Again, idk where my sound went. Shadow play is being stupid...
Anyways, this is a cute little artillery computer that I threw together in a couple of days, then forgot about. It uses basic kinematics to compute a firing solution on a target given the target location, your location, gravitational strength, and the muzzle velocity of your weapon.
There are some known limitations in the SE environment that make this not perfect:
Planet curvature throws off the estimate. IRL that isn't much of an issue, in SE, since planets are so small, it is noticeable
Gravity magnitude changes: The gravity fall off in spengies is exaggerated with the smaller planets
Gravity direction changes: Related to the first limitation, the curvature of the planet means that the gravity vector will shift directions and impact the trajectory of round in a way that basic kinematics will not capture
A more robust SE implementation would involve simulating the projectile trajectory and numerically solving, but that is not closed form nor is the solution time bounded. So I'd at least use this closed form solution, even with its flaws, as my initial guess and then numerically solve.