What do we call the invisible line about which an object rotates, or spins?

An axis is an invisible line around which an object rotates, or spins. The object can be a tiny particle, smaller than a single atom. Or it could be a star with the mass of a thousand suns.

In either case, an object's axis runs through its center of mass, or barycenter. An object's center of mass is a point where an outside force acting on the object acts as if the object were located at just that point—where the object appears "balanced." Earth's center of mass actually varies. Ocean tides shift the center of mass, although not enough to radically shift the planet's axis.

Each planet in our solar system rotates on its axis. So, each planet has a North and South Pole, the points where an axis meets the planet's surface.