A flyby probe at Jupiter gets its inclination, relative to the ecliptic, changed if it passes above or below Jupiter's equator. How sensitive is a trajectory to this effect?
I imagine that there could exist a function which approximately describes the change in a flyby probe's trajectory given the perijove latitude, the altitude and whether on the leading or trailing side of Jupiter's orbit around the Sun. (I don't request exact calculations, just some hand which waves a ball in the park, or however the sayings go). Would a polar passage at Jupiter throw a probe into a trajectory perpendicular to the ecliptic?