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. Of course, this is true if and only if the planet is lucky enough to have a big moon like us.

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. We are used to our four seasons with mild springs and autumns, hot summers and cold winters. But these four season are just the consequence of our planet ecosystem, atmosphere, the peculiar axial tilt, if the orbit is particularly eccentric, distance from the sun in different period of the year can be a strong modifier too! In multi-star system, we can have more than 4 seasons, in planets with strange mechanics we can not have seasons at all (or better, the “season” depends on where are you on the planet).

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. For this reason, I want to try to save some of them here. In this way, I will have a good place where to look back at my notes and, moreover, I can be useful to other people trying to do some low-accuracy orbital calculations. I want to start from the beginning: orbital period and orbital trajectory.

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? How could be the calendar for Mars or Venus? Every time I try to sketch a Sci-Fi world, I want to try thinking to a calendar that make sense for that particular planet. Because the calculations are long and boring, I built for myself this little tool. However, before going to the tool, I want to provide a small introduction to the problem.