False! They all exist in a complex system of gravitational pull where all bodies, not just these two, have differing degrees of influence on each other dictated by distance and mass!

The barycenter of the earth-sun orbit is within the surface of the sun, therefore the earth is understood to orbit the sun.

The JUPITER-Sun orbit barycenter, however, is outside the surface of the sun.

I liek spec

The center of solar system is not always between those two objects. Half the time they’re both on the same side of the center