  The astrometric signature imposed by a planet on its primary increases
substantially towards longer periods (proportinal to P^2/3), so that
long-period planets can be more easily detected, in principle. For example, a
one Solar-mass (M_Sun) star would be pulled by roughly 1 mas by a one
Jupiter-mass (M_J) planet with a period of one-hundred years at a distance of
20 pc. Such position accuracies can now be obtained with both ground-based and
space-based telescopes. The difficulty was that it often takes many decades
before a detectable position shift will occur. However, by the time the next
generation of astrometric missions such as SIM will be taking data, several
decades will have past since the first astrometric mission, HIPPARCOS. Here we
propose to use a new astrometric method that employs a future, highly accurate
SIM Quick-Look survey and HIPPARCOS data taken twenty years prior. Using
position errors for SIM of 4 muas, this method enables the detection and
characterization of Solar-system analogs (SOSAs) with periods up to 240 (500)
years for 1 (10) M_J companions. Because many tens of thousands nearby stars
can be surveyed this way for a modest expenditure of SIM time and SOSAs may be
quite abundant, we expect to find many hundreds of extra-solar planets with
long-period orbits. Such a data set would nicely complement the short-period
systems found by the radial-velocity method. Brown dwarfs and low-mass stellar
companions can be found and characterized if their periods are shorter than
about 500 years. This data set will provide invaluable constraints on models of
planet formation, as well as a database for systems where the location of the
giant planets allow for the formation of low-mass planets in the habitable
zone. [Abridged]
