  We present new time-resolved photometric observations of the bright
trans-Neptunian object (20000) Varuna and use them to study the rotation
period, shape, and color. In observations from 2001 February and April, we find
a best-fit two-peaked lightcurve with period 6.3442 +-0.0002 hr. The
peak-to-peak photometric range in the R-band is 0.42 +-0.02 mag. We find no
rotational variation in colors over the 0.45 < lambda < 0.85 micron wavelength
range. From the short double-peaked period and large amplitude we suggest that
Varuna is an elongated, prolate body perhaps close in shape to one of the
Jacobi ellipsoids. If so, the ratio of the axes projected into the plane of the
sky is 1.5:1 and the density is near 1000 kg m^(-3). (20000) Varuna may be a
rotationally distorted rubble pile, with a weak internal constitution due to
fracturing by past impacts. The high specific angular momentum implied by our
observations and recent detections of binary Trans-Neptunian Objects both point
to an early, intense collisional epoch in which large Trans-Neptunian Objects
were about 100 times more abundant than now. In order to maintain a
cosmochemically plausible rock:ice mass ratio of about 0.5, Varuna must be
internally porous.
