Prove Binary System Brighter by 3/4 Magnitude Than Single Star

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Discussion Overview

The discussion centers on proving that a binary star system of equal mass and temperature is brighter by a magnitude of 3/4 compared to a single star of equal mass and temperature. The focus is on the mathematical relationship between the fluxes of the two systems.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant seeks to prove the brightness difference using the formula (m1-m2)=-2.5log(f1/f2).
  • Another participant questions the value of f1/f2 for a binary system compared to a single star.
  • A further clarification is made that f1 should represent the flux of the binary system and f2 the flux of the single star.
  • One participant concludes that if f1/f2 is 1/0.5, the proof works, indicating a potential resolution to their inquiry.

Areas of Agreement / Disagreement

The discussion appears to be progressing towards a resolution, but it is not clear if all participants agree on the interpretation of the flux values or the implications of the calculations.

Contextual Notes

Participants have not fully detailed the assumptions behind their calculations or the definitions of flux in this context, leaving some aspects unresolved.

sheepcountme
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I have to prove that a binary system of stars of equal mass, temp, etc. is brighter by a magnitude of 3/4 than a single star of equal mass, temp, etc.

I've been trying to work it out with (m1-m2)=-2.5log(f1/f2)

Might anyone be able to tell me if I am even on the right track?
 
Last edited:
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Sure. So what's f1/f2 for a binary system versus a single star?
 
Well, f1/f2 for a binary is 1, but how do I compare that to a single star?
 
Let me rephrase that. You want to compare the binary system (system 1) to the single star single (system 2). So, let f1 be the flux of the binary system, and let f2 be the flux of a single star. Then what's f1/f2?
 
Ah! so if f1/f2, is 1/.5 it works! Thank you!
 

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