does the orientation of orbital plane of our solar system rotate with the galaxy

As I understand it, our solar system travels through the milky way with the orbital plane tilted about 60 degrees so that we are sort of traveling in the direction of earth's north. My question is if our orbital plane rotates with our galactic orbit so that it maintains its orientation in relation to the center of the galaxy as I've show in this first picture.

Or is the orientation unaffected by the galactic orbit as I've shown in this second picture.

• +1 Great question! Great graphics too!
– uhoh
Jan 30 '19 at 14:41
• I think it might be helpful to look at a smaller scale example. Does the orbital plane of the inner moons of Uranus process? And if it does, does it make one revolution in one Uranian year? I think answering this question could shed some light on the OP's question. Jan 20 at 0:23