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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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We report the detection of three transiting planets around a Sun-like star, which we designate Kepler-18. The transit signals were detected in photometric data from the Kepler satellite, and were confirmed to arise from planets using a combination of large transit-timing variations (TTVs), radial velocity variations, Warm-Spitzer observations, and statistical analysis of false-positive probabilities. The Kepler-18 star has a mass of 0.97 M ⊙, a radius of 1.1 R ⊙, an effective temperature of 5345K, and an iron abundance of [Fe/H] = +0.19. The planets have orbital periods of approximately 3.5, 7.6, and 14.9 days. The innermost planet "b" is a "super-Earth" with a mass of 6.9 ± 3.4 M ⊕, a radius of 2.00 ± 0.10 R ⊕, and a mean density of 4.9 ± 2.4gcm3. The two outer planets "c" and "d" are both low-density Neptune-mass planets. Kepler-18c has a mass of 17.3 ± 1.9 M ⊕, a radius of 5.49 ± 0.26 R ⊕, and a mean density of 0.59 0.07gcm 3, while Kepler-18d has a mass of 16.4 ± 1.4 M ⊕, a radius of 6.98 ± 0.33 R ⊕ and a mean density of 0.27 ± 0.03gcm3. Kepler-18c and Kepler-18d have orbital periods near a 2:1 mean-motion resonance, leading to large and readily detected TTVs. © 2011. The American Astronomical Society. All rights reserved.
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