# 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?

Yes, Jupiter can make a trajectory perpendicular to the ecliptic, which is exactly what it did for Ulysses, which observed the poles of the Sun:

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.

See this reference for the calculations.

• I just got a new idea for something to try in KSP, thanks! – James Thorpe Feb 11 '16 at 16:07

Here is a good way to visualize this Notice pioneer 11 did not meet its aimpoint plan so the Pioneer 11 solid third stage is most likely is in a Ulyssis solar polar orbit of some kind

• How does this graph work? I understand the colored dots are the target points. But how can you infer their post-encounter orbits? do you draw a line from the target point through Jupiter's center, to a point opposite the target point? Also, can you link to the source of this graph? – Hobbes Dec 30 '16 at 14:25