Moon Phases, Eclipses & Tides Lab

About this model

Geometry. The Sun is far away along a fixed direction, so its rays are parallel. The Moon moves at a steady rate on a circle tilted 5.1° to the ecliptic (the plane of Earth’s orbit); its height above or below the ecliptic is tan β = tan 5.1° · sin(angle from the node). The lit fraction we see is (1 − cos of the Sun–Moon angle) / 2. Real orbits are slightly elliptical and the Moon speeds up and slows down; this model leaves that out. Distances and sizes in the pictures are not to scale, and the Orbit view draws the tilt 3× (Advanced can switch that off). Earth is drawn at an equinox and does not spin in the Orbit view.

Periods. Synodic month 29.53 d, sidereal month 27.3217 d, Earth’s year 365.256 d, tilt 5.1° (NASA Moon fact sheet). 1/T_synodic = 1/T_sidereal − 1/T_year. With “Let the line of nodes turn”, the nodes turn once per eclipse year (346.6 d) from the line of nodes turning once every 18.6 years (NASA), giving two eclipse seasons a year.

Eclipses. The model says an eclipse is possible when the Moon is within 1° of new or full AND within 1° of the ecliptic. These windows are a teaching threshold, not a forecast: the model has no dates, no total/annular/partial types, no distance changes and no parallax. In the Sky view the Sun, Moon and Earth’s shadow are drawn at their real angular sizes (Sun 0.53°, Moon 0.52°, umbra about 1.4° and penumbra about 2.5° across, from Meeus, Astronomical Algorithms).

Tides. An idealised (equilibrium) model: an ocean covering a smooth Earth, with the Moon’s tide = 1 and the Sun’s = 0.46 (NOAA). Each raises two opposite bulges, so they combine as A = √(1 + s² + 2s·cos 2E). The tide gauge shows that idealised water level at a harbour on the equator, turning under the bulges once per lunar day (24 h 50 min, NOAA). It is not a tide table: real coasts change the timing and height a lot.

No randomness. The model has no noise: the same settings always give the same numbers. The tests draw their questions with a seed per attempt.

Images. Moon and Earth maps: Solar System Scope (based on NASA imagery), CC BY 4.0, shared with Kepler’s Laws.

NASA Moon fact sheet · NASA: Moon phases · NASA: eclipses · NOAA: spring and neap tides · NOAA: the lunar day · Solar System Scope textures

What am I looking at?

How the lab works. Pick Explore or one lab at the top. Each lab has five tabs: Pre-lab, Bench, Data & graph, Claim · Evidence · Reasoning, and Test. On the Bench, the coach below the scene lists your steps; they tick themselves as you work. Press What do I do now? when you’re stuck.

① Orbit. Earth in the middle with sunlight coming from the left. The bright solid part of the Moon’s orbit is above the ecliptic (the blue grid: Earth’s orbit plane); the dashed part is below. ☊ and ☋ mark the nodes, where the orbit crosses the grid. Drag the Moon to move it, drag a node marker to turn the line of nodes, drag empty space to turn the camera, or use Tilted / Top / Edge-on. Dark cones are shadows. The star-frame box (top right) shows Earth moving around the Sun during the month.

② Sky from Earth. Left: the Moon as you would see it from the Northern Hemisphere. Right: the alignment check, a grid of 1° squares around the Sun (near new Moon) or Earth’s shadow (near full Moon). The amber dotted circle is the model’s 1° eclipse window; the dashed line is the Moon’s path this month.

③ Tides. Earth seen from above the North Pole with a pretend ocean covering it. The blue shell shows the two tidal bulges (hugely exaggerated). Cyan arrows: the Moon’s tide. Amber dashed arrows: the Sun’s tide. Drag around Earth to move the Moon. Right: an idealised tide gauge at the red harbour pin.

Keys: Space play / pause · → step · R reset · Z / X zoom.