As already suggested before the 2009 IAU General assembly (Klioner 2008; Capitaine & Guinot 2009), it is proposed to re-define the ua as a fixed number of SI metres through a defining constant. Such a change of status for the ua would limit its role to that of a unit of length of "convenient"size for some applications. Consequently, GMSun which would cease to have a "fixed" value in astronomical units and will have to be determined experimentally, which is shown to be desirable for modern dynamics of the solar system. The defining number to be adopted for the conventional definition of the ua should be, for continuity reason, the value for the current best estimate of the ua in m as adopted by IAU 2009 Resolution B2 (i.e. ua = 1.495 978 707 00 x 1011 m) (Luzum et al. 2011). Such a change of status of the ua would be a great simplification for the users of the astronomical constants, would let possible variations of the mass of the Sun (and/or G) appear directly, and would avoid an unnecessary deviation from the SI.