GTR Continued

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# GTR Continued - PowerPoint PPT Presentation

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

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
• 30 points possible (120% maximum)
• Final: Monday, May 5, 7:50- 9:50 A.M.
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
• 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
• 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
• 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
• Following in the footsteps of others, Hubble determines recessional velocities from Doppler shifts.
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 used Doppler shifts and distances to study galaxies. He found a linear relationship.

v = HR

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.