  In the early 1990s, contemporary interstellar dust (ISD) penetrating deep
into the heliosphere was identified with the in-situ dust detector on board the
Ulysses spacecraft. Between 1992 and the end of 2007 Ulysses monitored the ISD
stream. The interstellar grains act as tracers of the physical conditions in
the local interstellar medium surrounding our solar system. Earlier analyses of
the Ulysses ISD data measured between 1992 and 1998 implied the existence of
'big' ISD grains [up to 10^-13kg]. The derived gas-to-dust-mass ratio was
smaller than the one derived from astronomical observations, implying a
concentration of ISD in the very local interstellar medium. We analyse the
entire data set from 16 yr of Ulysses ISD measurements in interplanetary space.
This paper concentrates on the overall mass distribution of ISD. An
accompanying paper investigates time-variable phenomena in the Ulysses ISD
data, and in a third paper we present the results from dynamical modelling of
the ISD flow applied to Ulysses. We use the latest values for the interstellar
hydrogen and helium densities, the interstellar helium flow speed of
v_ISM,inf=23.2km/s, and the ratio of radiation pressure to gravity, beta,
calculated for astronomical silicates. We find a gas-to-dust-mass ratio in the
local interstellar cloud of R_g/d=193^+85_-57, and a dust density of
2.1+/-0.6x10^-24kg/m^3. For a higher inflow speed of 26km/s, the
gas-to-dust-mass ratio is 20% higher, and, accordingly, the dust density is
lower by the same amount. The gas-to-dust mass ratio derived from our new
analysis is compatible with the value most recently determined from
astronomical observations. We confirm earlier results that the very local
interstellar medium contains 'big' (i.e. 1 um-sized) ISD grains. We find a dust
density in the local interstellar medium that is a factor of three lower than
values implied by earlier analyses.
