Science · Middle school

Phases of the Moon

Move the Moon around the Earth and see how much of its sunlit half we can see from here.

In the learning section below the figure, predict, try, complete the tasks and check yourself with short questions.

Fig. 1Phases of the Moon

Drag the Moon or use the slider

Seen from the EarthWaxing crescent

Lit: 10%
Day: 3.0 of 29.5
Sun–Moon angle: 37°

Since new moon

What if?

Move the Moon closer or farther: how big does it look, how much stronger are the tides, how long do the phases take?

The Sun and the Moon in the sky, to the same scale.Left: the SunRight: the Moon; dashed circle is today’s size

Apparent size: 0.52°; ×1 today’s
Tidal force: ×1
Full moon brightness: ×1
Cycle of phases: 29.5 days

Today the Moon is on average 384,400 km away and looks 0.52° wide; the Sun looks 0.53°. The Sun is 400 times as wide as the Moon and 389 times as far: by this coincidence the two look almost the same size.

In reality: The Sun’s tidal pull is 46% of the Moon’s: at new and full moon the two pull the same way and the tides grow. The Moon moves away by about 3.8 cm a year; in the very far future there will be no total solar eclipses.

Assumptions: Circular orbit; the Moon’s mass, the Earth’s spin and the distance to the Sun stay the same. For the tides only the ratio of the force is worked out (∝ 1/d³); how high the sea actually rises depends on the coast and the ocean basin. Brightness is taken as proportional to the Moon’s apparent area. Apparent size and eclipses are worked out as seen from the Earth’s centre (geocentric). Numbers come from the radii, masses and distances in NASA’s fact sheets.

Learn

Progress is kept on this page only; no points are given.

1Predict
2Try
3Explain

From the Earth, half of the Moon’s disc looks lit (first quarter). How much of the Moon is the Sun lighting at that moment?

Gold: the half lit by the Sun (always half of the Moon)Purple: edge of the half facing the Earth, and the line of sightThe numbers come from the model in this article: one cycle of phases (a synodic month) lasts 29.53 days on average, the Sun–Moon angle ψ grows steadily with time, and the visible lit fraction is k = (1 − cos ψ) / 2. The Moon is fixed to its arm, so it always turns the same face (the same dark plains) to the Earth. Sunlight is taken as parallel; sizes and distances are not to scale, and the orbit’s tilt of about 5° and its slight ellipse are left out, so the figure shows no eclipses. A main phase is named within 1 day of its exact moment. The window shows the view from the Northern Hemisphere.

How do the phases of the Moon happen? From crescent to full moon, step by stepRead the article