If the sun had a uniform surface (i.e., if there were no sunspots to look at), is there a practical way to measure its rotation? In other words, if some external force flipped the sun's spin suddenly, could anyone on the planets notice?
My intuition is that general relativistic effects would cause the planetary orbits to change slightly, but I'm hoping someone could quantify that and see if it's detectable. My guess is that this flip would cast some slight "effective drag force" slowing down planetary orbits.
EDIT: To avoid surface effects from the sun, let me simply assume that the "shell" of the sun is not spinning, but the underlying matter has all the spin.