I'm confused about this assertion that Eridani is a star. Is it not a constellation?
I am willing to say what you want, within reason. I went back to the episode in question to see what they said and it is complicated. In the cold open, Nurse Chapel says they are on their way to "The Vulcan system" to "survey the moon of Kirkov on the far side of the sector". It isn't clear to me whether Kirkov is on the far side of the sector from the Vulcan system or whether Kirkov AND the Vulcan system are on the far side of the sector from where they were on her last log entry. Same mentions Eridani B in backchat a few minutes later. I checked the flyby and they don't say anything. I'm not sure where else to look and it is time to go to work.