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Physics of Astronomy week 2 – Thursday 15 Jan 2004 Celestial Mechanics • • • • • Star Date Boas: Spherical Coordinates Gravity lecture and applications Workshop moons of Jupiter Learning plans and assignments Boas: Spherical coordinates Guiding Questions: Celestial Mechanics 1. How did ancient astronomers explain the motions of the planets? 2. Why did Copernicus propose that the Earth and the other planets revolved around the Sun? 3. What did Galileo see in his telescope that supported the geocentric model? 4. How did Tycho Brahe attempt to test the ideas of Copernicus? 5. What phenomenological laws did Kepler induce from Tycho’s data? 6. How do Newton’s laws explain Kepler’s conclusions? 7. Why don’t the planets fall into the Sun? Derive Kepler’s 3d law from Newton’s second law: F=ma Gravitational force F=GmM/r2 acceleration in circular orbit a = v2/r Solve for v2: Speed v = distance/time = 2pr/T. Plug this into v2 and solve for T2: This is Kepler’s third law: T = period and r = orbit radius. Apply Kepler’s 3d law: For objects orbiting the Sun, a=radius in AU and p=period in years A satellite is placed in a circular orbit around the Sun, orbiting the Sun once every 10 months. How far is the satellite from the Sun? 2 10 a = p = _______ 12 3 2 a ______ NB: This simple form of K3 only works for our solar system. Why? Sidereal and Synodic periods A satellite is placed in a circular orbit around the Sun, orbiting the Sun once every 10 months. How often does the satellite pass between the Earth and the Sun? 1 1 1 sidereal period Earth ' s sidereal year synodic period 1 1 1 P P S 1 1 1 10 1 S 12 1 ________________ S S ________________ We can use Newton’s gravity to approximate the size of a black hole! Gravitational energy kinetic energy GmM 1 m v2 r 2 Solve for r ____________ Not even light can escape (v=c) if it is closer than r to a black hole. This is the Schwarzschild radius: R=_____________________ Keplerian orbits: close = faster http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html 4p2r3 = GM T2 a3=p2 for planets around the Sun Orbit radius: r(m) or a(AU); Period T(sec) or p(years) Use Kepler’s 3d law to weigh the Sun Solve 4p2r3 = GMT2 for central mass M=_______ Earth data: period = 1 year ~ 3 x 107 sec orbit radius = 1 AU ~ 150 x 109 m M= M= Saturn data: period ~ 30 year = __________________ sec orbit radius = 10 AU ~ ________________ m M= M = Use Kepler’s 3d law to weigh Jupiter. Then, use Kepler’s 3d law to weigh galaxies and discover dark matter Learning Plan for weeks 3-4: Mon.19.Jan: Holiday; Tuesday Boas HW due. Tues.20.Jan: ML on Universe Ch.3: Moon & Eclipses Thus.22.Jan: ML on Universe Ch.4: Gravity & Orbits Mon.26.Jan: Workshop on Jupiter’s moons & Dark matter Tues.27.Jan: HW due on Universe 3+4; Quiz Review Physics Ch.3+4; ML Physics Ch.6 Thus. 28.Jan: Lecture and ML on Astrophysics Ch.2 Tues.3.Feb: HW due on Physics Ch.6; CO Ch.2; Quiz Assignments for week 3: Tues.20.Jan: Universe Ch.3: Moon & Eclipses (Boas due) Team 1: Ch.3.1, Motion of Moon, # 23 Team 2: Ch.3.2, Motion of Moon, # 43 Team 3: Ch.3.3-4, Lunar Eclipses, # 30 Team 4: Ch.3.5, Solar Eclipses, #33 Team 5: Ch.3.5, Distances: demonstrate and diagram Eratosthenes’ calculation Thus.22.Jan: Universe Ch.4: Gravity & Orbits Team 1: Ch.4.1-2, Retrograde motion, #48 Team 2: Ch.4.3, Galileo’s observations, #50 or 52 Team 3: Ch.4.4-5, Tycho + Kepler, #35 Team 4: Ch.4.6-7, Newton + orbits, #39 Team 5: Ch.4.8, Tides #44 (or Physics Ch.6 #54) Assignments for week 4: Mon.26.Jan: Workshop on Jupiter’s moons & Dark matter Tues.27.Jan: HW due: Physics Ch.6 # 54 Universe Ch.3 # 23, 43, 30, 43, Ch.4 # 48, 52, 35, 39, 44 Review Physics Ch.3+4; ML Physics Ch.6, Gravitation: Team 1: Ch.6.1-3, #13, 14 Team 2: Ch.6.4-5, #28 Team 3: Ch.6.6-8, #47 Thus. 28.Jan: Lecture on Astrophysics Ch.2 Team 4: Ch.2.1, #2.1 & 2.2 Team 5: Ch.2.3, #2.7 Tues.3.Feb: HW due: Physics Ch.6 # 13, 14, 28, 47, 57, 60 CO (Astrophysics) Ch.2 # 1, 2, 7, 8, 11