Does the earth and moon orbit a gravitational center that they share?
Yes.
Does that center revolve around the sun?
No, it revolves around its shared centre with the sun. Things get complicated fast in gravity with more than two objects involved.
How imperceptible is this, considering the shared point is likely inside the earth given the difference between its mass and lua’s?
It’s how we can detect exoplanets. Well, we can tell there must be these and these planets based on the star’s wobble dunno if we can do the same for moons of planets: It would certainly work in principle but our instruments might not be good enough.
Yes.
No, it revolves around its shared centre with the sun. Things get complicated fast in gravity with more than two objects involved.
It’s how we can detect exoplanets. Well, we can tell there must be these and these planets based on the star’s wobble dunno if we can do the same for moons of planets: It would certainly work in principle but our instruments might not be good enough.