  The dust detector system onboard Galileo records dust impacts in circumjovian
space since the spacecraft has been injected into a bound orbit about Jupiter
in December 1995. This is the sixth in a series of papers dedicated to
presenting Galileo and Ulysses dust data. We present data from the Galileo dust
instrument for the period January to December 1996 when the spacecraft
completed four orbits about Jupiter (G1, G2, C3 and E4). Data were obtained as
high resolution realtime science data or recorded data during a time period of
100 days, or via memory read-outs during the remaining times. Because the data
transmission rate of the spacecraft is very low, the complete data set (i. e.
all parameters measured by the instrument during impact of a dust particle) for
only 2% (5353) of all particles detected could be transmitted to Earth; the
other particles were only counted. Together with the data for 2883 particles
detected during Galileo's interplanetary cruise and published earlier, complete
data of 8236 particles detected by the Galileo dust instrument from 1989 to
1996 are now available. The majority of particles detected are tiny grains
(about 10 nm in radius) originating from Jupiter's innermost Galilean moon Io.
These grains have been detected throughout the Jovian system and the highest
impact rates exceeded $\rm 100 min^{-1}$. A small number of grains has been
detected in the close vicinity of the Galilean moons Europa, Ganymede and
Callisto which belong to impact-generated dust clouds formed by (mostly
submicrometer sized) ejecta from the surfaces of the moons (Kr\"uger et al.,
Nature, 399, 558, 1999). Impacts of submicrometer to micrometer sized grains
have been detected thoughout the Jovian system and especially in the region
between the Galilean moons.
