Left panel: a sketch of the orbit orientation on the sky, consistent with the current nominal trajectory of the G2/DSO (i.e., arriving from the south-east direction and going into pericentre from the north, then leaving towards the south-east, showing the offset from the SMBH position in the origin). Two eccentric orbits of the S-stars are also indicated. Right panel: two cases of the possible evolution a gaseous/dusty stellar envelope, initially bound to the star: (i) with a radial wind blowing from the centre (v_w = 1000km s^-1; bluish colours); and (ii) without the outflowing wind (reddish colours). Here the same nominal trajectory as in the left panel is plotted, now with respect to the (x,y) orbital plane. See the text for details.