1. Astronomy and Cosmology week 4 – Tuesday 22 April 2003 Weighing the Sun and Planets Star Date Keplerian orbits Weigh the Sun Workshop: use moons to weigh JupiterWorkshop break Minilecture by Derek and Andy Thursday: Ch.5 Light

2. We derived Kepler’s 3d law from Newton’s second law, F=ma: Gravitational forceacceleration in circular orbit F=GmM/r 2 a = v 2 /r GmM/r 2 = mv 2 /r v 2 = GM/r Speed v = distance/time = 2  r/T v 2 = 4  2 r 2 /T 2 = GM/r 4  2 r 3 = GM T 2 This is Kepler’s third law: T = period and r = orbit radius. Algebra review at http://regentsprep.org/Regents/physics/phys06/keplers/default.htm

3. Keplerian orbits: closer = faster 4  2 r 3 = GM T 2  a 3 =p 2 for planets around the Sun Orbit radius: r(m) or a(AU); Period T(sec) or p(years) http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html

4. Use Kepler’s 3d law to weigh the Sun. Solve 4  2 r 3 = GMT 2 for central mass M=_______ Earth data: period = 1 year ~ 3 x 10 7 sec orbit radius = 1 AU ~ 150 x 10 9 m M= M sun = Saturn data: period ~ 30 year = __________________ sec orbit radius = 10 AU ~ ________________ m M= M sun =

5. Use Kepler’s 3d law to weigh Jupiter.weigh Jupiter

6. Week 8: use Kepler’s 3d law to weigh galaxies and discover dark matter