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Olbers’ Paradox Finite Shell Demonstration — result sheet
Estimate the finite shell contribution and cumulative flux in a simplified uniform-star model to explore why an infinite static universe creates a paradox.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For a uniform Euclidean shell, star count ≈ 4πr²nΔr and flux per star = L/(4πr²), so shell flux ≈ nLΔr; cumulative finite flux through R ≈ nLR after parsec-to-metre conversion.
The inverse-square dimming of each distant star is cancelled by the increasing number of stars in a spherical shell under the deliberately simplified uniform model. This calculator keeps the horizon finite so the arithmetic remains meaningful and labels the result as a demonstration; the real night sky also depends on finite cosmic age, expansion, stellar evolution, absorption, and non-uniform structure.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Average stellar luminosity — W; minimum 1.0E-6; maximum 1.0E+40
- Uniform star density — stars/pc³; minimum 1.0E-12; maximum 1000000
- Shell thickness — pc; minimum 1.0E-6; maximum 1000000
- Finite horizon radius — pc; minimum 1.0E-6; maximum 1000000000
- Reference distance for one-star flux — pc; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Average stellar luminosity | 3.828E+26 |
| Uniform star density | 0.004 |
| Shell thickness | 1 |
| Finite horizon radius | 10000 |
| Reference distance for one-star flux | 1 |
The finite uniform-star model returns a shell contribution and cumulative flux that remain finite for a 10,000 pc horizon; the accompanying outputs show the star count and one-star reference flux used in the demonstration.
Assumptions and limits
- Stars have one average luminosity and are uniformly distributed in an otherwise static Euclidean space.
- The shell is thin enough that its radius can be represented by the supplied horizon scale for the shell estimate.
- The horizon is finite and converts parsecs to metres for an ideal isotropic flux result.
- No extinction, redshift, cosmic expansion, stellar evolution, angular source size, or finite stellar radius is modeled.
- The result is not an observed sky brightness, cosmological measurement, or proof that the real universe is finite or static.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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