I'm writing a spaceship that just performed an Oberth maneuver around the sun, 10 million km out, and is accelerating toward a gravity sling with Jupiter. It had a high--not certain how high yet--initial velocity, and 1.5 G of thrust at perihelion, but then lost its engines for about three days. It has escape velocity (where do I find that for various solar orbital distances?), but not having thrust when you need it to climb out of a gravity well has to be a problem.
When my ship's crew gets its engines back online, their thrust is limited: I haven't decided how much yet, but well under one g, possibly 0.1 g; and for a few days, at least, they can only thrust 1/2 the time.
I can do simple time-acceleration-distance calculations, or use online relativistic spaceship calculators and get ~ the same answers for a simple, continuous acceleration. But nothing I have found in weeks of surfing tells me how to figure-in climbing out of a deep gravity well, or how to handle intermittent thrust, or what a realistic curved distance for a fast transit orbit Sol to Jupiter might be.
Are there any orbital mechanics in the crowd?