • Consequently, Copernicus reconsidered Aristarchus’s heliocentric model with the Sun at the center of the solar system**Astronomy in the Renaissance**• Heliocentric models explain retrograde motion as a natural consequence of two planets (one being the Earth) passing each other • Copernicus could also derive the relative distances of the planets from the Sun**Copernican Revolution**• Stated that the Earth traveled around the sun in a circular path. Earth was the third planet from the Sun • Model included: • Planets moved counterclockwise • Earth tilted on axis • Only the Moon travels around Earth • Planets closer to the sun move faster than those further away.**Copernicus’s Model(published in 1512)**Problems: • Still held to some ancient Greek ideas: • Circular orbits – so he still had to keep epicycle movement (complexity) • Stars still fixed points • Could not explain lack of parallax • Went against Church doctrine • though wasn’t banned until 1616 (Galileo)**Tycho Brahe - Danish**• Studied both Copernicus and Ptolemy's models - felt that both didn’t accurately show the position of the planets • Took very detailed observations on the positions of planets and stars – 20 yrs. • Made his own tools and instruments (however no telescope just yet) • Hired Johannes Kepler as his assistant in 1600.**Astronomy in the Renaissance**• Tycho Brahe • Made observations (supernova and comet) that suggested that the heavens were both changeable and more complex than previously believed • Proposed compromise geocentric model, as he observed no parallax motion!**Johannes Kepler - German**Supported heliocentric model Wanted to find a unifying principle to explain planetary motion without using epicycles 9 years after Tycho’s death discovered the problem with prior models – the shape of the orbit was not a circle but an ellipse Using Tycho’s very precise Mars data, Kepler showed the orbit to be an ellipse Did this using triangulation (1571-1630)**Discovered that planets do not move in circles around the**Sun, rather, they follow ellipses with the Sun located at one of the two foci! Astronomers use the term eccentricityto describe how round or “stretched out” an ellipse is – the higher (closer to 1) the eccentricity, the flatter the ellipse. Johannes Kepler (1571-1630)**Kepler’s 1st Law**• Planets move in elliptical orbits with the Sun at one focus of the ellipse**Kepler’s 1st Law**• Eccentricity of the ellipse is the ratio of the distance between the foci and the length of the major axis. • The length of the semi-major axis and the eccentricity tells us the size and shape of a planets orbit. • Most planets orbits look more like circles than flattened circles – except Mercury & Pluto**Kepler’s 2nd Law**• The orbital speed of a planet varies so that a line joining the Sun and the planet will sweep out equal areas in equal time intervals • The closer a planet is to the Sun, the faster it moves aphelion perihelion**Kepler’s 1st & 2ndLaws**Explained why a planets brightness would change (no more epicycles) Apply to any orbiting object Published in 1609; only proven for Mars at this point.**3rd Law is the Harmonic Law**• The square of a planets orbital period is proportional to the cube of it’s semi-major axis. • The time it takes a planet to travel one orbit around the sun is called its period. • Basically – relates the size of a planets orbit to its sidereal orbital period.**Kepler’s 3rd Law**• The amount of time a planet takes to orbit the Sun is related to its orbit’s size • The square of the period, P, is proportional to the cube of the semimajor axis, a**Kepler’s 3rd Law**• This law implies that a planet with a larger average distance from the Sun, which is the semimajor axis distance, will take longer to circle the Sun • Third law hints at the nature of the force holding the planets in orbit**P2=D3**P is the period measured in years (earth) D is distance in AU (astronomical units) Basically - the further a planet is from the sun, the longer its revolution AU – is the semi-major axis of the Earth around the Sun (average distance of earth to Sun) 3rd Law