"It is not, in fact, obvious to the layperson that the Jupiter-Sun System would have a barycenter that doesn't lie inside the mass of the sun." a point doesn't

"It is not, in fact, obvious to the layperson that the Jupiter-Sun System would have a barycenter that doesn't lie inside the mass of the sun." a point doesn't lie in a mass, it lies in closed surface. ;p someone, somewhere, might have an 'Aha!' moment from that.