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For what it's worth, modern science teaches neither heliocentrism nor geocentrism. With the advent of relativity, it is realized that there are no preferred frames of reference and that calculations can be carried out in either system with equal accuracy. Again - there are no preferred frames of reference, so neither is stationary except by convention.
However, in the Earth-Sun system, the center of mass is definitely within the sun. Hence, when you use the center-of-mass frame, the system looks heliocentric.
However, in the Earth-Sun system, the center of mass is definitely within the sun. Hence, when you use the center-of-mass frame, the system looks heliocentric.