  The late time accelerated expansion of the Universe demands that even in
local galactic-scales it is desirable to study astrophysical phenomena,
particularly relativistic accretion related phenomena in massive galaxies or in
galaxy mergers and the dynamics of the kiloparsecs-scale structure and beyond,
in the local-galaxies in Schwarzschild-de Sitter (SDS) background, rather than
in Schwarzschild or Newtonian paradigm. Owing to the complex and nonlinear
character of the underlying magnetohydrodynamical equations in general
relativistic (GR) regime, it is quite useful to have an Newtonian analogous
potential containing all the important GR features that allows to treat the
problem in Newtonian framework for study of accretion and its related
processes. From the principle of conserved Hamiltonian of the test particle
motion, here, a three dimensional Newtonian analogous potential has been
obtained in spherical geometry corresponding to SDS/Schwarzschild anti-de
Sitter (SADS) spacetime, that reproduces almost all of the GR features in its
entirety with remarkable accuracy. The derived potential contains an explicit
velocity dependent term of the test particle that renders an approximate
relativistic modification of Newtonian like potential. The complete orbital
dynamics around SDS geometry and the epicyclic frequency corresponding to SDS
metric have been extensively studied in the Newtonian framework using the
derived potential. Applying the derived analogous potential it is found that
the current accepted value of $\Lambda \sim 10^{-56} \rm cm^{-2}$ moderately
influences both sonic radius as well as Bondi accretion rate, especially for
spherical accretion with smaller values of adiabatic constant and temperature,
which might have interesting consequences on the stability of accretion disk in
AGNs/radio galaxies.
