Baz, there are some elements of truth in what you say, but only some.
Antenna polarization is a complex phenomenon, and one that can at times be difficult to grasp. Polarization is determined by the E field rather than the M field, though both might be legitimate measures. The polarization of simple dipole antennas is parallel to the conductor, such that a horizontal wire will have a horizontal E field, a vertical wire, will have a vertical E field.
So far I haven't said much different from what you already know.
Now if an antenna is made of a number of parallel elements such as a Yagi, the polarization will continue to be parallel to the plane of the elements.
But suppose we made up a crossed Yagi, ie. one that had elements both horizontal and also vertical. Then in that case we would have either and most probably an elliptical polarization or possibly a circular polarization. In either case, the E field will be rotating, and just to make life interesting; the rotation will be either clockwise or anticlockwise. The things that affect the sense of rotation are exact phase difference of each antenna set (I think) and believe it or not, relative motion between the transmitter and receiver.
That is why satellite antennas are circularly polarised because a satellite will either be coming at you or running away from you.
Jupiter: coming at you or running away, it too will have a circular to elliptical polarization pattern. Exactly why this is so? don't ask me, I haven't got a clue, unless it is due to the rotation of Jove and any significant tilt in its electromagnetic axis to its rotation (though this is probably slight).
All for now,
Cheers,
Doug