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Exact expressions for the pericenter precession caused by some Dark Matter distributions and constraints on them from orbital motions in the Solar System, in the double pulsar and in the Galactic center

We analytically calculate the secular precession of the pericenter of a test particle orbiting a central body surrounded by a continuous distribution of Dark Matter (DM) by using some commonly adopted density profiles for it. We obtain exact expressions without resorting to a-priori simplifying assumptions on the orbital geometry of the test particle. Our formulas allow us to put constraints on the parameters of the DM distributions considered in several local astronomical and astrophysical scenarios, such as the Sun's planetary system, the double pulsar, and the stellar system around the supermassive black hole in Sgr A$^{\ast}$, all characterized by a wide variety of orbital configurations.