I took a physics class in high school, and considering how little I’ve since exercised the skills I learned in the class, I must say I’m pretty proud of myself for having come this far. But now I’ve hit a wall. I enjoy reading and writing science fiction, but to write good science fiction you need a base of science fact, so I’ve been trying to learn how to calculate ballpark travel times between planets for spacecraft using Newtonian physics. I’m having an issue, however, with a concept I either never learned, of have since forgotten completely: Calculating velocity when acceleration is accelerating. Changing velocity of a rock dropped off a roof? No problem. Should be roughly 9.81m/s^2. Changing velocity of a rock that falls from being motionless at a distance of +12,000,000 km? Big problem. That’s a long ways, and some lone firing synapse reminded me that the gravitational force is inversely proportional to the square of the distance. So I know how to calculate the gravitational pull for given distance, but no idea how to find the acceleration of acceleration or use it to calculate the velocity of an object at a certain distance when it fell from a much greater distance. If anybody could explain how one goes about calculating things like these, it would be much appreciated.