Gravitational Radiation Calculation from Rotating Rods

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SUMMARY

The calculation of gravitational radiation emitted from a rotating rod is defined by the formula L_{GW} = \frac{2}{45} M^2 l^4 \omega^6 in geometric units, where M represents the mass, l is the length, and ω is the angular frequency of rotation. When converted to standard units, the formula becomes L_{GW} = \frac{2}{45} \frac{G}{c^5} M^2 l^4 \omega^6, incorporating the gravitational constant G and the speed of light c. This discussion references MTW's "Gravitation," specifically page 980, for further details on the derivation and application of this formula.

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  • Understanding of gravitational radiation concepts
  • Familiarity with angular frequency calculations
  • Knowledge of geometric and standard unit conversions
  • Basic principles of general relativity as outlined in MTW's "Gravitation"
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anybody know link where i can see how to calculate the power of the gravitational radiation emitted from a rotating rod?
 
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MTW's "Gravitation" gives a formula on pg 980.

In geometric units, the formula is:

[tex]L_{GW} = \frac{2}{45} M^2 l^4 \omega^6[/tex]

where M is the mass of the bar
l is the length of the bar
[itex]\omega[/itex] is the angular frequency of rotation of the bar, [itex]\frac{2 \pi}{T}[/itex], where T is the period of rotation of the bar.

Converting this to standard units we get

[tex]L_{GW} =\frac{2}{45} \frac{G}{c^5} M^2 l^4 \omega^6[/tex]

the added constants are c, the speed of light, and G, the gravitational constant.
 
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