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the attractive force of gravity is proportional to the mass of an object. a less massive object is always pulled around by a more massive one.
then you have to look at the hill sphere. that's the region around a body where that body is gravitationally dominant. ignoring that the earth is well, well, within the sun's hill sphere, the earth's hill sphere is about 4x the earth-moon distance. at that distance, the earth would be deep under the surface of the sun.
it'll look like the smaller is orbiting the larger, but that's all. the actual orbits will still be heliocentric.