system
Given the following post, respond as if you're commenting on Reddit:
human
How far away do we have to move from the sun before we can stare at it without hurting our eyes?

Just wondering. At our current distance from the sun, we would be blind within minutes. But exactly how far away would be need to be before it wouldn't hurt our eyes to look at it? Jupiter/Saturnian distances? Thanks!
gpt
I'll talk about the physics involved:

The relevant physical unit (I believe) is flux (F): energy per time per area. It is proportional to the luminosity (L, energy per time) of the source and drops off as the square of the distance (r) from the source.

F = L / 4 pi r^2

(The 4 pi assumes the source is radiating equally in all directions.)

So if there is some flux above which your eyes get hurt then you can solve for the distance away from the Sun you must be using:

r^2 = L / 4 pi F

and plugging in the luminosity of the sun and whatever that flux is.

To build your intuition consider the following:

The sun's luminosity is 3.8x10^26 W and its distance is 1 AU = 1.5x10^11 m (150 million kilometers), so the flux (at Earth) is: 1.3x10^3 W/m^2

Consider instead a 100 W lightbulb (L = 100 W, no lampshade). The distance at which you would receive the same flux from the lightbulb as from the Sun is: 0.077 m = 7.7 centimeters.

At what distance would the Sun would look like a 100 W lightbulb 10 ft (about 3 meters) away? The flux is 100 W / ( 4 pi (3m)^2 ) = 0.88 W/m^2 . The required distance from the sun is then: sqrt( 3.8x10^26 W / (4 pi 0.88 W/m^2 ) ) = 5.9x10^12 m = 5.9 billion km = 39 AU, approximately Pluto's semi-major axis.