In article , "Richard D.
Saam" writes:

the quantities are
determined, as is everything, by the constants of nature and by initial
conditions,

Since most of the mass of a planetary system is in the star, the limit
to its mass is the limit of the mass of a star.

I'm not sure what you mean. Above a certain mass, nuclear fusion will
set in, so anything more massive is a star, by definition. (There is
also the Hayashi limit related to convection, so the lower limit for
stable nuclear fusion might be a bit higher, around 0.08 solar masses.)
The upper limit for a star is a few hundred solar masses. (Probably
anything more massive can't form before what has already contracted has
ignited, keeping out additional material.) I'm not an expert here, but
the mass range in stars is 2--3 orders of magnitude. It is not directly
(and if indirectly, very indirectly) to any size of the universe.

Assuming your 2--3 orders of magnitude range
galactic size (presently ~10^20 - ~10^24cm)
and star planetary system size (presently ~10^13 - ~10^17 cm)
contained in a Hubble radius (presently ~10^28 cm)
What establishes the voids
on the order of 3 orders of magnitude between
and do these ratios maintain themselves with redshift
and within what theoretical framework?

Richard D Saam

[[Mod. note -- This wording presupposes that there are "voids" and that
they are "established". I know of no good reasons to reject the null
hypothesis that there's no particular connection between these size
scales.
-- jt]]

Indeed. Note that galaxies range over more orders of magnitude in mass.
Between solar-system scale and galactic scale there are things like
giant molecular clouds; between galactic scale and Hubble-length scale
there are groups of galaxies, clusters, superclusters. There is also
the structure of dark matter, about which less is known.

To a first approximation, the sizes of solar systems and galaxies don't
change with the expansion of the universe. The Hubble radius changes if
the Hubble constant changes. The Hubble constant has increased since
the big bang, but as the universe approaches exponential expansion
asymptotically, the Hubble radius will approach a constant value.

[[Mod. note -- In addition to the things the poster mentioned, globular
clusters and dwarf galaxies are some other important astro-things that
lie between solar-system and galactic size.
-- jt]]