Understanding Virial Theorem: Comparing Equations

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The discussion centers on the differences between two equations related to the Virial Theorem found in an astrophysics book and a Wikipedia article. The equation from the book expresses pressure in terms of gravitational energy and volume, while the Wikipedia version uses kinetic and potential energy along with the concept of "virial." Despite the different variables, it is suggested that both formulations should yield equivalent results. The conversation highlights the importance of understanding the context and definitions of the variables used in each equation. Clarifying these distinctions can enhance comprehension of the Virial Theorem in astrophysics.
Stratosphere
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In my astrophysics book, it says it's \bar{P}=-\frac{1}{3}\frac{E_{gr}}{V}

This Wikipedia article has a different equation. http://en.wikipedia.org/wiki/Virial_theorem

Can someone explain the difference?
 
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Stratosphere said:
In my astrophysics book, it says it's \bar{P}=-\frac{1}{3}\frac{E_{gr}}{V}

This Wikipedia article has a different equation. http://en.wikipedia.org/wiki/Virial_theorem

Can someone explain the difference?

Yes; the variables being used are different. Your formula is using pressure and volume. Wikipedia is using kinetic and potential energy, and the "virial". Should work out to be the same, I think.

Cheers -- sylas
 
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