  We show how astrometric and spectroscopic errors introduced by an unresolved
binary system can be combined to give estimates of the binary period and mass
ratio. This can be performed analytically if we assume we see one or more full
orbits over our observational baseline, or numerically for all other cases. We
apply this method to Gaia DR3 data, combining the most recent astrometric and
spectroscopic data. We compare inferred periods and mass ratios calculated
using our method with orbital parameters measured for non-single stars in Gaia
DR3 and find good agreement. Finally, we use this method to search the subset
of the Gaia DR3 RVS dataset with rv_method_used=1 for compact object
candidates. We select sources with significant astrometric and spectroscopic
errors ($RUWE_{ast}>1.25$ and $RUWE_{spec}>2$), with large inferred mass
ratios, and large inferred companion masses ($q>1$ and $M_c>3 M_\odot$) giving
a catalogue of 4,641 candidate hierarchical triples and Main Sequence+Compact
Object pairs. We apply more stringent cuts, and impose low levels of
photometric variability to remove likely triples ($RUWE_{phot}<2$) producing a
gold sample of 45 candidates.
