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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

• 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’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.”

• Following in the footsteps of others, Hubble determines recessional velocities from Doppler shifts.

• 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 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.