# Ludwig's star distance

Mizar and Alcor, each about 83 light-years away (in fact Mizar presents system of four stars and Alcor is binary system. It is not yet known if those 6 stars presents one or two star systems. In further years, data provided by GAIA space telescope will show us if there is one or two systems), have a fainter line-of-sight companion known as Ludwig's star, which was mistaken for a planet in 1722. The Wikipedia page only says it is "roughly five times more distant," citing A New View of Mizar by Leos Ondra. Is a better distance estimate available?

SIMBAD lists a Gaia DR2 parallax of 10.85±0.03 milli-arcseconds for that star. Without going into the biases and uncertainties in current Gaia parallax data, $$r \approx \frac{1}{\varpi}$$ where $$\varpi$$ is the parallax in arcseconds and $$r$$ is the distance in parsecs. This works out to a distance of roughly 92 parsecs or 300 light-years.

• Where can I read from SIMBAD distance that you quoted?
– Fil
May 20, 2019 at 13:29
• Actually, the SIMBAD page does show the distance: scroll down to "Collections of Measurements" and select "display all measurements". It gives the distance as 92.1353±0.2377 pc. May 21, 2019 at 23:33
• Your error bar does not take account of the published systematic uncertainty in the Gaia parallax zero-point. An additional 0.1 mas of error is warranted at present. May 22, 2019 at 10:26

The Gaia EDR3 catalogue gives a parallax of $$10.965 \pm 0.028$$ milli-arcseconds.

This differs from the DR2 parallax by 0.115 milli-arcseconds. This is not unexpected because there are systematic errors of order 0.1 milli-arcsec in the DR2 parallaxes.

The new EDR3 parallax is expected to have systematic errors that are no bigger than the statistical error bar quoted. The error is small enough that the parallax can be inverted to give a distance of $$91.20 \pm 0.23$$ pc (or if you prefer $$297.5 \pm 0.8$$ light years).