Lecture 24: General Relativity
Astronomy 101/103
Terry Herter, Cornell University
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Lecture
Topics
  • The Principal of Equivalence
  • Consequences of General Relativity
    • slowing of clocks
    • curvature of space-time
  • Tests of GR
  • Escape Velocity

    • General
    Relativity
    • A Theory of Gravity
      • Albert Einstein
      • 1916
    • Incorporates accelerated motions into Special Relativity

    Principle of
    Equivalence

    Principle of Equivalence

    • Gravity and acceleration due to a force are indistinguishable.
      • In a small local environment (Must be a small enough "box")
    • This is the foundation of General Relativity.

    Principle #1

    • Imagine yourself in a closed room.
    • By the principle of equivalence you could not tell if you were on earth or in space in an accelerating rocket.

    Principle #2

    • Now imagine yourself falling in a closed room.
    • By the principle of equivalence you could not tell if you were falling towards earth or floating in space.

    Gravity and Time


    • Imagine two clocks in an accelerating rocket.
    • Clock A is in the front.
    • Clock B is in the back.
    • Clock A emits pulses 1 second apart.
    • How far apart are they at Clock B?

    Clocks in GR:
    Body at
    Rest



    NO ACCELERATION

    • Flash emitted from A
    • To reach B it travels a distance d1.
    • Since the rocket is not accelerating, we have for the next flash
      • d2 = d1
    • Flashes arrive 1 second apart.

    Clocks in GR:
    Accelerating
    Bodies



    ACCELERATION

    • Flash emitted from A
    • To reach B it travels a distance d1.
    • Since the rocket is now accelerating, we have for the next flash
      • d2 < d1
    • Flashes arrive less than 1 second apart.

    GR:
    Clocks
    and
    Consequences

    Clocks in GR

    • Clock A runs faster than Clock B.
    • The equivalence principle states gravity and acceleration are the same.
    • Therefore, the same thing happens in a gravitational field!
    • A clock on a mountain top will run faster than a clock at sea level.

    Consequences of GR

    • GR changes our concepts of space and time (gravity and geometry are linked).
    • Einstein no longer thought of gravity as a force but a curvature of space-time.
    • Space is "curved" by massive objects causing objects to fall toward them.

    Curvature of
    Space-time

    • Empty space is "flat" space-time.
    • Space with matter is "curved" space-time.

    Bending of
    Light


    • Near a massive object, GR predicts that light will be deflected.
    • GR predicts 1.75" for light grazing the Sun.
    • Measurements of stars during a solar eclipse verified this to within 1%. (Eddington - 1919).

    Time
    Delay
    of Light

    • Near a massive object, GR predicts that light will travel a longer path due to curved space-time.
    • Verified by timing signals from Viking spacecraft passing by the Sun.

    Binary
    Pulsar
    • 1974 - R. Hulse and J. Taylor (UMass) discovered a binary pulsar
      • Work done at Arecibo Observatory
      • Orbit period = 8 hr, Orbit speed = 0.1c !!
    • Serves as a test of General Relativity
      • Precession (movement of orbit) on sky.
      • Decay of orbit due to Gravitational Radiation (New type of radiation!!).

    Gravitational
    Redshift
    • Light from the surface of a massive object will be redshifted.
      • The more massive and/or more compact an object, the greater the redshift.
    • ~ 0.01 A shift for the Sun.
    • ~ 1 A shift for a white dwarf.
    • Gravitational redshift verified to 0.01% by hydrogen masers (one in space and the other on ground).

    Escape
    Velocity
    • Escape velocity is the speed an object would need to escape from a celestial body.
    • Gravity is low on an asteroid. You could throw a ball off it, or jump off it.
      • Thus, low escape velocity
    • The escape velocity depends on mass.

    Sample
    Escape
    Velocities
    • Earth: 11.2 km/sec (25,000 mph)
    • Moon: 2.4 km/sec
    • 1 km asteroid: 1.3 m/sec
    • Sun: 618 km/sec
    • White Dwarf: 6000 km/sec !!
    • What would happen if the escape velocity equaled the speed of light?
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