# What are the gravitational assist effects on the inclination of a probe's trajectory, from passing by Jupiter at different latitudes?

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?

The function is just vector addition. It depends on the $V_\infty$ with respect to Jupiter and the flyby distance, from which you get a change in direction in the plane of the trajectory relative to Jupiter, which is a $\Delta V$ vector. You change from the Jupiter-centered plane to to the Sun-centered frame to get the $\Delta V$ vector in that frame and add that to the velocity vector of the spacecraft in that frame before the swing-by. Then the new plane formed by that vector and the Sun is the plane of the new orbit.