“Answers on the Web vary from a few thousand meters to 48 kilometers. Now a pair of physicists have carried out an experiment to find out.
Today, Kevin Krisciunas and Don Carona at Texas A&M University in College Station put this question to the test. And the answer is considerably less than the web would have us believe.
The big problem with testing this idea is the distance involved. For an observer on the ground, the Earth’s surface curves away at a distance of about five kilometers so a candle further than this would be below the horizon. Then there is the problem of obstructions such as trees and buildings and of other light sources that might fool the eye or change its receptiveness.
Krisciunas and Carona make some calibrating assumptions and say that a candle flame is the same brightness as a magnitude 0 star at a distance of 392 meters. Magnitude 0 stars [the brightest] are 251.2 times brighter than magnitude 6 stars [the dimmest that can be seen by an unaided human eye]. So while again taking into account the differences between starlight and candle light, it is possible to work out how far away the candle should be to appear equally bright as a magnitude 6 star.
Krisciunas and Carona say this would occur at a distance of 2,576 meters or roughly 1.6 miles, and that at 10 miles a candle would appear as bright as a magnitude 9.98 star. “This is far beyond the capabilities of the most sensitive human eyes,” they say.
You shouldn’t need a candle to read the whole article at technologyreview.com.