  Measurements of flux density are described for five planets, Mars, Jupiter,
Saturn, Uranus, and Neptune, across the six Planck High Frequency Instrument
frequency bands (100-857 GHz) and these are then compared with models and
existing data. In our analysis, we have also included estimates of the
brightness of Jupiter and Saturn at the three frequencies of the Planck Low
Frequency Instrument (30, 44, and 70 GHz). The results provide constraints on
the intrinsic brightness and the brightness time-variability of these planets.
The majority of the planet flux density estimates are limited by systematic
errors, but still yield better than 1% measurements in many cases. Applying
data from Planck HFI, the Wilkinson Microwave Anisotropy Probe (WMAP), and the
Atacama Cosmology Telescope (ACT) to a model that incorporates contributions
from Saturn's rings to the planet's total flux density suggests a best fit
value for the spectral index of Saturn's ring system of $\beta _\mathrm{ring} =
2.30\pm0.03$ over the 30-1000 GHz frequency range. The average ratio between
the Planck-HFI measurements and the adopted model predictions for all five
planets (excluding Jupiter observations for 353 GHz) is 0.997, 0.997, 1.018,
and 1.032 for 100, 143, 217, and 353 GHz, respectively. Model predictions for
planet thermodynamic temperatures are therefore consistent with the absolute
calibration of Planck-HFI detectors at about the three-percent-level. We
compare our measurements with published results from recent cosmic microwave
background experiments. In particular, we observe that the flux densities
measured by Planck HFI and WMAP agree to within 2%. These results allow
experiments operating in the mm-wavelength range to cross-calibrate against
Planck and improve models of radiative transport used in planetary science.
