Solving for the Speed of a Star in a Binary System | Physics Wave Question

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SUMMARY

The discussion focuses on calculating the speed of a star in a binary system using the Doppler effect. A spectral line from the star has a wavelength of 515.2 nm, while the same line in the lab measures 518.6 nm. The Doppler formula, f' = f.V/(V+Vs), is essential for determining the star's velocity (Vs) relative to Earth. A positive Vs indicates the star is moving away, while a negative value signifies it is approaching Earth.

PREREQUISITES
  • Understanding of the Doppler effect
  • Familiarity with spectral lines and wavelength measurements
  • Basic knowledge of classical mechanics
  • Awareness of relativistic effects in physics
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  • Study the Doppler effect in detail, focusing on both classical and relativistic scenarios
  • Learn how to apply the Doppler formula in various astrophysical contexts
  • Research the implications of general relativity on binary star systems
  • Explore methods for measuring stellar velocities using spectroscopy
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Astronomy students, astrophysicists, and anyone interested in understanding stellar motion and the application of the Doppler effect in astrophysics.

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Homework Statement



a spectral line coming from a star in a binary system has a wavelength of 515.2 nm. in the lab the same spectral line would have a wavelength of 518.6 nm. what is the speed of the star in relation to earth?

Homework Equations


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The Attempt at a Solution


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look up doppler effect, I'm not going to propose solution, because once you learn it for yourself -- I'm sure you'll figure it out in an instant (at least in a classical sense, not accounting the general relativity corrections -- there's not enough info in the problem to use that anyway).
 
Or you could try relativistic doppler effect.
 
Use the Dopple formula:

f'=f.V/(V+Vs)

V=c=3.10^8 m/s :speed of the radio wave.
Vs: velocity of the star (source).

U should find Vs, if it's positive then the star is moving away from the earth, otherwise it's moving closer.
 

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