Moon Phases & Eclipse Geometry Explorer

Three modes let you explore the lunar cycle, eclipse conditions, and seasonal variations. Adjust the Moon's age to see illumination changes, set the node angle to trigger eclipses, or pick any day and latitude to compute day length and solar altitude.

Mode

Presets

0.0 days
0 (New)29.53 days

Orbital View

SunEarthMoon🌑 New MoonIllumination: 0.0%Moon age: 0.0 daysPhase angle: 0.0°

Moon Phase Results

Phase
🌑 New Moon
Illumination
0.0%
Phase Angle
0.0°
Moon Age
0.0 days
Rise Time
06:00
Set Time
18:00

Rise/set times are approximate, based on the average relationship between phase angle and moonrise. Actual times vary with observer latitude, date, and orbital eccentricity.

Moon Phase
🌑 New Moon
Illumination
0.0%
Season
Spring
Day Length
11.9 hr

Reference Guide

Lunar Phases and the Synodic Month

The Moon completes one cycle of phases every 29.53 days (the synodic month). The phase angle measures how far the Moon has traveled in its orbit relative to the Sun-Earth line.

θphase=d29.53×360°\theta_{\text{phase}} = \frac{d}{29.53} \times 360°

Illumination follows a cosine curve. At New Moon (0°) the illuminated fraction is 0%. At Full Moon (180°) it is 100%.

f=1−cos⁡θ2×100%f = \frac{1 - \cos\theta}{2} \times 100\%
🌑 New Moon0° 🌓 First Quarter90° 🌕 Full Moon180° 🌗 Third Quarter270°

Eclipse Geometry

Eclipses require the Moon to be near a node, where its orbital plane crosses the ecliptic. The Moon's orbit is tilted about 5°, so eclipses only occur when the Moon is close to the line of nodes at New or Full Moon.

Eclipse typePhaseMax node angle
Total lunar Full Moon < 3.5°
Total solar New Moon < 2°
Annular solar New Moon < 10°
Penumbral lunar Full Moon < 11.5°

Seasons and Axial Tilt

Earth's axis is tilted 23.44° from the orbital plane. This tilt causes the Sun's declination to oscillate throughout the year, producing the seasons.

δ=23.44°×sin⁡ ⁣(360°365(d−81))\delta = 23.44° \times \sin\!\left(\frac{360°}{365}(d - 81)\right)

At the summer solstice (around June 21), the Northern Hemisphere receives maximum sunlight. At the winter solstice (around December 21), it receives the least.

The equator always receives close to 12 hours of daylight regardless of the time of year. Polar regions experience midnight sun or polar night when the declination exceeds the complement of the latitude.

Day Length and Solar Altitude

Day length is computed from the sunrise equation. The hour angle at sunrise or sunset depends on latitude and solar declination.

ω=arccos⁡(−tan⁡ϕ⋅tan⁡δ)\omega = \arccos\bigl(-\tan\phi \cdot \tan\delta\bigr)
D=2ω15°/hrD = \frac{2\omega}{15°/\text{hr}}

Solar altitude at noon is the maximum elevation of the Sun above the horizon for a given day and location.

hnoon=90°−∣ϕ−δ∣h_{\text{noon}} = 90° - |\phi - \delta|

Where φ is the observer's latitude and δ is the solar declination on that date.