Question about how brightness changes over a distance

[AStaunton]

I believe that it is the case that if I were on Pluto, say the sun would appear much smaller, the area of the disc I'd be looking at would be (R_Pluto/R_Earth)^2 times smaller than if I were looking at the sun from Earth. However,I heard today that that small little area as viewed from Pluto would still be is bright as an equally sized piece of the area of the sun as viewed from Earth.
Can someone please explain why that is?

 

[Drakkith]

Hrmm...I've never heard of that being true, but I don't really know.

 

[Penn.6-5000]

It's a trick with the phrase "that small little area as viewed from Pluto would still be is bright as an equally sized piece of the area of the sun as viewed from Earth." If you measure the area as "square degrees" or "fraction of my field of view," then the statement turns out to be true. What you're imagining right now is that if you cover up all but one square mile on the sun, that square mile will appear to have the same brightness from any distance. That image seems wrong because it is. What you *should* imagine is that you have a piece of cardboard and you cut a small hole in it. Hold the cardboard up in front of your face so that part of the sun shines through the hole. The sun will appear to have a certain brightness. Now go to Pluto and hold the same piece of cardboard up in front of your face. You will see the same amount of light as before. That makes sense, because now that the sun is farther away, each "pixel" of light that makes it to your eye is being powered by a much larger part of the sun's surface. On the Earth, the sun was really big and only, um, 0.1% of its light was able to get through the hole. But on Pluto, the sun appeared smaller. You're 30 times farther away so the sun looks 900 times smaller, so now it's only a little bigger than the hole---90% of its light fits through the hole now. But while you're able to see 900 times more of the sun in terms of square miles of light-generating solar surface, it's also 900 times dimmer because it's so far away. Those two factors cancel out exactly and the same amount of light makes it into your eye.

 

[klimatos]

I believe that it is the case that if I were on Pluto, say the sun would appear much smaller, the area of the disc I'd be looking at would be (R_Pluto/R_Earth)^2 times smaller than if I were looking at the sun from Earth. However,I heard today that that small little area as viewed from Pluto would still be is bright as an equally sized piece of the area of the sun as viewed from Earth.
Can someone please explain why that is?

I doubt if that hypothesis is valid. If it were, no star would be too dim to see. It might be point, but it would be a bright point. Instead, the intensity of any electromagnetic source diminishes with the square of the distance from that source. At some distance (depending upon the sensitivity of your sensor) the light would be undetectable.

 

[Antiphon]

It's true. Brightness is a photometric quantity and doesn't decrease as the inverse square.

Penn.'s explanation was correct. I'll restate the same explanation a different way.

If you make a flat tungsten disk the size of a small saucer, hang it on the wall and heat it up to 6000K it will look and feel like the shining sun. They are both the same temperature and same brightness. The difference is only size and distance which counteract each other exactly. The inverse square law is irrelevant because brightness is a measure of energy/unit area of the source. This does not decrease with distance.

 

[Penn.6-5000]

A note to Mr. Klimatos on what would happen if the hypothesis were correct: This idea has come up in astronomy as "Olbers' Paradox." The paradox is that if the universe were infinitely large (and it were old enough for light from everywhere to have reached the Earth), then there would be stars everywhere, so that each point you look at in the sky hits a star *somewhere*. If we assume (incorrectly) that all stars are as bright as the sun, and (correctly) that the "amount of light per square degree of sky" is the same whether a star is nearby or far away, then we'd conclude that it would never be dark at night. The entire sky would glow with the brightness of the sun because these stars are everywhere. This reasoning may sound a little crazy, but it's actually correct. Apparently it was even enough to convince the 17th century astronomer Kepler that the universe was finite in size.

 

[klimatos]

I think we have a problem in professional terminology here. If astronomers want to define "brightness" as distinct from luminance or intensity of light, that is their privilege. In meteorology, "bright" sunlight is sunlight that casts a distinct (sharp edged) shadow. In this respect, it has an element of directness as opposed to diffusion.

In the common English language "brightness" is definitely associated with intensity. We speak of a "bright" light as opposed to a "dim" light; a "bright" sun as opposed to a "weak" sun, a "bright" color as opposed to a dark one. My dictionaries all incorporate the notion of intensity in their definitions.

If one uses a term in ordinary discussion is some specific sense, one should alert one's readers.

 

[cjl]

I doubt if that hypothesis is valid. If it were, no star would be too dim to see. It might be point, but it would be a bright point. Instead, the intensity of any electromagnetic source diminishes with the square of the distance from that source. At some distance (depending upon the sensitivity of your sensor) the light would be undetectable.

It's correct. The reason stars become too dim to see is because once they shrink below the minimum resolvable size of your sensor (or eye), then they appear to be a point that is at the minimum resolvable size, no matter how much smaller the actual angular extent becomes. Since the flux continues to decrease with distance, this causes the point to appear dimmer, even though surface brightness doesn't depend on distance.

 

[klimatos]

I am using "brightness" to denote luminance. Others are using it to denote radiance. According to Wikipedia (http://en.wikipedia.org/wiki/Brightness), the latter usage is incorrect.

Classical usage of the term "brightness" in Astronomy refers to orders of "magnitude". Here, perception of intensity of light is clearly indicated.

While Wikipedia is hardly the final word, two quotes from that source might be in order: 1) "With regard to stars, brightness is quantified as apparent magnitude and absolute magnitude."
2) ""brightness" should now be used only for non-quantitative references to physiological sensations and perceptions of light."