<p>I am trying to derive the virial theorem but for two stars orbiting each other. I know the derivation for the general virial theorem with i particles but I am wondering if there is a quicker or more elegant derivation when it comes to proving the virial theorem with only two masses (I am not assuming that the two bodies are in circular orbits around each other).</p>

CC BY-SA 4.0
2021-06-29T10:47:01.023Z
Do you consider the teo srars as two particles?
Deschele Schilder
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2021-06-29T13:29:13.623Z
Reducing the mass turns it into a one particle case, but integrating averages of KE and PE across the orbit equation seems to produce a lot of ugh algebra - some other approach is definitely needed.
Anders Sandberg
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2021-06-29T13:54:17.030Z
@DescheleSchilder Yes, I am assuming the two stars are particles.
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<orbital-mechanics><binary-star><celestial-mechanics>
Virial theorem for a binary system
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# Virial theorem for a binary system

(Asked by: username_0 on 2021-06-29)

I am trying to derive the virial theorem but for two stars orbiting each other. I know the derivation for the general virial theorem with i particles but I am wondering if there is a quicker or more elegant derivation when it comes to proving the virial theorem with only two masses (I am not assuming that the two bodies are in circular orbits around each other).

**Tags:** orbital-mechanics, binary-star, celestial-mechanics

> **Comments:**
> **username_1**: Do you consider the teo srars as two particles?  
> **username_2**: Reducing the mass turns it into a one particle case, but integrating averages of KE and PE across the orbit equation seems to produce a lot of ugh algebra - some other approach is definitely needed.  
> **username_0**: @DescheleSchilder Yes, I am assuming the two stars are particles.  

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## 0 answers

