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Overview

The mlim module calculates the visual limiting magnitude for an observer based on the Bortle dark-sky class and the altitude angle of the observed celestial object.

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calculate_mlim

Calculates the visual limiting magnitude adjusted for altitude angle. 
def calculate_mlim(
    bortle_class: int,
    h_deg: float,
    k: float = 0.25
) -> float

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Parameters

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bortle_class
int
required
Bortle class (1-9) representing sky darkness
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h_deg
float
required
Altitude angle above the horizon in degrees (clamped to 10-90°)
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k
float
default:"0.25"
Atmospheric extinction coefficient (typically 0.15-0.45)
  • 0.15: Exceptionally clear, high altitude
  • 0.25: Typical conditions (default)
  • 0.45: Hazy or humid conditions

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Returns

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mlim
float
Estimated limiting magnitude at the specified altitude

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Formula

The zenith limiting magnitude is calculated as: mlim,zenith=7.6−0.5⋅(B−1)m_{\text{lim,zenith}} = 7.6 - 0.5 \cdot (B - 1) Where BB is the Bortle class. This is then adjusted for altitude using atmospheric extinction: mlim(h)=mlim,zenith−k(1sin⁡h−1)m_{\text{lim}}(h) = m_{\text{lim,zenith}} - k \left( \frac{1}{\sin h} - 1 \right)

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Example

from TerraLab.light_pollution.mlim import calculate_mlim

# Bortle 3 site, observing at 30° altitude
mlim = calculate_mlim(bortle_class=3, h_deg=30.0, k=0.25)
print(f"Limiting magnitude: {mlim:.2f}")  # ~6.2

# Same site at zenith (90°)
mlim_zenith = calculate_mlim(bortle_class=3, h_deg=90.0)
print(f"Zenith limiting magnitude: {mlim_zenith:.2f}")  # ~6.6

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calculate_mlim_from_sqm

Convenience function to calculate limiting magnitude directly from SQM reading. 
def calculate_mlim_from_sqm(
    sqm: float,
    h_deg: float,
    k: float = 0.25
) -> float

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Parameters

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sqm
float
required
Sky brightness in mag/arcsec²
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h_deg
float
required
Altitude angle in degrees
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k
float
default:"0.25"
Atmospheric extinction coefficient

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Returns

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mlim
float
Estimated limiting magnitude

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Example

from TerraLab.light_pollution.mlim import calculate_mlim_from_sqm

# SQM reading of 21.5 mag/arcsec², observing at 45°
mlim = calculate_mlim_from_sqm(sqm=21.5, h_deg=45.0)
print(f"Limiting magnitude: {mlim:.2f}")
This function internally converts the SQM value to a Bortle class using sqm_to_bortle_class() and then calls calculate_mlim().

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See Also

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