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 Gaults 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.
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