  Fundamental properties of the planet Venus, such as its internal mass
distribution and variations in length of day, have remained unknown. We used
Earth-based observations of radar speckles tied to the rotation of Venus
obtained in 2006-2020 to measure its spin axis orientation, spin precession
rate, moment of inertia, and length-of-day variations. Venus is tilted by
2.6392 $\pm$ 0.0008 degrees ($1\sigma$) with respect to its orbital plane. The
spin axis precesses at a rate of 44.58 $\pm$ 3.3 arcseconds per year
($1\sigma$), which gives a normalized moment of inertia of 0.337 $\pm$ 0.024
and yields a rough estimate of the size of the core. The average sidereal day
on Venus in the 2006-2020 interval is 243.0226 $\pm$ 0.0013 Earth days
($1\sigma$). The spin period of the solid planet exhibits variations of 61 ppm
($\sim$20 minutes) with a possible diurnal or semidiurnal forcing. The
length-of-day variations imply that changes in atmospheric angular momentum of
at least $\sim$4% are transferred to the solid planet.
