2. Physics 362 – week 4 Modern Physics Seminars

3. 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

4. Distances beyond the solar system Trigonometric parallax 

5. Trigonometric Parallax 1 a.u.  d  d = 1 a.u. / sin  a.u.   in radiants 

6. Trigonometric parallax

7. 

8. Trigonometric Parallax 1 a.u.  d  d = 1 a.u. / sin  a.u. 

9. Trigonometric parallax Parsec = distance of a star when the parallax is equal to 1” d = 1 a.u. / sin  a.u.  in radiants   1 pc = 1 a.u. / (1”  1 rad) = 206,265 a.u.  1 pc = 3.1 10 13 Km = 3.26 light-years

10. 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  d max ~200 pc

11. Distance scales

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

13. Distances beyond 200 pc Calibrated candles!!! Light intensity: I d = I e / r 2 we can measure I d, and if we know I e  we can evaluate r

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

15. Spectroscopy redshift For approaching source

16. Redshift

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

18. 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 v max = c  R max = v max / H = 6000 Mpc ~ 2 10 23 Km = 2 10 10 light/years

19. 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 10 17 s ~ 1.5 10 10 years (15 Billion years)

20. 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  ) 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  has now been reintroduced to explain recent results in Cosmology