The phases of the moon cycle regularly. The dark of the new moon begins it, and then the moon waxes, slowly increasing its glow, through the first quarter to the gibbous moon and the full moon. Then the moon wanes, fading away to the last quarter and the new moon.
The moon orbits around the Earth in 27.3 days, but as the moon moves, the earth does as well. So from the vantage point of the earth, the moon takes 29.5 days to complete a rotation and go from one new moon to the next.
At the new moon phase, the moon is between the earth and the sun. The shadowed moon looks almost invisible in the sun's glow. A thin crescent appears when the moon's rotation allows people to see a sliver of the sunlit part-called the waxing crescent moon.
As it moves towards a ninety degree angle with the sun, half its sunlit surface becomes visible, and half remains shadowed. This is the moon's first quarter, when the dark area is on the left.
Then it waxes, becoming a waxing gibbous moon, meaning it's mostly illuminated. Half way through the cycle, the moon fully illuminates as the full moon. Now it begins to wane, becoming a waning gibbous moon. The last quarter shows the darkness on the right, and the darkness increases until the new moon returns.
The moon's gravity is the major cause of the tides. The earth is fairly far from the moon, but parts of the earth are closer and others farther away. The gravitational pull of the moon falls off sharply with distance, though, so the moon pulls on the part of the earth it is directly above with a force about 3.4 percent stronger than its average and with a force about 3.2 percent weaker than its average on the far side of the earth.
Since the pull is stronger on the nearby earth and weaker on the faraway side, the effect stretches the earth. The moon cannot stretch the rocky earth much, but easily stretches the oceans. High tides rise twice a day, when the moon is overhead or on the opposite side of the world.
New and full moons bring the strongest tides. Here, the moon and sun line up to tug together in an alignment called the syzygy.
At the full moon, the moon is on one side of the earth and the sun directly on the opposite. At the new moon, sun and moon tug on the same side of the world in conjunction.
The effect of the moon is stronger because the pull of gravitation falls off as the inverse square of the distance, and gravity moves the tides. The much larger sun, is about 389 times father away than the moon, so its pull is less than half as strong.
The strongest tides are called spring tides, because the water springs up. The weakest tides are when the moon is in the first or last quarter. Then the sun and moon partly cancel each other's pull, making neap tides.
Waxing and waning
People long believed that the brightening waxing moon favored sowing root crops and peas. Trees, however, should not be cut during a waxing moon because the moon draws the sap up into the wood, bowing boards cut from it and dulling saws that try to shape them.
The dimming waning moon was best for cleaning, breaking habits and weaning animals and children. This is pleasant nonsense, like the idea that sleeping in waxing moonlight will restore fertility, and sleeping in the bleached light of the full moon will madden or kill.
The moon is a mysterious beauty, but has little influence over anything on earth but the tides.