I admit this question is derived from a science fiction scenario, but I’m wondering what that actual astronomical terminogy would be here.

Assume you’re standing on a moon orbiting a gas giant. The moon is both tidally locked and in geostationary orbit, so if you look straight up, you’re always staring into a same storm raging on the planet below.

Each day on this moon is divided into four phases, and here’s where my question lie. As a layman, I refer to these phases as:

1. Morning: You get some oblique direct sunlight as the sun rises from your horizon before passing behind the gas giant.

2. False Day: The moon falls into total eclipse. Pretty dark, I assume.

3. Sunset: More oblique direct sunlight as the sun emerges from the gas giant before setting below your lunar horizon.

4. False Night: The sun is now below your horizon (but I assume you’re getting some twilight reflected off the gas giant filling your sky.

So, do these day-night-phases have actual technical terms?

Has anyone ever invented a "good" way to sort astronomical data? I am building a database and currently my best idea is to sort by increasing Right Ascension like a freak. I am trying to keep it pretty purpose/research-agnostic so it can be used easily by undergraduate students who may want to use the data later. I have a lot of targets in deep fields but some don't fit neatly into a conveniently-named area of the sky. My main itch about this is that whatever scheme I pick, I may unintentionally separate duplicates and close companions, or interleave two deep fields with similar RA values. Perhaps the solution in the end will be to add an easily-accessible interactive visualizer tool? Who knows. Let me know if you've seen a clever method in the past that you've found useful! Or let me know if I should just bite the bullet and do something that works.