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Study of exoplanets by spectroscopic methodsa Space Research Institute, Russian Academy of Sciences, Profsoyuznaya str. 84/32, Moscow, 117997, Russian Federation b Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnii Arkhyz, Zelenchukskiy Region, Karachai-Cherkessian Republic, Russian Federation c Institute of Astronomy, Russian Academy of Sciences, ul. Pyatnitskaya 48, Moscow, 119017, Russian Federation A review of spectroscopic methods for observations of stars in searching and studying exoplanets is presented. Instrumental errors in measuring ray velocities and ways to decrease (or fundamentally eliminate) them are considered. The role of astrometric and photometric methods is pointed out. The results of the study of the chemical composition of parent stars and the spectroscopy of transit phenomena are discussed. Some promising directions are evaluated. The development of ground-based and orbital domestic equipment for spectroscopy and spectropolarimetry of stars is reported.
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