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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 Jupiters. KOI-94 also hosts at least three 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. We report the properties of KOI-94b (M P = 10.5 ± 4.6 M ⊕, R P = 1.71 ± 0.16 R ⊕, P = 3.74 days), KOI-94c (M P = M ⊕, R P = 4.32 ± 0.41 R ⊕, P = 10.4 days), KOI-94d (M P = 106 ± 11 M ⊕, R P = 11.27 ± 1.06 R ⊕, P = 22.3 days), and KOI-94e (M P = M ⊕, R P = 6.56 ± 0.62 R ⊕, P = 54.3 days). The radial velocity analyses of KOI-94b and KOI-94e offer marginal (>2σ) 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 P < 150 M ⊕), we establish two fundamental planes for exoplanets that relate their mass, incident flux, and radius from a few Earth masses up to 13 Jupiter masses: (R P/R ⊕) = 1.78(M P/M ⊕)0.53(F/erg s–1 cm–2)–0.03 for M P < 150 M ⊕, and R P/R ⊕ = 2.45(M P/M ⊕)–0.039(F/erg s–1 cm–2)0.094 for M P > 150 M ⊕. These equations can be used to predict the radius or mass of a planet.
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Since the discovery of the first exoplanets, it has been known that other planetary systems can look quite unlike our own. Until fairly recently, we have been able to probe only the upper range of the planet size distribution, and, since last year, to detect planets that are the size of Earth or somewhat smaller. Hitherto, no planets have been found that are smaller than those we see in the Solar System. Here we report a planet significantly smaller than Mercury. This tiny planet is the innermost of three that orbit the Sun-like host star, which we have designated Kepler-37. Owing to its extremely small size, similar to that of the Moon, and highly irradiated surface, the planet, Kepler-37b, is probably rocky with no atmosphere or water, similar to Mercury. © 2013 Macmillan Publishers Limited. All rights reserved.