  Accurate measurement of the cosmic microwave background (CMB) anisotropy
requires precise knowledge of the instrument beam. We explore how well the
Planck beams will be determined from observations of planets, developing
techniques that are also appropriate for other experiments. We simulate planet
observations with a Planck-like scanning strategy, telescope beams, noise, and
detector properties. Then we employ both parametric and non-parametric
techniques, reconstructing beams directly from the time-ordered data. With a
faithful parameterization of the beam shape, we can constrain certain detector
properties, such as the time constants of the detectors, to high precision.
Alternatively, we decompose the beam using an orthogonal basis. For both
techniques, we characterize the errors in the beam reconstruction with Monte
Carlo realizations. For a simplified scanning strategy, we study the impact on
estimation of the CMB power spectrum. Finally, we explore the consequences for
measuring cosmological parameters, focusing on the spectral index of primordial
scalar perturbations, n_s. The quality of the power spectrum measurement will
be significantly influenced by the optical modeling of the telescope. In our
most conservative case, using no information about the optics except the
measurement of planets, we find that a single transit of Jupiter across the
focal plane will measure the beam window functions to better than 0.3% for the
channels at 100-217 GHz that are the most sensitive to the CMB. Constraining
the beam with optical modeling can lead to much higher quality reconstruction.
Depending on the optical modeling, the beam errors may be a significant
contribution to the measurement systematics for n_s.
