[Verginius Rufus]

The genitive form of the constellation's name is used with a star: Alpha Centauri, Beta Orionis, etc.

But -us is very unusual for a Latin genitive and appears actually to be a Greek genitive.

The constellation is Dorado in the nominative case.

Bennett's New Latin Grammar, 28, cites the Greek third-declension proper noun Dido as having a genitive form Didus. So that seems to be what's going on with Dorado/Doradus.

[SunkenCiv]

Thanks VR!

[minnesota_bound]

Size comparisons of stars.
https://www.schoolsobservatory.org/learn/astro/stars/class/starsize