  We define and analyze the photometric orbit (PhO) of an extrasolar planet
observed in reflected light. In our definition, the PhO is a Keplerian entity
with six parameters: semimajor axis, eccentricity, mean anomaly at some
particular time, argument of periastron, inclination angle, and effective
radius, which is the square root of the geometric albedo times the planetary
radius. Preliminarily, we assume a Lambertian phase function. We study in
detail the case of short-period giant planets (SPGPs) and observational
parameters relevant to the Kepler mission: 20 ppm photometry with normal
errors, 6.5 hour cadence, and three-year duration. We define a relevant
"planetary population of interest" in terms of probability distributions of the
PhO parameters. We perform Monte Carlo experiments to estimate the ability to
detect planets and to recover PhO parameters from light curves. We calibrate
the completeness of a periodogram search technique, and find structure caused
by degeneracy. We recover full orbital solutions from synthetic Kepler data
sets and estimate the median errors in recovered PhO parameters. We treat in
depth a case of a Jupiter body-double. For the stated assumptions, we find that
Kepler should obtain orbital solutions for many of the 100-760 SPGP that
Jenkins & Doyle (2003) estimate Kepler will discover. Because most or all of
these discoveries will be followed up by ground-based radial-velocity
observations, the estimates of inclination angle from the PhO may enable the
calculation of true companion masses: Kepler photometry may break the "m sin i"
degeneracy.
