  C/2002 CE$_{10}$ is an object in a retrograde elliptical orbit with Tisserand
parameter $-0.853$ indicating a likely origin in the Oort Cloud. It appears to
be a rather inactive comet since no coma and only a very weak tail was detected
during the past perihelion passage. We present multi-color optical photometry,
lightcurve and thermal mid-IR observations of the asteroidal comet.
\textcolor{blue}{ With the photometric analysis in $BVRI$, the surface color is
found to be redder than asteroids, corresponding to cometary nuclei and
TNOs/Centaurs. The time-resolved differential photometry supports a rotation
period of 8.19$\pm$0.05 h. The effective diameter and the geometric albedo are
17.9$\pm$0.9 km and 0.03$\pm$0.01, respectively, indicating a very dark
reflectance of the surface. The dark and redder surface color of C/2002
CE$_{10}$ may be attribute to devolatilized material by surface aging suffered
from the irradiation by cosmic rays or from impact by dust particles in the
Oort Cloud. Alternatively, C/2002 CE$_{10}$ was formed of very dark refractory
material originally like a rocky planetesimal. In both cases, this object lacks
ices (on the surface at least). The dynamical and known physical
characteristics of C/2002 CE$_{10}$ are best compatible with those of the
Damocloids population in the Solar System, that appear to be exhaust cometary
nucleus in Halley-type orbits. The study of physical properties of rocky Oort
cloud objects may give us a key for the formation of the Oort cloud and the
solar system.
