Georg, that is not strictly correct, in fact in context it is so misleading that I must ask you to reconsider your reply.

Many people have a drastically simplistic impression of orbital mechanics, often in consequence of school physics or applied maths, in which most of the calculations assume point masses. This is a convenient approximation when the distances separating objects are large relative to their dimensions.

For example, if I have two hockey sticks orbiting each other at a distance of say, 1000 km, then it hardly matters whether one of them has been crushed into a compact ball or not. On the other hand, if they orbit each other at a distance of say 3 m, their behaviour will be altogether more complex and the point mass assumption no longer applies.

Again, consider two masses, both spherical, but one of them symmetrically hollow. Assume that they both are machined steel. (I do not suggest that this is a realistic condition in nature, but a little gentle science-fiction can simplify some problems in applied mathematics that otherwise might be unnecessarily refractory.) Well then, assume that both are in free fall in space, and sufficiently far from any other bodies for us to regard them as a two-body system. The solid ball is of negligible mass relative to the hollow ball, say a kilogram. The hollow ball is of planetary dimensions, say of Earth mass, and twice Earth diameter.

Now, given that both bodies are radially symmetrical and rigid, we can tell that if the smaller body is outside the larger body in an orbit that is closed and effectively stable, it will, to a close approximation, be in an elliptical orbit around the barycentre of the system. For most practical purposes we might take that to be the geometric centre of the large body of course, and I remind you that for most practical purposes also, we can take that as applying to most real life examples of orbital paths as well. Not many of us are responsible for determining the orbits of spacecraft to centimetric precision. All of this would remain true for any reasonable orbital radius, whether metres or light years from the surface of the large body.

However, inside the hollow the rules are entirely different, and wherever the barycentre might roam, the small ball would behave as if in a zero-resultant gravitational field.

Now, we do not, as I am sure you were ready to point out, exist in any so geometrically stable and generally exotic a system. However, we do live in a system in which our relationships to the total barycentre vary considerably and some of the bodies move within the orbits of other bodies. It does not follow that each body orbits the total barycentre. It might help you to visualise this by reflecting that if Jupiter happened to pass by Earth very closely, there is no way in which our orbit would then resemble any approximation to an ellipse about the barycentre of the solar system in general. For a slightly less hypothetical example, consider the orbits of Phobos and Deimos. Both of them are members of the solar system, and both their orbits closely approximate ellipses around the barycentre of Mars, which is not at all the same thing.

Conversely, analogously to our orbiting hockeysticks, if there is a Jupiter-sized planet orbiting our sun at a suitable inclination and several light years away, then it would to a good approximation, indeed orbit our barycentre, but mainly because our solar system would approximate to a point source.

In general, when dealing with trajectories in systems where our simplistic assumption of dealing with point sources of gravity cannot be sustained, we must be extremely careful of the calculations on which we base our predictions of their behaviour.

In case you still are not convinced, bear in mind that although our solar system is not isolated, yet in spite of their relatively trivial masses in comparison, the lesser bodies in our solar system, with certain perturbations undoubtedly, orbit either their nearest primaries, or the sun. They pay scant attention to the location of the barycentre of our galaxy, much less our local group, or even our observable universe.

I am certain that you are well aware of all these principles, but you did not seem to apply them sufficiently explicitly to avoid confusion in the minds of some readers who had not yet made a study of the subject.

Cheers,

Jon