As Mick Jagger famously remarked, you can’t always get what you want. Kepler’s photometric transit observations provide excellent measurements of the planetary orbital periods, the transit epochs and the planet-to-star radius ratios, but they are stingy and tight-lipped when it comes to the planet’s masses, eccentricities, and longitudes of periastron.
Occasionally masses can be inferred from transit timing variations, especially if a system contains more than one transiting planet. Alternately, one can assume a planetary mass-radius relation (keeping in mind, of course, what happens when u assume). For example, M=R^2.06 in units of Earth masses and radii works quite well in our solar system for V-E-S-U-N. Or, dispensing with the trickery, one can pony up and measure radial velocities.
With photometric data alone, information about the orbital eccentricity distribution of the planet census can be deduced by statistically comparing transit durations to orbital periods. The idea is a full elaboration of the simple observation that if a central transit that is substantially shorter than expected, then it’s quite possible that the planet is occulting the parent star near the periastron of an eccentric orbit.
In one of the flurry of Kepler-related papers that accompanied the February data release, ...