You think there is no problem seeing an object that is 4,104,064,879,005,551.04km away?
Seems legit
Smart aleck!
But, why shouldn't we be able to see something 323–433 light years away? Do you have any valid reasons?
I have trouble resolving the bottom line of letters when I visit the optometrist and that's only a few meters away.
Well I don't, but that is totally irrelevant. The typical resolution for the eye is about 1 minute of arc, written as 1'.
When viewing a star you are not trying to "resolve anything", just to see the presence or absence of light.
It does not make any difference how small the source of light is - as long as:
- there is sufficient contrast between the object and the background - light against a dark background is ideal and
- sufficient light reaches the eye
we can see the object.
A very bright object (a star) against a black background can be seen at any distance, provided sufficient light enters the eye.
On the question of
How Far Can the Human Eye See a Candle Flame?
Answers on the Web vary from a few thousand meters to 48 kilometers.
Now a pair of physicists has carried out an experiment to find out.
See the details in: How Far Can the Human Eye See a Candle Flame?
The result claimed is:
We show that a candle flame situated at ~2.6 km (1.6 miles) is comparable in brightness to a 6th magnitude star with the spectral energy distribution of Vega. The human eye cannot detect a candle flame at 10 miles or further, as some statements on the web suggest.
A 6th magnitude star is regarded as about the limit of unaided vision.
Guessing the candle flame as 15 mm high x 5 mm wide, its angular size would be: 0.02 x 0.007 minutes of arc -
far smaller than the resolution limit of the eye.To
resolve two candles they would need to be at least 750 mm apart
This is just a quick example, but the visibility distance is bright object against a dark background is
limited only by the brightness.
The magnitude scale for stars has a long history, see
Wikipedia, Magnitude (astronomy).
The scale is logarithmic, and defined such that each step of one magnitude changes the brightness by a factor of the fifth root of 100, or approximately 2.512. For example, a magnitude 1 star is exactly a hundred times brighter than a magnitude 6 star, as the difference of five magnitude steps corresponds to 2.5125 or 100.
I imagine that if a stellar brightness scale were designed now if might be "simpler numbers".
But, whatever, the larger the "magnitude" the dimmer the star and the magnitude of Polaris is 1.97 making it an easily visible star.