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Physics 362 – week 4

Physics 362 – week 4. Modern Physics Seminars. Distances in the solar system. The movement of the planets is described using celestial mechanics F = G mM/r 2 Kepler’s laws (P 2 =k r 3 ) astronomical unit = average distance of the Earth from the Sun 1 a.u. = 149,598,073 Km. a.

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Physics 362 – week 4

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  1. Physics 362 – week 4 Modern Physics Seminars

  2. Distances in the solar system • The movement of the planets is described using celestial mechanics • F = G mM/r2 • Kepler’s laws (P2=k r3) • astronomical unit = average distance of the Earth from the Sun • 1 a.u. = 149,598,073 Km

  3. a Distances beyond the solar system Trigonometric parallax

  4. Trigonometric Parallax d 1 a.u. p  d = 1 a.u. / sin p ~ 1 a.u. / p(p in radiants)

  5. Trigonometric parallax

  6. a Trigonometric parallax

  7. Trigonometric Parallax d 1 a.u. p  d = 1 a.u. / sin p ~ 1 a.u. / p

  8. Trigonometric parallax • Parsec = distance of a star when the parallax is equal to 1” • d = 1 a.u. / sin p ~ 1 a.u. / p (p in radiants) • 1 pc = 1 a.u. / (1”  1 rad) = 206,265 a.u. • 1 pc = 3.1 1013 Km = 3.26 light-years

  9. Trigonometric parallax • Closest star: Alpha Centauri is 1.3 pc away • Parallax = 0”.76 • Only a small number of stars can be measured!!! Current accuracy: ~0”.005  dmax~200 pc

  10. Distance scales

  11. Distances beyond 200 pc • Motion of the sun in the galaxyv ~ 30 Km/s ~ 4.1 a.u. / year • In 10 years 41 a.u. Can be used to measure up to ~ 2000 pc

  12. Distances beyond 200 pc Calibrated candles!!! Light intensity: Id = Ie / r2we can measure Id, and if we know Ie we can evaluate r

  13. Calibrated candles • Stars from the H-R diagram • Variable stars • Type II supernovae • Galaxies

  14. redshift Spectroscopy For approaching source

  15. Redshift

  16. Hubble law  v = H · r (H = Hubble constant)

  17. Hubble law H > 0  The universe is expanding Earth at the center of the Universe? NO! H = v / r ~ 70 km / s / Mpc  H = time-1 vmax = c  Rmax = vmax / H = 6000 Mpc ~ 2 1023 Km = 2 1010 light/years

  18. Hubble law Rewind the film  BIG BANG!!! Age of the universe: Objects at distance = R = v / H Time to get this far:T = R / v = 1 / H ~ 6.2 1017 s ~ 1.5 1010 years (15 Billion years)

  19. Einstein and Hubble • The theory of general relativity predicts a dynamic universe (either expanding or contracting) • Einstein didn’t believe in a dynamic universe and modified his theory, introducing an extra term (the vacuum energy density L) in his equations, to have a static universe • When Hubble published his results Einstein defined his modified theory “the biggest blunder of my life” • A term similar to L has now been reintroduced to explain recent results in Cosmology

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