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GTR Continued. Sections 29.3 - 29.4. Reminders. Lab this week LAB B1- WA Wave Addition : due by 4 p.m. Friday CCR Extra Credit due Thursday , May 1 Examination #3 on Thursday: Addresses Chapters 8, 9, 11-13 only 26 multiple-choice questions 2 extra credit questions

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gtr continued

GTR Continued

Sections 29.3 - 29.4

reminders
Reminders
  • Lab this week LAB B1-WA Wave Addition: due by 4 p.m. Friday
  • CCR Extra Credit due Thursday, May 1
  • Examination #3 on Thursday:
    • Addresses Chapters 8, 9, 11-13 only
    • 26 multiple-choice questions
    • 2 extra credit questions
    • 30 points possible (120% maximum)
  • Final: Monday, May 5, 7:50- 9:50 A.M.
einstein gtr and the universe
Einstein, GTR, and the Universe
  • Einstein’s equation of general relativity:
  • The equation required an expanding universe, so Einstein arbitrarily added a “cosmological” constant to avoid this conclusion…
  • Recall that galactic nebulas had yet to be discovered as galaxies, and neither had the expanding universe!
friedmann s universe 1
Friedmann’s Universe 1
  • Starts with total energy:
  • Makes 3 simplifying assumptions:
    • Universe is essentially empty (on a larger scale)
    • Universe is isotropic (no preferred direction)
    • Universe is homogeneous (no preferred point)
  • and gets:
friedmann s universe 2
Friedmann’s Universe 2
  • Inserting E=mc2 and taking into account GTR, the prior equation results in:
  • where k is the curvature of the universe:
    • If k < 0, then universe is closed and bounded (positively curved).
    • If k > 0, then the universe is open and unbounded (negatively curved).
    • If k = 0, then the universe is flat.
friedmann s universe
Friedmann’s Universe
  • Solving this equation, Friedmann predicted that the universe had to be expanding if it were to exist.
  • Einstein added the “cosmological constant” to his own field equations because he could not believe in an expanding universe. Later Einstein remarked, “That was the greatest scientific blunder that I ever made.”
hubble s relationship 1
Hubble’s Relationship 1
  • Following in the footsteps of others, Hubble determines recessional velocities from Doppler shifts.
hubble s relationship 2
Hubble’s Relationship 2
  • Hubble determines distances to “nebulas” using a variety of means:
    • Study of variable stars whose periods are related to their intrinsic brightness
    • Angular diameters by type
    • Presence of brightest stars in a galaxy by type
    • Presence of globular star clusters
    • Presence of supernovas by type (I and II)
hubble s law for galaxies
Hubble’s Law for Galaxies
  • Hubble used Doppler shifts and distances to study galaxies. He found a linear relationship.

v = HR

abb georges lama tre
Abbé Georges Lamaître
  • Introduces the “Big Bang”
  • Concludes that time since universal expansion began could be found from Hubble parameter.
  • v = HR; now d/v = t;
  • v/R = H and d/v = 1/H
  • The current value of H (21-23km/s/Mly) shows the age of the universe to around 13.8 billion years.
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