  We determine the fraction of G-dwarf stars that could host stable planetary
systems based on the observed properties of binaries in the Galactic field, and
in various postulated primordial binary populations, which assume that the
primordial binary fraction is higher than that in the field. We first consider
the frequency of Solar System analogues - planetary systems that form either
around a single G-dwarf star, or a binary containing a G-dwarf where the binary
separation exceeds 100-300au. If the primordial binary fraction and period
distribution is similar to that in the field, then up to 63 per cent of G-dwarf
systems could potentially host a Solar System analogue. However, if the
primordial binary fraction is higher, the fraction of G-dwarf systems that
could host a planetary system like our own is lowered to 38 per cent.
  We extend our analysis to consider the fraction of G-dwarf systems (both
single and binary) that can host either circumprimary planets (orbiting the
primary star of the binary) or circumbinary planets (orbiting both stars in the
binary) for fiducial planetary separations between 1 - 100au. Depending on the
assumed binary population, in the circumprimary case between 65 and 95 per cent
of systems can host a planet at 1au, decreasing to between 20 and 65 per cent
of systems that can host a planet at 100au. In the circumbinary case, between 5
and 59 per cent of systems can host a planet at 1au, increasing to between 34
and 75 per cent of systems that can host a planet at 100au.
  Our results suggest that the assumed binary fraction is the key parameter in
determining the fraction of potentially stable planetary systems in G-dwarf
systems and that using the present-day value may lead to significant
overestimates if the binary fraction was initially higher.
