Lecture 5. Motions of the Planets
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1 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
2 Loops Two classes of apparent motions: 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. URL for this demo: 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 Diurnal: Stars Annual: Sun Moon Planets Earth Rotation Orbit of Earth around Sun Orbit of Moon around Earth Orbits of planets around Sun about celestial poles "ecliptic", tilted 23.5 deg to equator tilted 5 deg to ecliptic tilted up to 17 deg to ecliptic How apparent motions were explained is a good illustration of the "Scientific Method"... Synodic Event E to W 23 h 56 m solar day = 24 h W to E (direct) solar days solar year, seasons W to E 27 d 8 h phases, eclipses direct, retrograde years conjunction, opposition Jan 27, 2006 Astro 100 Lecture 5 4
3 Scientific Method Most Useful Theories: Experiment Raw Data Calibrated data Analyzed data Prediction 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 Observer Analyst Pure Theorist Theory Speculation Hypothesis Model/Theory Jan 27, 2006 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
4 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 = 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
5 Jupiter & Saturn Movie W E Jan 27, 2006 Astro 100 Lecture 5 9 Eratosthenes Observation Figure 1.19, p41, Arny Jan 27, 2006 Astro 100 Lecture 5 10
6 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
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