Olbers Paradox Calculator
Explore Olbers paradox by estimating sky brightness from star density, luminosity, and observable universe radius.
What Is Olbers' Paradox?
Olbers' paradox asks a simple question: if the universe is infinite and filled with stars, why is the night sky dark? In a static, infinite cosmos, every line of sight should eventually hit a star, and the sky should glow as brightly as a stellar surface.
Shell Brightness in a Static Universe
Imagine concentric spherical shells around Earth, each of thickness \(dr\). Flux from one star at distance \(r\) scales as \(L/(4\pi r^2)\), but the number of stars in a shell grows as \(r^2\). The shell contribution becomes:
$$f_{\mathrm{shell}} = L \cdot n_0 \cdot dr$$Integrating over all shells in an infinite universe gives infinite total flux, which contradicts our dark night sky.
How Modern Cosmology Resolves the Paradox
The observable universe is finite in age and size, so only a limited volume contributes light. Expansion redshifts distant sources, further dimming their flux. Together, finiteness and expansion reduce sky brightness to the faint glow we actually see.
Related tools: Redshift Calculator, Hubble's Law Calculator, and Luminosity Calculator.
Frequently Asked Questions
Who proposed Olbers' paradox?
Heinrich Olbers popularized the puzzle in 1823, but earlier thinkers including Kepler had raised similar questions about a dark night sky.
Can dust between stars explain the darkness?
Only temporarily. Dust absorbs light but eventually warms and re-radiates it. Dust attenuation alone cannot fully resolve the paradox.
What is star number density?
It counts how many stars occupy a unit volume of space, often expressed per cubic light year. Higher density pushes predicted sky brightness upward.
Why does expansion reduce sky brightness?
Receding stars deliver redshifted photons with lower energy flux. The cosmological model in this calculator includes that dimming factor.
How bright is the Sun at Earth?
Solar flux at Earth's orbit is about 1.36 kW/m². Compare calculator output against that reference to see how extreme the paradox prediction is.
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