Solar and Lunar Eclipses – Umbra, Penumbra and the Moon's Nodes

What it shows

An eclipse needs the Sun, Earth and Moon in a straight line in three dimensions. The Moon's orbit is tilted by 5.1° to Earth's orbit, so at most new moons it passes above or below the Sun and at most full moons above or below Earth's shadow. Eclipses happen only when a new or full moon falls near a node, where the two orbits cross. The model uses real angles: the sizes of the Sun and Moon in the sky, Earth's umbra and penumbra at the Moon's distance, a 29.53-day synodic month and a 346.6-day eclipse year. Orbits are circles and the Moon's distance is set by the slider.

How to use

Press Run and let time pass; when an eclipse is coming the simulation slows down automatically so you can watch the Moon cover the Sun or turn red in Earth's shadow. Drag the Distance to the Moon slider, or use Perigee and Apogee, to turn a total solar eclipse into an annular one. Set Orbit tilt to 0° and eclipses happen every month. Change Sun–node angle to move the node line. Next new moon and Next full moon jump straight to the next alignment.

Parameters you can change

• Simulation speed 0.5–20 days/s
• Earth–Moon distance 356–407 thousand km
• Tilt of the Moon's orbit 0–10 °
• Angle between the Sun direction and the ascending node at the first new/full moon 0–359 °
• Start Just before a new moon, Just before a full moon
• Slow down during solar and lunar eclipses

Questions to explore

1. Why is there not a solar eclipse every month, even though there is a new moon every month?
2. At the same alignment, what decides whether a solar eclipse is total or annular?
3. Run the model for about a year: how many eclipses happen, and how far apart are the groups of eclipses?