A micro-gravity experiment to study the growth of dust particles has been proposed to be flown on one of the Columbus precursor flights. The micro-gravity environment will allow for low collision velocities (of order of mm s-1) of the dust grains and for a large Knudsen number of the embedding gas; conditions expected in the early solar nebula. The outcome of the experiment will yield estimates of the sticking efficiency and the critical velocity for agglomeration. The values of these two parameters will provide substantial improvements in the constraints for models of the formation of planetesimals. In particular the questions related to growth rate and mode of the aggregation process will be answered. The range of material type, collision velocities, properties of the environment in which growth takes place, and other factors permit a natural extension of this experiment to take advantage of the capabilities of the space station Columbus. Other astrophysical applications, such as processes in Saturnian rings, with somewhat different regimes could also be investigated.