Potpourri: Gravity

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Potpourri Gravity

• by 
• Robert Nemiroff
• Michigan Technological University

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Physics X About This Course

• Officially "Extraordinary Concepts in Physics"
• Being taught for credit at Michigan Tech
• Light on math, heavy on concepts
• Anyone anywhere is welcome
• No textbook required
• Wikipedia, web links, and lectures only
• Find all the lectures with Google at
• "Starship Asterisk" then "Physics X" 
• http//bb.nightskylive.net/asterisk/viewforum.php?
  f39

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Birkhoff's Theorem

• A very useful theorem that leverages spherical
  symmetry in General Relativity.  Two common
  applications
•  
• Outside a spherically symmetric mass distribution
  (hence not rotating), the solution is always the
  Schwarzschild metric. 
• useful for ignoring stellar pulsations
• Inside a spherically symmetric mass shell, the
  gravitational "field" will vanish. 
• useful for ignoring the outside universe

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Virial Theorem

• A relation between the average total kinetic
  energy of a system of particles (Ktot) and the
  average potential energy of the particles (Vtot).
   For Newtonian gravity
• 2 Ktot - Vtot
• Useful for determining the amount of dark matter
  in clusters of galaxies (for example).  Theorem
  can apply to even one particle.

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Gravothermal Catastrophe

• The center of a gravitationally bound system of
  particles will heat up at it gravitationally
  collapses.  For those particles, the increase in
  energy comes from a conversion of potential
  energy to kinetic energy.
• However, some other particles will be thrown out
  from the center and will "cool down".
• Runaway For sufficiently condensed systems of
  particles acting gravitationally, the center will
  be unstable to becoming increasingly dense and
  hot, since that will decrease system entropy.  A
  single temperature will no longer describe the
  system.

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Gravitomagnetism

• A gravitational force that complements standard
  gravity like magnetism complements standard
  electric force.
• Predicted by General Relativity (and even other
  gravitational theories that predate GR).
• A small effect -- it is being tested by Gravity
  Probe B, although these results have not yet been
  announced.  

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Gravitomagnetism

• Typically a very small effect.
• If two wheels are spun on a common axis, their
  mutual gravitational attraction will be
  (slightly) greater if they spin in opposite
  directions.
• A ring rotating about its minor axis (a circle
  inside the ring) will accelerate matter through
  the ring while that matter feels no
  acceleration. 
• Earth's gravitomagnetic acceleration at the
  Equator is about 10-7 g.
• Cannot be used to create a perpetual motion
  machine.

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Frame Dragging

• The General Relativity expected effect that
  rotating objects drag spacetime around with them.
•  
• A gravitomagnetic effect.
• Also known as the Lens-Thirring Effect
• When near a massive rotating object, you may feel
  that you are not rotating with respect to the
  universe, even though you can see that you are.
• Typically a small effect.

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Frame Dragging

• FD has never been measured in the laboratory
• very difficult to do
•  
• Would rotating a bucket create the same effect as
  rotating the entire universe?
•  
• Might be relevant to jets emitted from active
  galaxies.

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Gravitational Radiation

• Emitted by accelerating masses in GR, in analogy
  to electromagnetic radiation emitted by
  accelerating charges.
• Acceleration must be non-spherically symmetric.
• Very weak compared to common photon energies.
• Not yet directly detected on Earth.
• Ongoing searches include LIGO

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Gravitational Radiation

• Strongly emitted by massive and rapidly changing
  astronomical objects.
• Supernovas (we know)
• Gamma ray bursts (we think)
• Steadily emitted by decaying binary star systems
• binary pulsar's orbital decay can be attributed
  to gravitational radiation to high accuracy

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Gravitational Radiation

• moves at the speed of light.
• has wavelength and frequency like light lambda
  c f.
• A passing polarized gravitational wave would have
  this effect on a ring of particles