Small planets, 1-4x the size of Earth, are extremely common around Sun-like stars, and surprisingly so, as they are missing in our solar system. Recent detections have yielded enough information about this class of exoplanets to begin characterizing
their occurrence rates, orbits, masses, densities, and internal structures. The Kepler mission finds the smallest planets to be most common, as 26% of Sun-like stars have small, 1-2 R_e planets with orbital periods under 100 days, and 11% have 1-2 R_e planets that receive 1-4x the incident stellar flux that warms our Earth. These Earth-size planets are sprinkled uniformly with orbital distance (logarithmically) out to 0.4 AU, and probably beyond. Mass measurements for 33 transiting planets of 1-4 R_e show that the smallest of them, R < 1.5 R_e, have the density expected for rocky planets. Their densities increase with increasing radius, likely caused by gravitational compression. Including solar system planets yields a relation: rho = 2.32 + 3.19 R/R_e [g/cc]. Larger planets, in the radius range 1.5-4.0 R_e, have densities that decline with increasing radius, revealing increasing amounts of low-density material in an envelope surrounding a rocky core, befitting the appellation mini-Neptunes. Planets of ~1.5 R_e have the highest densities, averaging near 10 g/cc. The gas giant planets occur preferentially around stars that are rich in heavy elements, while rocky planets occur around stars having a range of heavy element abundances. One explanation is that the fast formation of rocky cores in protoplanetary disks enriched in heavy elements permits the gravitational accumulation of gas before it vanishes, forming giant planets. But models of the formation of 1-4 R_e planets remain uncertain. Defining habitable zones remains difficult, without benefit of either detections of life elsewhere or an understanding of lifes biochemical origins.
We measure the mass of a modestly irradiated giant planet, KOI-94d. We wish to determine whether this planet, which is in a 22-day orbit and receives 2700 times as much incident flux as Jupiter, is as dense as Jupiter or rarefied like inflated hot Ju
piters. KOI-94 also hosts 3 smaller transiting planets, all of which were detected by the Kepler Mission. With 26 radial velocities of KOI-94 from the W. M. Keck Observatory and a simultaneous fit to the Kepler light curve, we measure the mass of the giant planet and determine that it is not inflated. Support for the planetary interpretation of the other three candidates comes from gravitational interactions through transit timing variations, the statistical robustness of multi-planet systems against false positives, and several lines of evidence that no other star resides within the photometric aperture. The radial velocity analyses of KOI-94b and KOI-94e offer marginal (>2sigma) mass detections, whereas the observations of KOI-94c offer only an upper limit to its mass. Using the KOI-94 system and other planets with published values for both mass and radius (138 exoplanets total, including 35 with M < 150 Earth masses), we establish two fundamental planes for exoplanets that relate their mass, incident flux, and radius from a few Earth masses up to ten Jupiter masses. These equations can be used to predict the radius or mass of a planet.
