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How does distance affect brightness? Distant stars are exactly as bright as close stars - however, the "brightness" is just spread over a greater area of space.
by jbri 14y ago
How does distance affect brightness? Distant stars are exactly as bright as close stars - however, the "brightness" is just spread over a greater area of space.
In particular, the perceived brightness of a star falls off according to the square of distance - you can work this out for yourself by comparing the surface area of a sphere of radius d, with the surface area of a sphere of radius 2d.
But how many stars are at that distance? If you assume uniform density, then the answer is exactly the opposite of what we found above! The number of stars at a distance of d is proportional to the square of the distance.
This means that the total amount of light perceived from stars at a distance d is exactly the same, irrespective of the value of d.
Then if the universe was also both eternal and infinite, then there would be an infinite amount of light reaching the earth!
- surrealize 14y agoOkay, if the universe were perfectly homogenous, i.e., uniformly dense at all scales, then this argument would be easy to buy. If you allow density variation at some scales, like the difference in density between the interior of a star and interstellar space, then it changes a bit, right? If you're really close to a star, then obviously that star is brighter than the average brightness of the universe. Right? If so, then the night sky wouldn't be "as bright as the sun" (like the video says), as observed from earth. But would the night sky be uniformly bright? Doesn't it depend on the average density of the universe? I.e., if the average density gets low enough, then don't those small-scale density variations start to matter at some point?
- jbri 14y agoIt's generally hard to speculate on how things "would" be if the universe were markedly different than it how it actually is. Or rather, it's easy to speculate, but it's nigh-impossible to come up with one solution to the exclusion of others. I can come up with many hypothetical universes where the night sky would be uniformly bright, and many hypothetical universes where there would be substantial amounts of variation. The general statement of the paradox is that the total amount of light coming from distant stars massively outweighs the light coming from a local star, so while the local star might create a slightly brighter patch of sky, that difference is small enough that even in its absence the sky would look "bright".
- andrewcooke 14y agoyou're right that it's not going to work out exactly equal to the brightness of the sun. another way to see this is to imagine an alien who lives on a (undiscovered) planet incredibly close to the sun - the sun would appear much brighter to the alien who would, presumably, expect a correspondingly brighter sky everywhere else (which clearly makes no sense since looking in other directions the alien should agree with us). but the effect of variations is most important when you have fewest stars (so the largest variation should be the sun, which seems reasonable). at large distances, with many stars, things will even out despite the fluctuations (for physically reasonable fluctuations). to make the argument rigorous, you need to work out how bright things would be "on average". another (more convincing?) way to understand the problem is to see that if we have an infinite, static universe, full of stars, all burning away, it should get hotter and hotter over time... (and if it's infinitely old, should be infinitely hot by now!). clearly something is wrong with that model.
- specialist 14y ago> How does distance affect brightness? Red shift. The universe is filled with photons. But as the universe expands, everything moving away from everything else, the human visible light moves into the infrared spectrum.
- AgentConundrum 14y agoJust to be clear here, distance doesn't affect brightness; velocity does.
- jlgreco 14y agoUnless I am mistaken, they both do. There are multiple kinds of red shift. > "Redshifts are attributable to the Doppler effect, familiar in the changes in the apparent pitches of sirens and frequency of the sound waves emitted by speeding vehicles; an observed redshift due to the Doppler effect occurs whenever a light source moves away from an observer. Cosmological redshift is seen due to the expansion of the universe, and sufficiently distant light sources (generally more than a few million light years away) show redshift corresponding to the rate of increase of their distance from Earth. Finally, gravitational redshifts are a relativistic effect observed in electromagnetic radiation moving out of gravitational fields. Conversely, a decrease in wavelength is called blueshift and is generally seen when a light-emitting object moves toward an observer or when electromagnetic radiation moves into a gravitational field." The increasing distance between stars due to expansion is not velocity as we traditionally think of it. Things that far away get red-shifted because at distances that large expansion becomes a factor, not because of how they are otherwise moving about. It's basically the general idea behind Hubble's Law.