An eclipsing binary star system is observed over the course of an entire orbital

Question

An eclipsing binary star system is observed over the course of an entire orbital period. The spectrum below shows an absorption line from each star at the point when the two lines have the greatest separation. Both stars are main-sequence stars. Which star will leave the main-sequence first and why?

Star A will leave the main-sequence first. The spectrum above shows that at maximum separation of the absorption lines, Star B has a smaller Doppler velocity than Star A. Since spectrum is at maximum separation, the Doppler velocities of the stars are the orbital velocities for the two stars. Star B’s orbital velocity is less than Star A’s orbital velocity so Star A must have a larger mass than Star B. Since both stars are on the main sequence, Star A will use up its hydrogen more quickly than Star B and will leave the main-sequence first.

Explanation / Answer

Star B will leave the main-sequence first. The spectrum above shows that at maximum separation of the absorption lines, Star B has a smaller Doppler velocity than Star A. Since spectrum is at maximum separation, the Doppler velocities of the stars are the orbital velocities for the two stars. Star B’s orbital velocity is less than Star A’s orbital velocity so Star B must have a larger mass than Star A. Since both stars are on the main sequence, Star B will use up its hydrogen more quickly than Star A and will leave the main-sequence first.

Option C

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