Despite the fact that the Standard Model (SM) of strong and electroweak interactions successfully describes all observed phenomena at currently accessible energies $M_W \sim 100$ GeV, where $M_W$ is the electroweak scale, there are several indications for new physics beyond the SM to exist. It is widely believed that an unified theory of all fundamental forces in nature can be consistently constructed in space-time with more than four dimensions. In the first part of this article we will analyze the possibility of measuring a change in the maximum mass of a white dwarf and a neutron star in spaces with 1-6 relatively large extra dimensions. In the second part of this article we present a way of measuring a spectrum of massive graviton resonances, that the Randall-Sundrum model predicts, in an experiment that could be performed at the upcoming ATLAS and CMS program at LHC, starting in the year 2005.