How does distance constrain the mass of the binary, please? Let us assume data like radial velocity, light curves, and astrometry. Is there any problem in the determination of the mass of the system with unknown mass? Thank you
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1$\begingroup$ Why do you think it does? $\endgroup$– ProfRobJan 23 at 22:29
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1$\begingroup$ My supervisor said that the masses were determined better when we know the distance than before when the distance was not known. Or for what parameter is the distance the crucial constraint? What if astrometry would be also involved? $\endgroup$– Anna-KatJan 24 at 13:49
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1$\begingroup$ Yes, we need to know their distance from the barycenter or the center of gravity, which can be fit into kepler's law for mass $\endgroup$– user47732Jan 24 at 14:06
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1$\begingroup$ Thank you. And the distance towards the Earth? $\endgroup$– Anna-KatJan 24 at 14:10
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1$\begingroup$ Thanks. You also need the radial velocity, which can be predicted using spectroscopy using a diffraction grating via the doppler shift which creates redshift. I think there is only an indirect relation because of the doppler effect since velocity is defined as a displacement in distance over the course of time thus velocity would be more important rather than distance $\endgroup$– user47732Jan 24 at 14:47
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If you have an astrometric binary (one where both components can be resolved in an image - for example Sirius AB), then knowing the distance to the binary system can tell you what the physical scale of the orbit is by mutiplying the angular size of the orbit by the distance to the binary. i.e. You can then measure what the semi-major axis is and use this in Kepler's third law (along with the measured orbital period) to get the total system mass.
Radial velocities and light curves are irrelevant to this - the masses of eclipsing binaries can be estimated from radial velocity and light curves without knowing the distance to the binary.
