# How do I approximate sunrise and sunset times in this simplified model of a solar system?

For a small game I'm working on I'm interested in simulating a basic celestial model for a planet, two moons and a sun. The main use is determining when specific eclipses happen and what type they are, but I figure it would be interesting to use it to determine sunrise and sunset as well.

I found the sunrise equation as well as this other question, but both go into far more detail than I need. I'm also having a lot of trouble wrapping my head around it. Every equation only seems to split into more equations, ad infinitum.

Since I'm using an extremely simplified model with nice, circular orbits I feel like there should be a relatively straightforward way to calculate (or approximate) the sunset/sunrise time based on the day of the year, but I'm having trouble seeing it.

The model I have so far is geocentric. Because I'm using circular orbs, I can easily determine the direction of the sun (in degrees) with (day_of_year / length_of_year) * 360°.

I can calculate the direction a point on the planet is facing similarly with (hour_of_day / length_of_day) * 360°, but that is only if the axial tilt is 0°.

For an axial tilt of 0°, I know that sundown/sunrise is when the sun is at 90° behind/ahead compared to the direction my location of interest is facing.

However, I'm stuck at how to figure in the axial tilt. I don't need an exact measurement, a rough approximation would be fine.