We present an analysis of 43 years (1972 to 2015) of spectroscopic observations of the Seyfert 1 galaxy NGC 5548. This includes 12 years of new unpublished observations (2003 to 2015). We compiled about 1600 Hβ spectra and analyzed the long-term spectral variations of the 5100 Å continuum and the Hβ line. Our analysis is based on standard procedures, including the Lomb–Scargle method, which is known to be rather limited to such heterogeneous data sets, and a new method developed specifically for this project that is more robust and reveals a ∼5700 day periodicity in the continuum light curve, the Hβ light curve, and the radial velocity curve of the red wing of the Hβ line. The data are consistent with orbital motion inside the broad emission line region of the source. We discuss several possible mechanisms that can explain this periodicity, including orbiting dusty and dust-free clouds, a binary black hole system, tidal disruption events, and the effect of an orbiting star periodically passing through an accretion disk.

We study some possible observational signatures of Rn gravity at Galactic scales and how these signatures could be used for constraining this type of f(R) gravity. For that purpose, we performed two-body simulations in the Rn gravity potential and analyzed the obtained trajectories of S2-like stars around the Galactic center, as well as the resulting parameter space of the Rn gravity potential. Here, we discuss the constraints on Rn gravity which can be obtained from the observations of orbits of S2-like stars with the present and next generations of large telescopes. We make comparisons between the theoretical results and observations. Our results show that the most probable value for the parameter rc in the Rn gravity potential in the case of S2-like stars is $\sim${}100\,\,AU, while the universal parameter $\beta${} is close to 0.01. Also, the gravity potential induces the precession of S2-like star orbits in the opposite direction with respect to general relativity; therefore, such a behavior of orbits is qualitatively similar to the behavior of Newtonian orbits with a bulk distribution of matter (including a stellar cluster and dark matter distributions).