Moon Phases

The Sun always lights half of the Moon, just as Earth has a day side and a night side. What changes through the month is how much of that lit half faces us, and that depends only on the angle between the Sun and the Moon as seen from Earth. The lit fraction of the disk is (1 - cos A) / 2 for an angle A: nothing at new Moon (0 degrees), half at the quarters (90 and 270), all of it at full (180). Phases are not caused by Earth's shadow, which reaches the Moon only during a lunar eclipse. NASA lists the eight phases as new, waxing crescent, first quarter, waxing gibbous, full, waning gibbous, third quarter and waning crescent.

From one new Moon to the next takes 29.53 days, the synodic month. Measured against the stars the Moon circles Earth in 27.32 days, the sidereal month, but by then Earth has moved along its own orbit, so the Moon needs about two more days to line up with the Sun again (NASA Moon Fact Sheet). The game looks down from above the North Pole, where the Moon moves counterclockwise, and draws the Moon as seen from the Northern Hemisphere, where a waxing Moon is lit on the right. From the Southern Hemisphere the Moon appears upside down, so a waxing Moon is lit on the left; NASA publishes a south-up version of its Moon phase maps for that view.

The Moon's orbit is tilted 5.145 degrees to the plane of Earth's orbit and crosses it at two points, the nodes. Most months the new and full Moon pass above or below the Sun, and a solar eclipse can only happen at a new Moon inside one of the month-long eclipse seasons, when the line of nodes points at the Sun (NASA Scientific Visualization Studio). Level 6 runs on the synodic month (29.530589 days) and the draconic month, node to node (27.212221 days), from the NASA Eclipse Web Site. Together they give an eclipse year of 346.62 days, so eclipse seasons come about 173 days apart, a little less than half a year because the nodes slowly drift backward, once around every 18.6 years.

What the game simplifies: sizes and distances are not to scale (the Moon is really about 30 Earth diameters away), orbits are drawn as circles and the Sun is treated as infinitely far away. It counts an eclipse when the Moon is within 8 degrees of new or full and within 1.5 degrees of the Sun-Earth line, one limit for every kind; real limits differ for solar and lunar, partial and total eclipses. During a lunar eclipse the Moon can turn red because the only sunlight reaching it has passed through Earth's atmosphere, which scatters away most of the blue.