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Actually, in order for one object to be “circling” another, you have to assume that one is in a fixed position. Since modern science tells us that both the earth and the sun are in motion, its just as logical to say the sun is revolving around the earth as vice versa. Just sayin...

I am sorry, have to disagree with that. Even though they are both in motion the earth is in an orbit around the sun, the sun is not in orbit around the earth, if it were our seasons would be totally fubar. So, while the sum may move from x to y in a given time period the earth moves the same distance in the same direction and thus the effects are the same as if the sun and the earth were stationary.

This is not a guess or an opinion but fact.

Two bodies locked in orbit each move about "a common center of gravity" for the pair.

Since the Sun is sooooo much more massive than the Earth, the Sun-Earth common center of gravity lies INSIDE the sphere of the Sun. From a PRACTICAL standpoint, since the Earth's motion about the center of gravity is about a ZILLION times more than the Sun's, it's OK to say that the Earth is circling the Sun.

HOWEVER you CANNOT be so sloppy with this as the two bodies in question start to have similar masses. For example, the Earth-Moon center of gravity is STILL inside the sphere of the Earth, but only just so (about 3/4 from the center to the surface) The Sun-Jupiter center of mass lies OUTSIDE the sphere of the Sun (by about 28 thousand miles or so). So, it is ABSOLUTELY accurate to say that you can think of the Sun as going around and around a circular path due to Jupiter. For binary star systems, the effect is even MORE pronouced, as the center of gravity approaches the center of the physical distance separating the stars.

(Yes, I know I said "circle" when "ellipse" would have been more precise, but we have verbs like "circling" but we don't have verbs like ellipsessing...)