Previously, I outlined method for deriving planetary parameters based on your world map. I will now continue with this.
I. Surface gravity: Though we have already covered escape velocity, surface gravity is different. I have not found a calculator to do this, but it is not difficult. The formula is g = G * M / r2. G here is the gravitational constant. Multiply your planet’s mass by 6.67 * 10-11. Note the negative integer. Take the resulting value and divide it by your planet’s radius (in meters) squared. The result is in meters/second2. You can find calculators on the internet that will convert this to feet/second2 if you wish.
II. Axial tilt. The Earth is tilted 23.25°. This tilt changes over the course of thousands of years, and the Earth is currently at about the midpoint of its range. This, like rotation, is determined at planet formation and influenced by bombardment of comets and asteroids and other bodies. You can set it at any value that you wish. Greater tilt means more severe seasons, and less tilt more mild seasons. Reddit and Stack Exchange are full of discussion of radical axial tilt. What seems different is actually commonplace. Planetary mean temperature is a function of the distance to the star and the axial tilt, but there is really no need to go into this unless you are really interested. And bored. Axial tilt does have an impact on climate and weather, which will be discussed.
III. Atmospheric Circulation. This is how all of this got started. I asked a question: Given Earth-like conditions and the geography that I have decided exists, will the weather be what I want it to be? And what can I do to make it what I want?
The answers and what I learned to get them will have a major impact on your planet’s climate. Around the equator and stretching 300 to 600 miles in width is the Inter Tropical Convergence Zone (ITCZ). The ITCZ is where the sun is overhead during the equinoxes (roughly the equator), and it heats the ocean resulting in evaporation. Warm air rises and flows toward the poles, creating the Hadley cells. This creates low pressure and surface air flows in to replace it. The air descends at about 30°. This air is dry, having dropped most of it’s moisture to create the rain in the tropics. Most of the world’s deserts occur around 30° latitude. Coastal areas, particularly east coasts, typically avoid being deserts due to ocean currents.
On Earth, there are three cells per hemisphere, but rather than flow straight north and south, the Coriolis Effect causes the air flow of the Hadley Cells to drift eastward. The Temperate cell flows toward the Hadley Cell. The Hadley Cell transports warm air towards the poles and the Polar Cell and Temperate cell facilitate the return trip. If you know where the boundaries of these cells are, you have an approximate location of the jet streams (Jet Stream, Temperate Jet, Polar Jet) which are strong determiners of weather. The references below include more detailed descriptions of this.
Here’s where it gets complicated. The whole damn thing moves. The Tropic of Cancer is the latitude where the sun appears overhead on the summer solstice, and the Tropic of Capricorn is where it appears overhead on the winter solstice. The ITCZ follows the sun and shifts the atmospheric cells. The size of the cells can also fluctuate, but that is beyond the scope here. For our purposes, it is enough to know that depending on where you are on your planet and when, winds can shift depending on season. If your axial tilt is only ten degrees, that means that during the winter, the sun will barely rise above the horizon.
All of this is absurdly simplified, but giving some consideration to this will help you establish wind direction and basic weather patterns. See the references for more, but be prepared to do your own research. I found the cengage.com link very clear, though it does involve some reading (don’t worry there are clear illustrations, too).
IV. Orbital Resonance: Orbital resonance refers to the regular gravitational influence that planetary bodies exert upon each each other, typically involving low number ratios. In other words, the influence of other planets helps keep your planet in its orbit. This is pretty complicated stuff, but Wikipedia has a nice animation demonstrating the idea. I have not chosen to explore this much, even in addressing the moons of Kemen. A handwave seems appropriate here. I have ruled that there are two inner and at least two outer planets in the Kemen system to keep everything on track. If you wish to include other planets in your campaign, orbital resonance may be interesting to you.
Underground fireballs are dangerous,