I started looking at how to determine what the seasons would be like, or how far the polar caps might extend, on Home (as before, axial tilt 31 degrees, semimajor axis around 1.05 AU or so, sun luminosity star).

On earth (and other spheres), the poles receive less energy from the sun than the equator when integrated over the course of a year due to the higher angles that the poles have with respect to the sun most of the time, which makes them cooler overall. The same is likely to be true for Home, but there are several more steps I need to take to characterize it appropriately.

In the meanwhile, take an object sitting on a field - the 800 DTon starship, for example, at the typical location of +55 degrees north. It's 20 days past the start of fall, and I'm guessing that temperatures overnight now fall below freezing and warm up during the day to around freezing. There might be some snowfall at night that, with enough solar energy, would melt away. What would that look like?

First, a plot of the local celestial hemisphere through the time I'm considering and motion of shadow across the ground:

Much of the ground (which is discretized to 2x2 meter squares) receives sunlight the entire time that the sun is above the horizon, but at different levels of power based on the angle of the sun from zenith. However, some squares are in shadow part of the time and receive less energy over the day. That looks like this:

https://i.imgur.com/QySS7Et.png (I don't plot the sphere representing the starship so it's easier to see the surface).

The darkest areas received the least energy and are least likely to have snow melt off during the day. Obviously, to be useful this sort of thing would have to take the geometry of a town or base that the players are moving through with terrain and do the energy plot of that, but this is just a start so far. Done over a world scale you should be able to estimate the growing seasons - when plants would have enough energy to grow once you have a rudimentary soil, atmosphere and ocean temperature model in place.

The more interesting topics are always related to how people or cultures behave based on their environment more than the character of the environment, and I'm really trying to answer questions like "when is the growing season" (at this point on the surface), "when will snow first appear and when will the local surface be entirely covered with snow" and "when will the snow melt" and "how hot will it be in summer" and so on. How does a culture build a calendar with no moon to provide that timestep? But while figuring all of that out little mini experiments like this pop up.