  Following an old idea of Fritz Zwicky, we make an attempt to establish a
universal mass function for astronomical objects on all scales. The object
classes considered are: solar system planets and small bodies, exoplanets,
brown dwarfs, stars and stellar remnants, open and globular clusters, molecular
clouds, galaxies, groups and clusters of galaxies. For comparison we also
include CDM halos taken from numerical simulations. We show that the mass
functions of individual object classes, when properly normalized, can indeed be
concatenated to build a surprisingly continuous mass function of the universe,
from approximately M = 10^(-20)Msun (sub-kilometer size asteroids) up to M =
10^(16)Msun (rich clusters of galaxies), covering 36 orders of magnitude in
mass. Most individual mass functions roughly follow a power law of the form
phi(M) propto M^(-2). A notable exception are planets and small bodies which
seem to obey a flatter distribution. CDM halos from high-resolution numerical
simulations show a very similar relation, again of universal slope -2, from
clusters of galaxies all the way down to the planetary mass scale. On the scale
of stars and star clusters this is a remarkable coincidence, as the formation
processes involved are thought to be totally different (bottom-up gravitational
clustering of DM halos versus top-down gravoturbulent fragmentation of gas
clouds).
