  This paper is the first in a series which studies interactions between M31
and its satellites, including the origin of the giant southern stream. We
construct accurate yet simple analytic models for the potential of the M31
galaxy to provide an easy basis for calculation of orbits in M31's halo. We use
an NFW dark halo, an exponential disk, a Hernquist bulge, and a central black
hole point mass to describe the galaxy potential. We constrain the parameters
of these functions by comparing to existing surface brightness, velocity
dispersion, and rotation curve measurements of M31. Our description provides a
good fit to the observations, and agrees well with more sophisticated modeling
of M31. While in many respects the parameter set is well constrained, there is
substantial uncertainty in the outer halo potential and a near-degeneracy
between the disk and halo components, producing a large, nearly two-dimensional
allowed region in parameter space. We limit the allowed region using
theoretical expectations for the halo concentration, baryonic content, and
stellar $M/L$ ratio, finding a smaller region where the parameters are
physically plausible. Our proposed mass model for M31 has $M_{bulge} = 3.2
\times 10^{10} \Msun$, $M_{disk} = 7.2 \times 10^{10} \Msun$, and $M_{200} =
7.1\times 10^{11} \Msun$, with uncorrected (for internal and foreground
extinction) mass-to-light ratios of $M/L_R = 3.9$ and 3.3 for the bulge and
disk, respectively. We present some illustrative test particle orbits for the
progenitor of the stellar stream in our galaxy potential, highlighting the
effects of the remaining uncertainty in the disk and halo masses.
