# Mass measurement of a single unseen star and planetary detection efficiency for OGLE 2007-BLG-050

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Stephane Brillant, Jul 03, 2015 Available from:-
##### Article: Planetary Orbital Equations in Externally-Perturbed Systems: Position and Velocity-Dependent Forces

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**ABSTRACT:**The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the equations of motion of the unaveraged perturbed two-body problem in terms of planetary orbital elements by using a generalized form of Gauss' equations. We consider a varied set of position and velocity-dependent perturbations, and also derive relevant specific cases of the equations: when they are averaged over fast variables (the "adiabatic" approximation), and in the prograde and retrograde planar cases. In each instance, we delineate the properties of the equations. As brief demonstrations of potential applications, we consider the effect of Galactic tides. We measure the effect on the widest-known exoplanet orbit, Sedna-like objects, and distant scattered disk objects, particularly with regard to where the adiabatic approximation breaks down. The Mathematica code which can help derive the equations is freely available upon request.Celestial Mechanics and Dynamical Astronomy 10/2012; 115(2). DOI:10.1007/s10569-012-9455-6 · 2.08 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Gravitational microlensing is not only a successful tool for discovering distant exoplanets, but it also enables characterization of the lens and source stars involved in the lensing event. In high magnification events, the lens caustic may cross over the source disk, which allows a determination of the angular size of the source and additionally a measurement of its limb darkening. When such extended-source effects appear close to maximum magnification, the resulting light curve differs from the characteristic Paczynski point-source curve. The exact shape of the light curve close to the peak depends on the limb darkening of the source. Dense photometric coverage permits measurement of the respective limb-darkening coefficients. In the case of microlensing event OGLE 2008-BLG-290, the K giant source star reached a peak magnification of about 100. Thirteen different telescopes have covered this event in eight different photometric bands. Subsequent light-curve analysis yielded measurements of linear limb-darkening coefficients of the source in six photometric bands. The best-measured coefficients lead to an estimate of the source effective temperature of about 4700 +100-200 K. However, the photometric estimate from colour-magnitude diagrams favours a cooler temperature of 4200 +-100 K. As the limb-darkening measurements, at least in the CTIO/SMARTS2 V and I bands, are among the most accurate obtained, the above disagreement needs to be understood. A solution is proposed, which may apply to previous events where such a discrepancy also appeared.Astronomy and Astrophysics 05/2010; 518. DOI:10.1051/0004-6361/201014053 · 4.48 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**At present, microlensing light curves from different telescopes and filters are photometrically aligned by fitting them to a common model. We present a second method based on photometry of common field stars. If two spectral responses are similar (or the color of the source is known) then this technique can resolve important ambiguities that frequently arise when predicting the future course of the event, and that occasionally persist even when the event is over. Or if the spectral responses are different, it can be used to derive the color of the source when that is unknown. We present the essential elements of this technique and apply it to the case of MOA-2007-BLG-192, an important planetary event for which the system may be a terrestrial planet orbiting a brown dwarf or very low mass star. The refined estimate of the source color that we derive here, V-I=2.36 +- 0.03, will aid in making the estimate of the lens mass more precise. Comment: 16 pages including 3 figures. Submitted to ApJThe Astrophysical Journal 10/2009; 710(2). DOI:10.1088/0004-637X/710/2/1800 · 6.28 Impact Factor