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A body in Solar orbit beyond the Kuiper belt exhibits an annual parallax thatexceeds its apparent proper motion by up to many orders of magnitude. Apparentmotion of this body along the parallactic ellipse will deflect the angularposition of background stars due to astrometric microlensing ("inducedparallax"). By synoptically sampling the astrometric position of backgroundstars over the entire sky, constraints on the existence (and basic properties)of a massive nearby body may be inferred. With a simple simulation, we estimatethe signal-to-noise for detecting such a body -- as function of mass,heliocentric distance, and ecliptic latitude -- using the anticipatedsensitivity and temporal cadences from Gaia (launch 2011). A Jupiter-mass(M_Jup) object at 2000 AU is detectable by Gaia over the whole sky above5-sigma, with even stronger constraints if it lies near the ecliptic plane.Hypotheses for the mass (~3M_Jup), distance (~20,000 AU) and location of theproposed perturber ("Planet X") which gives rise to long-period comets may betestable.Comment: 17 pages, 6 figures. Figures revised, new figure added, minor text  revisions. Accepted to ApJ, to appear in the Dec 10, 2005 issue (v635

Astrometric Microlensing Constraints on a Massive Body in the Outer Solar System withGaia