The neutron capture cross section of radioactive isotopes for neutron energies in the keV region will be measured by a time-of-flight (TOF) experiment. NAUTILUS will provide a unique facility realizing the TOF technique with an ultra-short flight path at the FRANZ setup at Goethe-University Frankfurt am Main, Germany. A highly optimized spherical photon calorimeter will be built and installed at an ultra-short flight path. This new method allows the measurement of neutron capture cross sections on extremely small sample as needed in the case of 85Kr, which will be produced as an isotopically pure radioactive sample. The successful measurement will provide insights into the dynamics of the late stages of stars, an important independent check of the evolution of the Universe and the proof of principle.