Abstract
The field of exoplanetary science has diversified rapidly over recent years as the field has progressed from exoplanet detection to exoplanet characterization. For those planets known to transit, the primary transit and secondary eclipse observations have a high yield of information regarding planetary structure and atmospheres. The current restriction of these information sources to short-period planets may be abated in part through refinement of orbital parameters. This allows precision targeting of transit windows and phase variations which constrain the dynamics of the orbit and the geometric albedo of the atmosphere. Here we describe the expected phase function variations at optical wavelengths for long-period planets, particularly those in the high-eccentricity regime and multiple systems in resonant and non-coplanar orbits. We apply this to the known exoplanets and discuss detection prospects and how observations of these signatures may be optimized by refining the orbital parameters.
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