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by Robert Nemiroff Michigan Technological University

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1 by Robert Nemiroff Michigan Technological University
Potpourri: Gravity by  Robert Nemiroff Michigan Technological University

2 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" 

3 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

4 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.

5 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.

6 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.  

7 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.

8 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.

9 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.

10 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

11 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

12 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:

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