Moon Lab Report

In astronomy, a phase of the Moon is any of the aspects or appearances presented by the Moon as seen from Earth, determined by the portion of the Moon that is visibly illuminated by the Sun. The lunar phases vary cyclically as the Moon orbits the Earth, according to the relative positions of the Earth, the Moon, and the Sun. Since the Moon appears bright only due to the Sun's reflected light, only the half of the Moon facing the Sun is illuminated.

The lunar phase depends on the Moon's position in orbit around the Earth, and the Earth's position in orbit around the sun. This diagram looks down on Earth from the north. Earth's rotation and the Moon's orbit are both counter-clockwise here. From this diagram, we can see, for example, that the
Animation of the Moon as it cycles through its phases. The apparent wobbling of the Moon is known as libration.
According to geometry, when a sphere is illuminated on one hemisphere and viewed from an angle, then the portion of the illuminated area visible from that angle will be observed to have the two-dimensional shape of a half-ellipse inscribed within a half-circle, where the major axis of the ellipse is the same as the diameter of the semicircular arc. If the half-ellipse is convex with respect to the half-circle, then the shape will be gibbous, and if the half-ellipse is concave with respect to the half-circle, then the shape will be a crescent. If the eccentricity of the ellipse is 1, then a half-circle will be seen; while if the eccentricity of the ellipse is 0, then either a fully-illuminated or fully-dark circular disk will be seen (i.e. a full moon or new moon). Of course, actual observations of the Moon's lit area will not completely correspond with these abstract geometrical shapes, due to varying surface reflectivities, the lesser brightness of illuminated areas which are viewed at a low angle,
If the right side of the Moon is dark, the light part is shrinking: the Moon is waning (moving towards a New Moon). Simply, assuming you are in the northern hemisphere, it's always the right part of the Moon that is growing. The acronym mnemonic "DOC" represents this ("D" is the waxing Moon; "O" the Full Moon; and "C" the waning Moon). (There is also the phrase "Dog comes; Cat goes".)
In the Southern hemisphere, this is reversed, and the mnemonic is "COD". Since these two mnemonics are equal and opposite, they may be easily confused; however, one can remember "DOC" since the story of the Seven Dwarves was created in the Northern Hemisphere.
A French mnemonic is that the waxing Moon at its first "premier" quarter phase looks like a 'p', and the waning Moon at its last "dernier" quarter looks like a 'd'. The southern hemisphere equivalent for 'p' and 'd' is that the Moon is 'past it', or 'doing it'. The most popular Italian mnemonic for lunar phases is the rhyming proverb "Gobba a ponente, luna crescente. Gobba a levante, luna calante" ('Hump towards west, Moon [is] growing (waxing); hump towards east, Moon [is] shrinking (waning)'), where hump is a common metaphore for the Moon's