Do astronomical objects influence Earth's climate? This is a fascinating question that never seems to get robustly answered, and often seems to be misused by global climate change denialists. The latest salvo - spiral arm crossings - is discussed over at Real Climate.
I wasn't aware the spiral arm pattern speeds were so ill-determined.
The image of a current model for the spiral arm structure of our own Milky Way galaxy, taken from an excellent web page from the Canadian Galactic Plane Survey (CGPS) - go there for more information.