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We present exact analytic formulae for the eclipse of a star described by quadratic or nonlinear limb darkening. In the limit that the planet radius is less than a tenth of the stellar radius, we show that the exact lightcurve can be well approximated by assuming the region of the star blocked by the planet has constant surface brightness. We apply these(More)
'Hot Jupiter' extrasolar planets are expected to be tidally locked because they are close (<0.05 astronomical units, where 1 au is the average Sun-Earth distance) to their parent stars, resulting in permanent daysides and nightsides. By observing systems where the planet and star periodically eclipse each other, several groups have been able to estimate the(More)
The transits of a planet on a Keplerian orbit occur at time intervals exactly equal to the period of the orbit. If a second planet is introduced the orbit is not Keplerian and the transits are no longer exactly periodic. We compute the magnitude of these variations in the timing of the transits, δt. We investigate analytically several limiting cases: (i)(More)
We present the detection of five planets--Kepler-62b, c, d, e, and f--of size 1.31, 0.54, 1.95, 1.61 and 1.41 Earth radii (R⊕), orbiting a K2V star at periods of 5.7, 12.4, 18.2, 122.4, and 267.3 days, respectively. The outermost planets, Kepler-62e and -62f, are super-Earth-size (1.25 R⊕ < planet radius ≤ 2.0 R⊕) planets in the habitable zone of their host(More)
Occultation and microlensing are different limits of the same phenomena of one body passing in front of another body. We derive a general exact analytic expression which describes both microlensing and occultation in the case of spherical bodies with a source of uniform brightness and a non-relativistic foreground body. We also compute numerically the case(More)
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(More)
We report the detection of Kepler-47, a system consisting of two planets orbiting around an eclipsing pair of stars. The inner and outer planets have radii 3.0 and 4.6 times that of Earth, respectively. The binary star consists of a Sun-like star and a companion roughly one-third its size, orbiting each other every 7.45 days. With an orbital period of 49.5(More)
The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. ABSTRACT We report on the long-term dynamical evolution of the two-planet Kepler-36 system, which we studied through numerical integrations of initial conditions that are consistent with observations of the system. The orbits are chaotic(More)
The Open University's repository of research publications and other research outputs SDSS-III: massive spectroscopic surveys of the distant universe, the Milky Way, and extra-solar planetary systems Journal Article Eisenstein et al. ABSTRACT Building on the legacy of the Sloan Digital Sky Survey (SDSS-I and II), SDSS-III is a program of four spectroscopic(More)
In recent years, the evidence for the existence of an ultra-compact concentration of dark mass associated with the radio source Sgr A* in the Galactic Center has become very strong. However, an unambiguous proof that this object is indeed a black hole is still lacking. A defining characteristic of a black hole is the event horizon. To a distant observer,(More)