Olbers' paradox: why is the night sky dark?

Started Nov 12, 2012 | Discussions thread
Jonny Boyd
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Re: Olbers' paradox: why is the night sky dark?
In reply to Jonny Boyd, Dec 3, 2012

Another way of bridging the conceptual divide just occurred to me since you seem hung up on the issue of point sources. A point source is an object which cannot be resolved by a detector i.e. something occupying less than two pixels.

Another way of thinking about this is that a detector can record the brightness of a number of point sources equal to its resolution i.e. a 100x100 pixel detector can record the brightness of 10,000 point sources.

There are billions upon billions of stars in the sky, so obviously we can't built a detector that can register the brightness of each star individually and our eyes have nowhere near the resolution necessary. So instead of thinking about each star as a point source of light, why not think about looking at the sky and seeing a number of point sources of light equal to the number of pixels in your detector, so that each point source of light is then made up of multiple stars.

A 120 megapixel detector (the number of rods in our eyes) would therefore see 120 million point sources of light, each point source made up of multiple stars. If you work out the brightness of each point source, then you can work out the array of brightness values perceived by the eye.

To rephrase this, instead of working out the brightness of individual stars, you work out the brightness of the area of sky observed by each individual photodetector. There are several ways of doing this. One is described in the Wikipedia article on apparent brightness http://en.wikipedia.org/wiki/Apparent_brightness where it talks about the need to add magnitudes to get the magnitude of a system of binary stars for example. At the very least this hopefully makes clear that addition of brightness is necessary when objects cannot be resolved individually.

Of course, when you do the maths for this, you find that any combination of stars which results in the field of view of one pixel being completely covered by stars, then you find that the same brightness will be recorded by each pixel, therefore each cell in your array will contain the same value.

Also, here is some useful information about brightness in astronomy which will help with understanding what astronomers mean when they talk about Olbers' paradox:

http://en.wikipedia.org/wiki/Luminosity

Luminosity is generally understood as a measurement of brightness ...

In astronomy, luminosity measures the total amount of energy emitted by a star or other astronomical object in SI units of joules per second, which are watts ...

The field of optical photometry uses a different set of distinctions, the main ones being luminance and illuminance. Astronomical photometry, by contrast, is concerned with measuring the flux, or intensity of an astronomical object's electromagnetic radiation.

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