Is the Sun prograde or retrograde with respect to the rotation of the Milky Way? I recently learned about the terms prograde and retrograde. I've seen these terms used to describe the rotations and orbits of moons with respect to their planet, and planets with respect to their star. But I haven't been able to find what the relationship is between the rotation and orbit of the Sun with respect to the rotation of the Milky Way.

So, basically what I'm trying to do here is ask two questions:


Is the orbit of the Sun around the center of the Milky Way prograde or retrograde with respect to the rotation of the Milky Way?
Is the axial rotation of the Sun prograde or retrograde with respect to the rotation of the Milky Way?


Regarding question #2, I know it might be considered a slightly weird question to ask, simply because the plane of the Solar System is significantly tilted relative to the plane of the Milky Way (by about 60°), and furthermore the Sun itself has its equatorial plane tilted by a few more degrees relative to the plane of the Solar System (about 7°). But if we mentally "flatten out" the Solar System such that the Sun's equatorial plane aligns with the plane of the Milky Way, then we can talk about whether its axial rotation is in the same direction as the rotation of the Milky Way, so I think this is a valid application of the concept.
Prograde. This is usually the case for stars in spiral galaxies outside the most central regions.

A galaxy can be either rotation-dominated or dispersion-dominated, depending on whether its kinematics is dominated by ordered or random motion. Spiral galaxies such as the Milky Way belong to the first class, while ellipticals belong to the second. Irregular galaxies can be somewhere in between, with random motions but with an overall rotation.

In spirals, stars and gas generally rotate in the same direction (although they can have more random motion in their bulges, i.e. in the central parts). The Sun follows the overall rotation of the Milky Way, except for roughly 20 km/s in the direction wrt. the overall rotation; this direction is known as the Solar apex.

However, following a major merger event, the product can be two kinematically decoupled components. This is described well in Corsini (2014). Such a merger is required to perturb the system sufficiently.

On smaller scales, however, the turbulence of the gas clouds giving birth to stars are more random. Hence the rotation of a star may very well be in another direction than the overall disk rotation. As you say, the plane of the Solar System is tilted by 63º wrt. the plane of the Milky Way, in the direction that the Sun is traveling. This can be seen e.g. in this infrared IRAS image, where the angle between the bright Milky Way disk and the blue stripes — which is emission from dust in the plane of the Solar System — crosses at roughly 60º:



credit: Caltech.

The rotation of the Sun is also prograde wrt. the Milky Way (or else we would say that the tilt was 180º – 63º = 117º).