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The Lunar Cycle

The motions of the planetary bodies are pretty complex, and involve much more metaphysics than gravity in their strange motions. There are three main actors in this celestial dance: the sun, the moon, and the planet. The sun is, of course, a massive nuclear furnace in the far distance (approximately 10 light-minutes away). The moon is a natural satellite to the planet that orbits closely around one of the poles. The moon is large and dark, since its back is always turned towards the planet, its lit face staring down the sun. The planet is much larger than, lets say, some hypothetical planet called "Earth" that has a circumference of 24,901 miles, but its mass (1.3 x 1025 pounds) is actually exactly the same. What are the odds?
In any case, the exact circumference of the planet is hotly debated by the scientific community, since they can only get to 1/10th of the place, and no one's seemed to get the same mathematical result twice. (The gods know exactly what it is, but don't really care enough to tell anybody.) There are people who theorize that the planet isn't actually a full sphere, but is maybe a half-sphere, or an oblong, or the other side is totally malformed from its lack of exposure to civilization. But all that isn't really important. What's important is that the decisphere is a rough circle, and every day there is a solar eclipse.

Day/Night Cycle

Picture a flat disc1 with a flashlight held over it. The flashlight points straight down at the center of the disc, illuminating the whole thing. Now get yourself an imaginary pendulum, hang it from the flashlight, and send it in circles around the central point of the disc. That's pretty much how it works.
If you want to know the slightly more complex and more accurate story, the pole at the center of the decisphere is always pointed straight at the sun, no matter where the planet is in its annual revolution. The planet rotates clockwise around the pole; the moon orbits counterclockwise. Both of these orbits take 48 hours to get back to their starting point, so their opposed movement halves that time to 24 hours before the moon is above the same spot on the planet. Wherever the moon blocks the light from experiences night, and the rest has a straight line to the sun and experiences day.
From a worm's eye view, the moon is completely invisible past the blue sky and bright sun at noon. In the evening, the sun "wanes" as the moon crawls over it, and at the darkest time of night the moon covers the sun so completely that not even a corona2 is visible. In the morning, the moon retreats off the other side and the sun "waxes" into daylight. Pretty sick, right? If the moon is at all visible (like through a specialized telescope), it looks like its circling like a clock hand, the sun being one of the stationary numbers.

Seasons

The orbit of the planet means that part of the year it is closer to the sun than the rest of the year. When it is closer to the sun, the weather is warmer, and its summertime. When its further away, winter. The messy thing about it is that during the summer the days are shorter, the nights long. And in the winter, the days are longer, and the nights very short.
This phenomena is thanks to the nature of how light and shadow work. Picture that disk, flashlight, and paper again. When you move the flashlight closer to the paper and pendulum, the shadow cast gets larger. Move the flashlight away again, and the shadow shrinks. The size of the shadow dictate how long the nights are, because one place has to work its way all the way through that shadow in order to get to light again. Therefore, the summer nights are long, and the winters nights are short.

Solstices

At either peak of the year, when night is longest and when day is longest, there is a celebration of the solstice. The winter solstice is the longest day, and the summer solstice is the longest night. Midnight on the winter solstice also features the ring of light surrounding the moon called a corona2.

1 It is, of course, not a flat disc in reality, but a cross-section of a sphere. Or is it? No, it is. Some flat-decisphere-ers are out there, but it is curved. ...or is it?   2 A corona (in the context of a solar eclipse) is a ring of light that forms around the edge of the moon. This only occurs when the moon and the sun appear to be the same size in the sky. In this case, the moon is slightly larger in the sky, and no corona is visible. Except for one night of the year, when the planet's orbit takes it close enough to the sun for the two to look the same size, when a gorgeous fiery corona appears; the solstice.  

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