It might be stranger than you think.
That lack of symmetry comes from the sun’s movement through the Milky Way, as it experiences friction with the galactic radiation in front of it and clears out a space in its wake. “There’s a lot of plasma [charged particles] in the interstellar medium, and… the inner heliosphere, which is pretty round, is an obstacle in this stream of plasma which is flowing past it,” Reisenfeld told Live Science. “It has the same effect as water going around a rock in a stream,” with a rush of water crashing into the rock in front and a sheltered calm behind it.
I never really thought about our universe moving around the Milky Way. To read more and see some cool images, check out this Space.com story.