Astronomy 4

Final Review Sheet

Part I

• Special Relativity

  • no accelerations

  • space-time is flat

  • inertial reference frames move at constant velocity or is stationary

  • speed of light is constant: 300,000 km/s in vacuum

  • geodesics (light paths) are straight lines

• General Relativity

  • special relativity + gravity

  • space-time is curved by the presence of mass

  • inertial reference frames near a mass is a freely falling frame (cancel gravity)

  • speed of light is constant

  • geodesics are curves around a mass

• Curvature of Space-Time

  • 3 types of curvature: positive, flat, negative

  • Positive curvature:

    • sum of angles in a triangle greater than 180 degrees

    • parallel lines converge

    • circumference of a circle is less than p x diameter

  • Flat:

    • sum of angles in a triangle is exactly 180 degrees

    • parallel lines remain at a fixed distance from each other

    • circumference of a circle is exactly p x diameter

  • Negative Curvature:

    • sum of angles in a triangle is less than 180 degrees

    • parallel lines diverge

    • circumference of a circle is greater than p x diameter

• Space-Time Diagrams

  • represent time on y-axis and one space dimension on x-axis

  • world lines: trajectories in space-time diagrams

  • light cones: trajectory traced out by path of light

  • time-like vectors: connect points inside light cones

  • space-like vectors: connect outside light cones

• Black Holes

  • Traveling towards a black hole

  • Observer: will never see the Traveler cross the event horizon

    • Traveler's signals seem infinitely redshifted

    • Light from Traveler will quickly dim

• Traveler: will cross into the event horizon without noticeable time problems

  • Light from the outside world will be greatly distorted

  • Huge tidal forces will stretch everything to thin strings

• Evolution of the Universe

• Universe is expanding

• The temperature is now 3K

• The universe was hotter in the past

• 4 characteristics of the universe we want to know

  • size, shape (geometry), age, and ultimate fate

• 4 parameters to characterize the universe

  • deceleration parameter q_o, hubble's constant, age of universe, lambda

• Hubble Diagram

  • Plot of Distance vs. Redshift of distant objects

  • Shows the universe to be expanding uniformly

  • the slope of the plot is the Hubble Constant

    • measured in km/s/Mpc

    • can give us age of the universe

• Denisty Parameter

• W measures the total density/ critical density

• the critical density is the amount of mass needed to make the universe flat

• W is composed of matter (visible and dark) and lambda components

• Inflation

  • A period of very fast expansion early in the universe's history

  • Makes the current universe flat, and near critical density

  • Arises from the universe crossing from a false vacuum to a real vacuum

• Cosmological Constant

  • An addition to Einstein's equations of General Relativity

  • May represent the energy contained in vacuum

  • May contribute to the total density of the universe