  Asteroid (6478) Gault was discovered to exhibit a comet-like tail in
observations from December 2018, becoming a new member of the so-called active
asteroid population in the main asteroid belt. The aims are to investigate the
grain properties of the dust ejected from asteroid (6478) Gault and to give
insight into the activity mechanism(s). We use a Monte Carlo dust tail
brightness code to retrieve the dates of dust ejection, the physical properties
of the grains, and the total dust mass losses during each event. The code takes
into account the brightness contribution of the asteroid itself. The model is
applied to a large data set of images spanning the period from January 11, 2019
to March 13, 2019. In addition, both short- and long-term photometric
measurements of the asteroid have been carried out. It is shown that, to date,
asteroid (6478) Gault has experienced two episodes of impulsive dust ejection,
that took place around 2018 November 5 and 2019 January 2, releasing at least
1.4$\times$10$^7$ kg and 1.6 $\times$10$^6$ kg of dust, respectively, at escape
speeds. The size distribution, consisting of particles in the 1 $\mu$m to 1 cm
radius range, follows a broken power-law with bending points near 15 $\mu$m and
870 $\mu$m. On the other hand, the photometric series indicate a nearly
constant magnitude over several 5--7.3 h periods, a possible effect of the
masking of a rotational lightcurve by the dust. The dust particles forming
Gault's tails were released from the asteroid at escape speeds, but the
specific ejection mechanism is unclear until photometry of the dust-free
asteroid are conducted, in order to assess whether this was related to
rotational disruption or to other possible causes.
