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Astronomy and Cosmology week 4 – Tuesday 22 April 2003 Weighing the Sun and Planets

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##### Astronomy and Cosmology week 4 – Tuesday 22 April 2003 Weighing the Sun and Planets

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**Astronomyand Cosmologyweek 4 – Tuesday 22 April**2003Weighing the Sun and Planets • Star Date • Keplerian orbits • Weigh the Sun • Workshop: use moons to weigh Jupiter • break • Minilecture by Derek and Andy • Thursday: Ch.5 Light**We derived Kepler’s 3d law from Newton’s second law,**F=ma: Gravitational force acceleration in circular orbit F=GmM/r2 a = v2/r GmM/r2= mv2/r v2= GM/r Speed v = distance/time = 2pr/T v2 = 4p2r2/T2 = GM/r 4p2r3 = GM T2 This is Kepler’s third law: T = period and r = orbit radius. Algebra review at http://regentsprep.org/Regents/physics/phys06/keplers/default.htm**Keplerian orbits: closer = faster**http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html 4p2r3 = GM T2 a3=p2for 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.**Solve4p2r3 = GMT2for central mass M=_______ Earth data: period = 1 year ~ 3 x 107 sec orbit radius = 1 AU ~ 150 x 109 m M= Msun= Saturn data: period ~ 30 year = __________________ sec orbit radius = 10 AU ~ ________________ m M= Msun=**Week 8: use Kepler’s 3d law to weigh galaxies and discover**dark matter