The study of extrasolar planets progressed rapidly in the past decade, making a large part of astrophysical research. More than 3000 extrasolar planets were discovered from the 1990s until today and their number is still growing. Given the fact that this area of astrophysics is relatively young, there is still not enough needed information and literature available in the Croatian language. This thesis therefore describes the basic concepts and facts related to extrasolar planets and the methods of its detection. The main problem concerning the process of detection of extrasolar planets is defining the mass, which was until recently defined only by observing the dynamics of the parent star as a function of mass, but not as the ratio between the mass of the star and the planet. This thesis contains simulation calculations, which enable us insights into the possibility of the direct definition of the mass of extrasolar planets. The detection threshold is determined by simulated theoretical spectra of the star-planet systems, and the method used in the research of binary stars is used in their unraveling. The results give us an insight into the observational requirements of the new 39.3M reflector telescope, E-ELT.