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Lecture 5 Motions of the Planets; Geometric models of the Solar System Motion of Planets Opposition, Conjunction Retrograde Motion Scientific Method and "Models" Size of the Earth Geocentric vs Heliocentric Solar System Jan 27, 2006 Astro 100 Lecture 5 1 Motions of the Planets • Apparent motion is quite uneven, but paths are near ecliptic ("planet" is Greek for "wanderer") • Due to combination of apparent motion of Sun and actual motion of planets around Sun • First, definitions of angular position relative to sun: – Elongation: angle from sun – Conjunction: ~0 deg elongation • Inferior between Earth and Sun • Superior other side of the Sun – Quadrature: 90 deg elongation – Opposition: ~180 deg elongation (opposite sun) Jan 27, 2006 Astro 100 Lecture 5 2 1 Loops • Two classes of apparent motions: URL for this demo: http://www.mhhe.com/physsci/astronomy/applets/Retro/frame.html • Inferior planets: Mercury, Venus – Always near sun in sky, do both direct and retrograde (E to W) among stars – Never reach quadrature, largest angle (maximum elongation) = 28 deg (Mercury), 47 deg (Venus) – When W of sun, only seen in morning sky, when E, only seen in evening. • Superior planets: Mars, Jupiter, Saturn, (Uranus, Neptune, Pluto) – Generally direct motion, slower than sun, but near opposition, do retrograde loops Jan 27, 2006 Astro 100 Lecture 5 3 Handy Summary Table Solar System Apparent Motions: Summary What Due to Path Direction Sidereal Period Synodic Event Diurnal: Stars Earth Rotation about celestial poles E to W 23h 56m solar day = 24h Annual: Sun Orbit of Earth around Sun "ecliptic", tilted 23.5 deg to equator W to E (direct) 365.2422 solar days solar year, seasons Moon Orbit of Moon around Earth tilted 5 deg to ecliptic W to E 27d 8h phases, eclipses Planets Orbits of planets around Sun tilted up to 17 deg to ecliptic direct, 0.39 - 248 retrograde years conjunction, opposition How apparent motions were explained is a good illustration of the "Scientific Method" . . . Jan 27, 2006 Astro 100 Lecture 5 4 2 Scientific Method Experiment Theory Raw Data Calibrated data Analyzed data Speculation Hypothesis Prediction Model/Theory • Most Useful Theories: Law ("reality"??) – Predictive Power: can predict the result of some experiment which has not yet been done – Falsifiable: can suggest an experimental result which would be impossible with this theory – "Simplest": given two theories making same prediction, choose the simplest. In Astronomy, where you can't do experiments, only make observations, the culture is: Instrumentalist Jan 27, 2006 Observer Analyst Pure Theorist Astro 100 Lecture 5 5 Example: Greek's size and shape of Earth • The Greeks already had a sufficiently scientific outlook and enough data (purely visual!) to estimate the sizes and distances of the Earth, Moon, and Sun based on hypothesis that Earth and Moon are spherical • Eratosthenes (-200 BC) observes: Vertical object casts no shadow in one location at noon on a certain day, while shadow is never shorter than 7 deg at the same time 5000 "stades" north – vertical not same direction in different places (Earth curved) Jan 27, 2006 Astro 100 Lecture 5 6 3 Size of Earth • If Earth spherical, it is 5000 stades x 360 deg /7 deg in circumference – This is close to correct answer if "stade" – 1/6 km: Earth circumference = 250,000 stades = 40,000 km Earth diameter = circumference/ pi = 13000 km • Ultimate verification: circumnavigation of Earth So, let’s apply this method to the motions of the planets: Jan 27, 2006 Astro 100 Lecture 5 7 Geocentric Model of Solar System • (most elaborate: Ptolemy, 125 AD) – Moon and Sun motion consistent with real (almost uniform) circular motion around stationary Earth. – So associate Sun, Moon, and planets with spheres in uniform rotation with Earth at center. – Nonuniform apparent motion is allowed by attaching planets to little uniformly rotating spheres (epicycles) whose centers are attached to object's main sphere. Spheres do not overlap. Except for having Moon closer than Sun (to get solar eclipses), the size of each sphere is arbitrary. Can be made as exact as you like by adding epicycles to epicycles. Basically, Real = Apparent Jan 27, 2006 Astro 100 Lecture 5 8 4 Jupiter & Saturn Movie W Jan 27, 2006 E Astro 100 Lecture 5 9 Eratosthenes Observation Figure 1.19, p41, Arny Jan 27, 2006 Astro 100 Lecture 5 10 5 Geocentric Model Figure 1.23, p45, Arny Jan 27, 2006 Astro 100 Lecture 5 11 Geocentric Epicycles Figure 1.24, p45, Arny Jan 27, 2006 Astro 100 Lecture 5 12 6