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Heliocentric Models Copernicus and Kepler Intro to Solar System Kepler 1 Copernicus - 1500 A.D. helio-centric: Sun-centered Zeilik - 6/e • Sun at the center of the Cosmos • Earth revolves around the Sun on a yearly basis (period = one year) • Earth rotates on its axis daily Intro to Solar System Kepler 2 assumptions: uniform circular motion aesthetics: pleasing, harmonious predictions: no better than Ptolemy’s • distance from Earth to celestial sphere is MUCH greater than Earth-Sun distance – explains why no parallax observed • daily motion of heavens becomes the rotation of the Earth on its axis • motion of many spheres becomes the motion of only one Intro to Solar System Kepler 3 BUT ! no explanation of why things don’t fly off • apparent motion of Sun relative to stars results from annual revolution of Earth around the Sun • planets’ retrograde motions occur from the motion of the Earth relative to the planets – passing of planets • based the sequence of planets on their sidereal periods (periods of revolution wrt the stars) • calculated the distance of planets from the Sun Intro to Solar System Kepler 4 Using the unit of distance 1 AU = Earth-Sun distance PLANETS COPERNICUS MODERN Mercury Venus Earth Mars Jupiter Saturn 0.387 0.723 1.00 1.52 5.20 9.54 Intro to Solar System 0.38 0.72 1.00 1.52 5.22 9.17 Kepler 5 Problems with the Copernican model • predictions are, in the end, no better • no physical explanations (still natural motion) • enthralled with sphere – > circular orbits, constant speeds Intro to Solar System Kepler 6 Johannes Kepler - 1600 A.D. foundation for modern cosmological concepts • built on successes and failures • demanded that his model’s predictions be at least as accurate as the observations (1 arcmin error) “I have discovered among the celestial movements the full nature of harmony.” Intro to Solar System Kepler 7 Kepler - the Ellipse two focal points foci minor axis focal distance semi-minor axis - half the minor axis Intro to Solar System Kepler 8 Kepler - the Ellipse major axis minor axis semi-major axis - half the major axis (a) semi-minor axis - half the minor axis Intro to Solar System Kepler 9 Kepler - the Ellipse two focal points foci major axis minor axis focal distance semi-major axis - half the major axis (a) semi-minor axis - half the minor axis eccentricity = focal distance major axis Intro to Solar System Kepler 10 Kepler - the Ellipse major axis focal distance eccentricity = focal distance major axis Intro to Solar System Kepler e = 0 means ???? e = 1 means ???? 11 Kepler’s Three Laws I. Law of Ellipses Each planet’s orbit is an ellipse with the Sun at one of the foci. implication: distance of the planet to the Sun varies Intro to Solar System Kepler 12 Kepler’s Three Laws II. Law of Equal Areas A line drawn from a planet to the Sun sweeps out equal areas in equal times. implication: orbital speeds are non-uniform yet vary in a regular way Closer a planet is the the Sun, the faster it moves in its orbit (force ????) Intro to Solar System Kepler 13 Kepler’s Three Laws III. Harmonic Law Planet p (Earth years) a (AU) ============================ Mercury 0.24 0.39 Venus 0.62 0.72 Earth 1.0 1.0 Mars 1.9 1.5 Jupiter 12 5.2 Saturn 29 9.5 Intro to Solar System Kepler 14 Kepler’s Three Laws III. Harmonic Law Square of the orbital period is proportional to the cube of the average distance. p2 = k a3 implication: planets with large orbits move slowly Proportion holds for all planets => A PHYSICAL CAUSE !! Intro to Solar System Kepler 15 Kepler’s Third Law p2 = k a3 k = proportionality constant p (years) a (AU’s) => k = 1 True for any body orbiting the Sun, even spacecraft! “I contemplate its beauty with incredible and ravishing delight. Intro to Solar System Kepler 16 Kepler made perhaps the greatest leap in scientific thinking predictions were 10 times more accurate than either Ptolemaic model (geocentric) Copernican model (heliocentric) gave birth to astronomy as a physical science Intro to Solar System Kepler 17 Orbital Eccentricities Planet Orbital Eccentricity Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Intro to Solar System 0.206 0.007 0.017 0.094 0.048 0.054 0.048 0.007 0.253 Kepler 18