  We use a cross-calibration of Hipparcos and Gaia DR2 astrometry for $\beta$
Pic to measure the mass of the giant planet $\beta$ Pic b $(13\pm3$ $M_{\rm
Jup})$ in a comprehensive joint orbit analysis that includes published relative
astrometry and radial velocities. Our mass uncertainty is somewhat higher than
previous work because our astrometry from the Hipparcos-Gaia Catalog of
Accelerations accounts for the error inflation and systematic terms that are
required to bring the two data sets onto a common astrometric reference frame,
and because we fit freely for the host-star mass $(1.84\pm0.05$ $M_{\odot})$.
This first model-independent mass for a directly imaged planet is inconsistent
with cold-start models given the age of the $\beta$ Pic moving group $(22\pm6$
Myr) but consistent with hot- and warm-start models, concordant with past work.
We find a higher eccentricity $(0.24\pm0.06)$ for $\beta$ Pic b compared to
previous orbital fits. If confirmed by future observations, this eccentricity
may help explain inner edge, scale height, and brightness asymmetry of $\beta$
Pic's disk. It could also potentially signal that $\beta$ Pic b has migrated
inward to its current location, acquiring its eccentricity from interaction
with the 3:1 outer Lindblad resonance in the disk.
