  Non-Keplerian dynamics of planetary orbits manifest in the transit
light-curve as variations of different types. In addition to Transit Timing
Variations (TTV's), the shape of the transits contains additional information
on variations in the geometry of the orbit. This study presents an analytic
approach to light-curve fitting: dynamical variations in the orbital elements
are transformed to a light-curve using an analytic function with a restricted
set of fitting parameters. Our method requires no N-body integration, resulting
in a smaller number of degrees of freedom and a faster calculation. The
approach described here is for the case of secular perturbations. By assuming
that the orbital motion is dominated by nodal and apsidal precessions, analytic
expressions for the light-curve transit parameters are derived as a function of
the orbital variations. Detecting and characterizing such dynamical scenarios
provides information regarding the possible existence of non-transiting
companions, or the non-spherical mass distribution of the host star. The
variations may imply forces out of the orbital plane, and thus probe mutual
inclinations among components of the system. The derived models successfully
reproduce the vanishing transit signals of KOI 120.01, and suggest a possible
interesting scenario of a planet orbiting one member of a close-in binary
system undergoing unusually rapid nodal regression. The model parameters are
degenerate, so we provide relevant information for followup observations, which
are suggested in order to place further constraints on this unique Kepler
object.
