Here we are again! This is Part 3 of a small series on how to randomly generate a physically accurate calendar starting from planet’s orbital parameters. You can find the general motivation here, part one here and part two here. Said that, here we go with the next part: lunar phases. Why lunar phases Lunar phases are incredibly important in a calendar. So important, that many of the early humanity calendars are, in fact, lunar calendars or lunisolar calendars.

Welcome back to part 3 of the Procedural Calendar Generation series. In the first part we looked on how to compute celestial body position in a simple two-body system. The second part, instead is crash course on ellipse geometry. In this part, instead, we will tackle a fascinating consequence of the cosmic dance of our planet around its sun: seasons. Seasons are a strange beast because their behavior depends on a huge amount of factors.

As you probably know, I am working (slowly) on an astronomically accurate calendar generator. All the orbital calculations involved are quite challenging, and I am discovering a lot. It is a lot of fun (except for the all the times I need to do some trigonometric magic to make some formula work). Anyway, during this process, I am reshaping and producing many many formulas. I am sure that in six months I will forget all the motivations behind them.

In this article I want to show you a small proof of concept where we generate from scratch an alien calendar. The difference from other random calendar generators that just put random days and random month is that, in this tool, we can specify as input the orbital parameters of the planet and satellite and generate a calendar that makes sense. How could be the calendar for that planet orbiting a super-massive star?