Not the Sun, but Venus lies in the centre of mass of the Solar System!
Since the Sun was born in a binary system (with Andrea-star), the centre of mass of the system had to be outside the primordial Sun from the beginning. There has been formed one of the possible four primordial planets of the primordial Sun, which we still see today in the same place as Venus. The Earth must therefore be orbiting both the Sun and Venus at the same time. That is why it is not true what we were told in school (and still are) that the orbit of the Earth in the solar system would be an ellipse. Instead, it is a beautiful rosette on which the Earth comes very close to Venus five times in (almost) eight years, and also has to move far away from it five times to let the Sun pass between it and Venus. The Sun also orbits Venus, and not vice versa.
Let us not be taken for fools any longer. An example of a list of the Earth's true positions in its rosette orbit is shown below. Incidentally, the kink points of the orbit, where the Earth is decelerated and accelerated, correlate naturally, and quite unambiguously, with the increasing frequency of earthquakes of the Earth's crust.