[Ethan Clive Osgoode]

At sunset, when the center of the sun is exactly on the horizon... that light left the sun 8.3 minutes ago. The rotational velocity is constant, so when you're seeing that, the actual physical center of the sun should be about 2 degrees below the horizon from where you are.

So where would the actual physical Sirius be, when its observed position is likewise on the horizon? That light left Sirius 8.6 years ago.

[tacticalogic]

So where would the actual physical Sirius be, when its observed position is likewise on the horizon? That light left Sirius 8.6 years ago.

I'd think you'd need better measurements to determine that. If you're looking at an object that's exactly one light-day away, and stationary relative to the Earth, it's apparent position should be accurate, but the light you're using to locate the object actually left there at the same time yesterday.