Light Pollution Impact Calculator Formula

Understand the math behind the light pollution impact calculator. Each variable explained with a worked example.

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Formulas Used

Sky-to-Object Flux Ratio

flux_ratio = pow(10, (object_brightness - sky_brightness) / 2.5)

Object Contrast (%)

contrast_pct = 100 / (1 + pow(10, (object_brightness - sky_brightness) / 2.5))

Variables

VariableDescriptionDefault
sky_brightnessSky Brightness(mag/arcsec2)19
object_brightnessObject Surface Brightness(mag/arcsec2)22

How It Works

Light Pollution and Contrast

Light pollution raises the sky background, drowning out faint objects.

Key Relation

The flux ratio of sky to object is:

ratio = 10^((mag_obj - mag_sky) / 2.5)

A higher ratio means the sky overwhelms the target. Object contrast is approximately 1 / (1 + ratio).

Darker skies (higher mag/arcsec2) dramatically improve contrast for faint targets.

Worked Example

Sky = 19 mag/arcsec2 (suburban), object = 22 mag/arcsec2.

sky_brightness = 19object_brightness = 22
  1. 01ratio = 10^((22 - 19) / 2.5)
  2. 02ratio = 10^1.2 = 15.85
  3. 03contrast = 100 / (1 + 15.85) = 5.94%
  4. 04The object has only 5.9% contrast against the bright sky.

Ready to run the numbers?

Open Light Pollution Impact Calculator