Understanding the astronomy behind crescent moon visibility
Before the crescent moon can be sighted, a precise set of astronomical conditions must align. This page explains the key concepts used in visibility modelling — from first principles.
Conjunction occurs when the Moon passes directly between the Earth and the Sun, sharing the same ecliptic longitude. This marks the start of the lunar month astronomically.
Important: Conjunction does not mean the crescent is visible. The Moon is too close to the Sun to be seen — it rises and sets with the Sun.
Elongation is the angular separation between the Moon and the Sun, as seen from Earth. It is measured in degrees (0° – 180°).
A larger elongation means the Moon has moved further from the Sun after conjunction, making it easier to see and producing a brighter, wider crescent.
Altitude is the Moon's angular height above the horizon, measured in degrees, at the moment of local sunset. This is one of the most critical factors for visibility.
A negative altitude means the Moon has already set before the Sun — sighting is impossible. A higher altitude gives more time for the sky to darken before the Moon sets.
The Arc of Vision (ARCV) is the difference in altitude between the Moon and the Sun at sunset. When the Sun is exactly at the horizon (altitude ≈ 0°), ARCV ≈ Moon altitude.
ARCV determines how dark the sky is by the time the Moon is observed — a higher ARCV means the sky has darkened more, making the thin crescent easier to detect.
The Arc of Light refers to the length and brightness of the illuminated crescent arc as seen from Earth. It depends directly on the elongation.
A larger ARCL means a longer, brighter crescent that is easier to detect — especially for first-sighting near the Danjon limit where the crescent is extremely thin.
Even with the best geometric conditions, many real-world factors introduce uncertainty into whether any individual observer will successfully sight the crescent.
Geometric models like Yallop and Odeh provide probability zones, not certainties.
This platform offers three calculation methods. Each uses the same underlying astronomical data but applies different classification algorithms:
Simplified Model — A basic geometric threshold approach using fixed altitude and elongation cutoffs. Good for a quick overview.
Yallop Method (1997) — Developed for the HM Nautical Almanac Office. Uses a polynomial q-criterion derived from historical crescent sighting data. Produces five classification codes (A–E).
Odeh Method (2004) — Published by the International Astronomical Center. A modern refinement using a larger global dataset and slightly shifted thresholds. Produces three classification codes (NE, OA, NV).
This platform provides astronomical modelling for educational purposes only. All results are probabilistic and based on geometric criteria. Actual visibility is subject to atmospheric, geographical, and human factors not captured by these models.
Final religious decisions regarding the beginning of lunar months remain with local religious and civic authorities. This platform does not make religious rulings of any kind.