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Is there any method to measure the mass of eclipsing binaries without using Doppler shift effect?

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It depends.

For many categories of stars, it is possible to determine the approximate mass of the star from its non-redshifted spectrum. Stars on the main sequence: this table of spectral classifications lists the approximate mass for the various classifications. A more precise mass estimation should be possible with a more precise classification. Sol, for example, is a G2, near the high end of G, putting it near the top end of the range (0.80 - 1.04 stellar masses).

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  • $\begingroup$ A better mass comes from putting the components on an HR diagram and then demanding that both objects have the same age to fit an isochrone through both star and estimate the masses from their positions along that isochrone. Simple mass-spectral type relations are prone to error because they are age-dependent. $\endgroup$ – ProfRob 2 days ago

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