Expert: Tom Whiting - 5/10/2009

Question
hi tom, i always enjoyed reading your articles online. but i have a question for you today.. how far out in space would one have to travel before our sun becomes invisible to the unaided eye to an astronaut with 20/20 vision?  i'm guessing around 55-60 light years.  what do you think?  thank you in advance   dan

Answer
Hi Dan,
Yes, that would be pretty close for an older astronaut....double
10 parsecs would be 20 pcs or about 65 ly....about 1/4 dimmer, and a magnitude increase of about 1.5, and 4.8 + 1.5 = 6.3 apparent magnitude, near the average human eye limit.

It wouldn't be the visual acuity of the astronaut, it would be
more....his or her age.  Yes, the younger you are, the dimmer
the star you can see because your pupil opens wider, so a young
20-something age human (with super-excellent vision) can perhaps see down close to 7th, even 7.3 apparent magnitude objects, where a 40-something age astronaut may only see down to a more average 6th- 6.5 magnitude objects. So the question really is, at what distance does the sun drop below 6th or 7th magnitude to the human eye.

We know the inverse square law...objects emitting radiation drop off as the square of the distance...and we also know that each magnitude change is 2.5 times dimmer for each successive whole number rise in magnitude, on an exponential scale.  We also know that the sun has an Absolute magnitude of +4.8, (what it's apparent magnitude would be if 10 pc distant)...so if you triple the distance to 30 parsecs, you get an object 1/9th as bright, or about 2 1/2 magnitude increases....4.8 plus 2.5 = magnitude of 7.3....so a very young astronaut might just barely see the sun at triple 10 parsecs, or 30 parsecs or right around 100 ly.  So anywhere from 65 to 100 ly, depending on your age.
Clear Skies,
Tom Whiting
Erie, PA
PS....also 10 parsecs = 32.6 ly which I'll bet you already know.
And BTW, 20/20 is only average, 20/15 is far better, and 20/10 is
perfect for only one in a million people have 20/10 vision in both
eyes. (I was blessed with 20/15 vision according to the USAF).
tom