hmorgan

I think I see what you mean now, but what makes you think that the sun would be invisible at 544,000 AU?

Here are the numbers as far as I understand them.

Apparent magnitude of the sun: -26.74 Apparent magnitude of Sirius A: -1.46

Excepted magnitude of the sun after moving to 544,000 AU: 296 billion times weaker, leading to +1.96 magnitude, according to a calculator (https://www.1728.org/magntude.htm).

I don't trust that calculator a lot, so to check that math, I used a formula to calculate the difference between those magnitudes (https://lco.global/spacebook/distance/comparing-magnitudes-d...) and got a result of 23.34. Not far off from the expected 25x difference.

So the sun at 544,000 AU wouldn't make the top 25 brightest stars in the night sky, but it wouldn't be far from that (https://www.britannica.com/science/list-of-brightest-stars-2...) and definitely well within what would be visible (https://en.wikipedia.org/wiki/Limiting_magnitude).

I've found that when I have a thought that seems to contradict the "established" model of the world, I tend to just be missing some critical factor. A recent example is when I thought: "why don't we just use physical objects to communicate information? Wouldn't that be instantaneous?" Turns out, no, pushing on one end of an object only communicates information to the other end at the speed of sound. Not intuitive when you only think about observable experience (it sure seems like if I push a steel bar, the other end moves instantly), but that's how the world works.

In the case of your thought experiment, the critical factor is that our eyes are able to observe and adjust to a very wide range of brightness in different conditions. Sirius A really is billions of times dimmer than the sun to our eyes (hard to find a good reference for that, but this mentions it: https://ecampus.matc.edu/mihalj/astronomy/test5/stellar_magn...).