  The subtle influence of gravitational waves on the apparent positioning of
celestial bodies offers novel observational windows. We calculate the expected
astrometric signal induced by an isotropic Stochastic Gravitational Wave
Background (SGWB) in the short distance limit. Our focus is on the resultant
proper motion of Solar System objects, a signal on the same time scales
addressed by Pulsar Timing Arrays (PTA). We derive the corresponding
astrometric deflection patterns, finding that they manifest as distinctive
dipole and quadrupole correlations, or in some cases, may not be present. Our
analysis encompasses both Einsteinian and non-Einsteinian polarisations. We
estimate the upper limits for the amplitude of a scale-invariant SGWB that
could be obtained by tracking the proper motions of large numbers of solar
system objects such as asteroids. With the Gaia satellite and the Vera C. Rubin
Observatory poised to track an extensive sample of asteroids-ranging from
$O(10^5)$ to $O(10^6)$, we highlight the significant future potential for
similar surveys to contribute to our understanding of the SGWB.
