  The recent close approach of the NEA (3200) Phaethon offered a rare
opportunity to obtain high-quality observational data. We used the newly
obtained optical light curves to improve the spin and shape model of Phaethon
and to determine its surface physical properties derived by thermophysical
modeling. We also used the available astrometric observations of Phaethon,
including those obtained by the Arecibo radar and the Gaia spacecraft, to
constrain the secular drift of the orbital semimajor axis. This constraint
allowed us to estimate the bulk density by assuming that the drift is dominated
by the Yarkovsky effect. We used the convex inversion model to derive the 3D
shape model of Phaethon, and a detailed numerical approach for an accurate
analysis of the Yarkovsky effect. We obtained a unique solution for Phaethon's
pole orientation at $(318,-47)^{\circ}$ ecliptic longitude and latitude
(uncertainty of $5^{\circ}$), and confirm the previously reported
thermophysical properties ($D=5.1\pm0.2$ km, $\Gamma=600\pm200$ SI). Phaethon
has a top-like shape with possible north-south asymmetry. The characteristic
size of the regolith grains is 1-2 cm. The orbit analysis reveals a secular
drift of the semimajor axis of $-(6.9\pm1.9)\times 10^{-4}$ au Myr$^{-1}$. With
the derived volume-equivalent size of 5.1~km, the bulk density $\rho$ is
$1.67\pm0.47$ g cm$^{-3}$. If the size is slightly larger $\sim5.7$ km, as
suggested by radar data, $\rho$ would decrease to $1.48\pm0.42$ g cm$^{-3}$. We
further investigated the suggestion that Phaethon may be in a cluster with
asteroids (155140) 2005 UD and (225416) 1999 YC that was formed by rotational
fission of a critically spinning parent body. Phaethon's $\rho$ is consistent
with typical values for large ($>100$ km) C-complex asteroids and supports its
association with asteroid (2) Pallas. These findings render a cometary origin
unlikely for Phaethon.
