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Moon Phases, Eclipses & Seasons Lab

Investigate the relationship between Sun-Earth-Moon geometry and what we observe from Earth. Explore how the Moon's orbital position creates the eight named phases, why eclipses are rare, and how Earth's axial tilt drives seasonal changes in day length and solar altitude.

Guided Experiment: Moon Phases and Illumination

How does the Moon's illumination change over the 29.53-day synodic month? What is the relationship between orbital position and the phase we see?

Write your hypothesis in the Lab Report panel, then click Next.

SunNewQ1FullQ3EarthMoonAppearance🌑 New Moon0.0% illuminated

Controls

0 (New)7.4 (Q1)14.8 (Full)22.1 (Q3)29.5

Phase Details

🌑
New Moon
0.0% illuminated
Moon Age0 days
Phase Angle
Approximate Rise6:00 AM
Approximate Set6:00 PM
Illumination Formula
I=1cos(θ)2×100%=1cos(0°)2×100%=0.0%I = \frac{1 - \cos(\theta)}{2} \times 100\% = \frac{1 - \cos(0°)}{2} \times 100\% = 0.0\%

Data Table

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#DayPhaseIllumination %Eclipse PossibleSeasonDay Length (h)
0 / 500
0 / 500
0 / 500

Reference Guide

Moon Phases

The Moon orbits Earth every 29.53 days (synodic month). As the Sun-Earth-Moon angle changes, different amounts of the Moon's sunlit side face Earth, creating the eight named phases.

I=1cos(θ)2×100%I = \frac{1 - \cos(\theta)}{2} \times 100\%

At new moon (0°) illumination is 0%. At first and third quarter (90° and 270°) it is 50%. At full moon (180°) it reaches 100%. The pattern follows a smooth cosine curve.

Lunar & Solar Eclipses

Eclipses require the Moon to be near an orbital node (where the Moon's orbit crosses the ecliptic plane) during new or full moon. The Moon's orbit is tilted about 5° from the ecliptic, so most months the Moon passes above or below Earth's shadow.

A lunar eclipse occurs when Earth's shadow falls on the full Moon. A solar eclipse occurs when the new Moon passes between Earth and the Sun. Total solar eclipses require very precise alignment and are visible only from a narrow path on Earth's surface.

Earth's Seasons

Seasons arise from Earth's 23.44° axial tilt, not from distance to the Sun. As Earth orbits, the tilt causes the Sun's rays to strike different latitudes more or less directly, changing the solar declination throughout the year.

δ=23.44°×sin ⁣(360°365(d81))\delta = 23.44° \times \sin\!\left(\frac{360°}{365}(d - 81)\right)

At the summer solstice the Sun reaches its highest declination (+23.44°), giving the longest day in the Northern Hemisphere and the shortest in the Southern Hemisphere.

Day Length & Solar Altitude

Day length depends on both latitude and solar declination. The sunrise equation gives the number of daylight hours.

D=215arccos(tanφtanδ)D = \frac{2}{15}\arccos(-\tan\varphi \cdot \tan\delta)

At the equator, day length stays near 12 hours year-round. At higher latitudes, summer days grow longer and winter days shorter. Beyond the Arctic or Antarctic Circle, the Sun may not set (midnight sun) or not rise (polar night) for days or weeks.

Solar altitude at noon = 90° − |latitude − declination|. This determines how concentrated the sunlight is and drives seasonal temperature differences.