Olber's Paradox Calculator
Explore why the night sky is dark: from infinite brightness to cosmic reality
Investigate Olber's Paradox
Infinite, static, homogeneous universe with uniform star distribution
Average stellar luminosity in solar units (L☉ = 3.828×10²⁶ W)
Number of stars per cubic light year (typical: 10⁻¹⁰)
Calculation Results
Interpretation
This is Olber's paradox: infinite brightness makes the night sky impossibly bright!
Formula Used
f_total = ∫₀^∞ n₀ · L dr = ∞
Infinite static universe leads to infinite flux
Paradox Analysis
Historical Context
The Original Question (1823)
Heinrich Olbers asked: "Why is the night sky dark?"
If the universe is infinite and filled with stars, shouldn't every direction in the sky contain a star, making the night as bright as day?
The Modern Solution
• The universe has a finite age (~13.8 billion years)
• The universe is expanding, causing redshift
• Only a finite portion is observable
• Early stars hadn't formed yet when the universe was young
Quick Facts
Theory Comparison
Infinite Static
Predicts infinite brightness
With Dust
Partial solution, dust re-radiates
Finite Universe
Limited by stellar occlusion
Expanding Universe
Correct modern solution
Understanding Olber's Paradox
The Paradox Explained
Olber's Paradox asks a seemingly simple question: "Why is the night sky dark?" If the universe is infinite and uniformly filled with stars, then in any direction we look, our line of sight should eventually hit a star, making the entire sky as bright as the surface of the Sun.
Historical Attempts
- •Interstellar dust blocks distant starlight
- •The universe is not infinite
- •Star distribution is not uniform
- •Stars haven't existed forever
Modern Resolution
Key Factors:
- • Finite age of the universe (~13.8 Gyr)
- • Expansion causing redshift
- • Finite observable universe
- • Evolution of stellar populations
Mathematical Solution
Expanding Universe Formula:
f = n₀ · L · (c/H₀) · (2ln(2) - 1)
This gives a finite, reasonable flux of ~10⁻⁶ W/m²