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