<p>If you have an astrometric binary (one where both components can be resolved in an image - for example <a href="https://en.wikipedia.org/wiki/Sirius#/media/File:Orbit_Sirius_B_arcsec.png" rel="nofollow noreferrer">Sirius AB</a>), 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.</p>
<p>Radial velocities and light curves are irrelevant to this - the masses of eclipsing binaries can be estimated from radial velocity and light curves <em>without</em> knowing the distance to the binary.</p>

CC BY-SA 4.0
2023-01-24T18:32:05.457Z
2023-01-24T19:26:45.637Z
2023-01-24T19:26:45.637Z
ProfRob
<p>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</p>

CC BY-SA 4.0
2023-01-23T22:29:53.937Z
Why do you think it does?
ProfRob
CC BY-SA 4.0
2023-01-24T13:49:06.503Z
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?
Anna-Kat
CC BY-SA 4.0
2023-01-24T14:10:20.903Z
Thank you. And the distance towards the Earth?
Anna-Kat
CC BY-SA 4.0
2023-01-24T14:52:22.200Z
Thus, the distance is not important in the determination of other stellar parameters?
Anna-Kat
<binary-star><eclipsing-star-systems>
Binaries: mass and distance constraints
Anna-Kat
# Binaries: mass and distance constraints

(Asked by: username_0 on 2023-01-23)

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

**Tags:** binary-star, eclipsing-star-systems

> **Comments:**
> **username_1**: Why do you think it does?  
> **username_0**: 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?  
> **username_0**: Thank you. And the distance towards the Earth?  
> **username_0**: Thus, the distance is not important in the determination of other stellar parameters?  

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## 1 answers

### Answer by username_1 on 2023-01-24. Score: 1 | Accepted answer

If you have an astrometric binary (one where both components can be resolved in an image - for example [Sirius AB](https://en.wikipedia.org/wiki/Sirius#/media/File:Orbit_Sirius_B_arcsec.png)), 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.


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