Why does the Moon sometimes look like a crescent during the day?

This occurs because the phase is determined by the Moon's position relative to the Sun and Earth, not by the time of day. A crescent phase means the Moon is relatively close to the Sun in the sky, so it can be visible during daylight hours. The simulator shows that for a crescent, the phase angle is small, placing the Moon near the Sun from our viewpoint.

If the Sun is always illuminating half the Moon, why don't we always see a Full Moon?

We only see the portion of the lit half that is facing Earth. From our perspective on Earth, the Moon's orientation changes as it orbits us. During a New Moon, the lit half faces completely away from us. During a Quarter Moon, we see half of the lit half. The simulator's space view clearly shows this changing geometry.

Does the Earth's shadow cause the Moon's phases?

No, this is a common misconception. The Moon's phases are caused by the changing viewing angle of the Sunlit portion of the Moon as it orbits Earth. The Earth's shadow only causes a lunar eclipse, which is a separate, infrequent event. The simulator shows that phases occur even when the Moon is far from Earth's shadow.

What simplification does this model make about the Moon's orbit?

The model assumes the Moon's orbit is a perfect circle in the same plane as Earth's orbit around the Sun (the ecliptic). In reality, the Moon's orbit is slightly elliptical and tilted by about 5 degrees, which is why we don't have a solar and lunar eclipse every month.

Moon Phases

The Moon Phases simulator visualizes the geometric relationship between the Sun, Earth, and Moon that produces the lunar cycle. At its core, it models the synodic period—the approximately 29.5-day cycle from one New Moon to the next. The primary variable is the phase angle, the angle between the Sun and the Moon as seen from Earth. This angle directly determines the Moon's illuminated fraction, which is calculated using the formula: illuminated fraction = (1 + cos(phase angle)) / 2. When the phase angle is 0° (New Moon), the fraction is 0; at 90° (First Quarter), it's 0.5; and at 180° (Full Moon), it's 1. The simulator simplifies reality by assuming perfectly circular, coplanar orbits and using a distant, fixed Sun to illuminate the system. It ignores libration, the Moon's orbital inclination, and the elliptical nature of orbits. By manipulating the Moon's position and observing the resulting phase from both a space-based and Earth-based perspective, students learn the direct causal link between orbital geometry and the observed lunar phases, reinforcing concepts of angular relationships and cyclic patterns in the sky.

Who it's for: Middle-school and high-school students in introductory Earth science or astronomy courses, as well as educators seeking a clear visual tool to explain lunar phases.

Key terms

Lunar Phase
Synodic Period
Phase Angle
Illuminated Fraction
New Moon
Full Moon
Waxing and Waning
Orbital Geometry

How it works

The Moon’s phase depends on the angle between the Earth–Moon line and the direction to the Sun. After one synodic month (~29.5 days) the Moon returns to the same phase as seen from Earth. This page is a schematic diagram, not a planetarium ephemeris.

Key equations

visible lit fraction ∝ (1 − cos θ) / 2 (simplified)

Frequently asked questions

Why does the Moon sometimes look like a crescent during the day?: This occurs because the phase is determined by the Moon's position relative to the Sun and Earth, not by the time of day. A crescent phase means the Moon is relatively close to the Sun in the sky, so it can be visible during daylight hours. The simulator shows that for a crescent, the phase angle is small, placing the Moon near the Sun from our viewpoint.
If the Sun is always illuminating half the Moon, why don't we always see a Full Moon?: We only see the portion of the lit half that is facing Earth. From our perspective on Earth, the Moon's orientation changes as it orbits us. During a New Moon, the lit half faces completely away from us. During a Quarter Moon, we see half of the lit half. The simulator's space view clearly shows this changing geometry.
Does the Earth's shadow cause the Moon's phases?: No, this is a common misconception. The Moon's phases are caused by the changing viewing angle of the Sunlit portion of the Moon as it orbits Earth. The Earth's shadow only causes a lunar eclipse, which is a separate, infrequent event. The simulator shows that phases occur even when the Moon is far from Earth's shadow.
What simplification does this model make about the Moon's orbit?: The model assumes the Moon's orbit is a perfect circle in the same plane as Earth's orbit around the Sun (the ecliptic). In reality, the Moon's orbit is slightly elliptical and tilted by about 5 degrees, which is why we don't have a solar and lunar eclipse every month.

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Key equations

Frequently asked questions