  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.
