The directions are defined the same way as directions on the Earth or in the solar system using the right-hand rule to define north and east based on counter-clockwise rotation.

West can be defined in terms of spin direction, but western ( as in hemisphere) requires a meridian to define the boundary. I'd have assumed that we'd have put Earth on the galactic meridian, much like the Brits put London on the terrestrial one.

I expect it goes through Greenwich, as always!

You are correct, it is determined by spin. However, for some reason that has never been explained to me, we define galaxies to spin in the opposite direction from planets.

We don't define galaxies in general to spin in the opposite direction.

Just the Milky Way.

(The reason for this seems to be that Galactic "North" was defined long before we had the data to determine which way the Milky Way rotated -- or even that it rotated. By the time the rotation was definitively determined, it was too late to override convention. This may go back to William Herschel deciding that the "north pole" of the Galaxy should be in the same hemisphere of the sky that the Earth's north pole pointed toward. In retrospect, he had a 50% chance of being right...)

I never thought about this. Will most solar systems form roughly on the same plane as the galactic disk, and will they generally have orbits in the same or the opposite direction as the galactic rotation of their star?

It's basically random; the rotation of a solar system depends on the rotation of the gas clump that collapses to form the star and its system, and that depends on local details about the relative orientation of local gas clumps, the possible influence of winds from nearby massive stars and supernova shock waves, and general turbulent motions within molecular clouds.

It's not very random. The galaxy also formed from a clump of rotating gas, and this heavily influences the direction all of the sub-bodies will rotate and orbit. Systems influenced by other forces would be the exception to the norm.

No, it is pretty random, just as the orbits of binary stars are randomly oriented. The scales of star and solar-system formation are much, much smaller than the scale of the galaxy, so the memory of the latter has been scrambled by all the intermediate and local processes.

From this Cornell "Ask an Astronomer" page (http://curious.astro.cornell.edu/about-us/159-our-solar-syst...)

"The size of a solar system is so much smaller than the size of the Galaxy, that the Galaxy's structure has no impact on the orientation of a solar system. What determines their orientations is the direction of the angular momentum that the system had when it formed, and that's pretty much random."

Or take a look at these ALMA images of protoplanetary disks (solar systems in the making) around pre-main-sequence stars. All are at very similar distances, and most are at very similar positions relative to the Galactic plane, so they should all show very similar projected shapes and orientations if they followed the galaxy's orientation -- but they are all over the place.

https://www.eso.org/public/images/potw1904a/

Ah, I forgot that the galaxy rotates as well. That definitely makes things a bit simpler.

It's a quote from The Hitchhiker's Guide to the Galaxy. Only hit me at the very end of it... "digital watches are a pretty neat idea".

Okay, so once you have north, which way is east in a circle?

East on Earth is the direction in which we rotate. Should be the same for a galaxy.

That's because earth can be viewed as a plane. The galaxy can't, you need a median.

1. Milky Way is much more like a plane than Earth

2. it doesn't matter anyway any object which rotates can have direction named basing on that rotation

They use giant supercomputers to do simulations which results in these counter intuitive answers. The trick is to ask the right question.

It's more like spinwards and widdershins, really.

Spinwise/turnwise, and rimwards :)

You can try Polaris

They don't, AFAIK. You can only get away with it if you're writing exceptionally goofy science fiction.