"Chosp" wrote:

I had asked:

Is the "heliocentric" idea this: we choose a coordinate system in
which angular momentum is minimized?

I think it is a little more prosaic than that.
I suspect that the "heliocentric" idea in astronomy
means that the sun more or less physically occupies
the gravitational center of the solar system [ ... ]
The fact that an earth centered coordinate system would not
minimize angular momentum was not the necessarily the
main consideration or driving force of the proponents.
It was considered more of a reflection of reality than
merely arguing over equally arbitrary coordinate
systems.

Thank you. In historical terms you are probably right, but I was more
curious about the concept than about the history. Given that
coordinate systems are more or less arbitrary, there might be good
reasons for preferring the one that minimized angular momentum (now,
for instance, rather than in the 16th century).

Not being a physicist, I don't even know that my first assumption was
correct. When we make the origin of a coordinate system coincide with
the barycentre of a physical system of orbits, DOES that, in fact,
minimize angular momentum?

I'm not sure what reflections of reality might mean to other people -
to me it seems that if you pick a model to reflect reality, there must
be a reason.