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Which is the closest point to the Sun where it's not the brightest star anymore?

My intuition is that this is either on a direct line between the Sun and Alpha Centauri, or between the Sun and Sirius and can be calculated relatively easily based on absolute magnitudes. But which one, and how far away?

Conversely, which point is the farthest you can get away from the sun where it stops being the brightest star? I suppose this is much harder to answer.

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    $\begingroup$ partial duplicate: astronomy.stackexchange.com/questions/1062/… $\endgroup$
    – asdfex
    Commented Apr 17 at 15:34
  • $\begingroup$ related question with partial answers: space.stackexchange.com/questions/22898/… $\endgroup$
    – asdfex
    Commented Apr 17 at 15:35
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    $\begingroup$ Indeed, the first half of this question is a direct duplicate and needs editing to account for that. $\endgroup$
    – ProfRob
    Commented Apr 17 at 16:42
  • $\begingroup$ Duplicate of "At what distance from Earth would our Sun be the same apparent magnitude as the next brightest star in the sky?" @uhoh and doesn't mention alpha Cen ? The answer is 1.46 light years. The Space SE version then gives the answer to the other half of the Q. $\endgroup$
    – ProfRob
    Commented Apr 18 at 7:21
  • $\begingroup$ @ProfRob OK right. The closest star will be the one that brightens the fastest when traveling along the line to it. Since alpha Cen is the closest, it will brighten the fastest and so no other star need be considered. The Space SE argument that going directly away from Sirius is the only direction and star that needs to be considered for the 2nd part is still unclear to me, but then again, so are a lot of things. I yield to the clear-thinkers. $\endgroup$
    – uhoh
    Commented Apr 18 at 9:42

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