How far away until the Sun is no brighter than the full moon?

I’m often surprised by pictures from probes which show the far off planets much brighter than I would expect. When these same probes take pictures of the Sun, it is no more than a tiny dot. I would have thought the light would be quite dim by the time it gets as far away as Pluto, but it’s still bright enough to light up the planet (or whatever we’re calling Pluto these days).

So how far away would you have to be until the light from the Sun would be no brighter than the light we see from the full moon here on Earth?

The following recent thread discussed the brightness of the Sun on Pluto.

The first reply to this thread states that:

If we take that figure, then you would have to be at sqrt(250)=15.8 times Pluto’s average orbit (=about 600 times Earth’s orbit) for the Sun to be as bright as the full moon on Earth!

Apparent brightness in a photo is a product of exposure, aperture and sensitivity of the capture medium - in other words, that’s not exactly what you would see if you went there.

But it certainly is true that the Sun on Pluto would be much much brighter than the full moon on Earth.

It would appear as a dot, but extremely bright, like an electric arc. I don’t know if it would hurt to look at, but it wouldn’t be just another star.

Also remember that the human eye is very adaptive, and a photograph can’t represent the contrast that the human eye is capable of seeing. Ever take a picture in a dark room and the photo is just completely black, even though your eyes can see lots of details? Or white areas in full sun that are just washed out on a photo but your eye could see lots of detail in real life?

So a painting or a photo can’t just be a faithful copy of what the eye would see.

Probably. Even the Moon itself can be painful to look at, if your eyes are dark-adapted. Most likely, if you stared straight at the Sun on Pluto, you’d get exactly the same sort of eye damage as if you did the same on Earth, just over a smaller area of your retina.