We observe the sun and the moon traversing the sky. We know that the moon is objectively orbiting the earth but the sun is not. Where then is the sun that is observed traversing the sky in daily and annual cycles? It is not in 3D length. It is in 3D duration.
Binary stars orbit their common barycenter. If the sun and earth were the only celestial bodies, it might not be clear as to which was orbiting which. But since there are other planets orbiting the sun, the only objective view is that all the planets are orbiting the sun (more precisely, the barycenter of the solar system, which is in or near the sun).
Compare sun-centered (heliocentric) and earth-centered (geocentric) frames of reference (click to enlarge):