I've been working on my story planet and have come up with an unlikely but possible scenario to help explain some of my stories origins as well as myths and folklore. Over the last day or so, I've been playing around with a small moon in a geostationary orbit around the planet. Now I just need to clarify how the phases of the moon would appear to my surface-dwellers.
A moon in a geostationary orbit is possible as answered here on astronomy SE. Unlikely but possible. For any particular location the moon would appear fixed and always in the same place in the sky. There would be no rising or setting of such a moon, it's just always there. A constant Big Brother looming over you. Some locations on the planet wouldn't even know of its existence.
Typically a moon takes at least a few days to orbit a planet. The way that the light from a star reflects off the moon surface gives observers the phases of the moon. Here is a helpful image from Wikipedia which shows the lunar phases in relation to their position around Earth over a one month lunar cycle.
If we now interpret this image as a one day lunar cycle, with the moon always in the same location above the planet. Ignoring how long such an orbit would remain stable, am I correct in figuring that from an surface observer's point of view the moon would appear to wax and wane fully in one day?
OR would it be always in the same phase for a particular location?. eg observer in Location A would always see a crescent moon and Location B always a full moon?
Note: for the purposes of this scenario, it's a very small moon and as such won't have huge tidal forces on the planet. It also won't block out large portions of the sky during lunar eclipses or reflect too much light in the evenings. All of which, while very interesting, are not part of this question.
I also don't mind that it probably would be located within the Roche Limit for its mass and density, as that is all part of the story!
I just need help to figure out the phases. sadly, no werewolves are involved...