Gravitational acceleration and tidal effects in spherical-symmetric
  density profiles
  Pure power-law density profiles, $\rho(r)\propto r^{b-3}$, are classified in
connection with the following reference cases: (i) isodensity, $b=3$, $\rho=$
const; (ii) isogravity, $b=2$, $g=$ const; (iii) isothermal, $b=1$,
$v=[GM(r)/r]^{1/2}=$ const; (iv) isomass, $b=0$, $M=$ const. A restricted
number of different families of density profiles including, in addition, cored
power-law, generalized power-law, polytropes, are studied in detail with regard
to both one-component and two-component systems. Considerable effort is devoted
to the existence of an extremum point (maximum absolute value) in the
gravitational acceleration within the matter distribution. Predicted velocity
curves are compared to the data inferred from observations. Tidal effects on an
inner subsystem are investigated and an application is made to globular
clusters within the Galaxy. To this aim, the tidal radius is defined by
balancing the opposite gravitational forces from the Galaxy and the selected
cluster on a special point of the cluster boundary, lying between related
centres of mass. The position of 17 globular clusters with respect to the
stability region, where the tidal radius exceeds the observed radius, is shown
for assigned dark-to-visible mass ratios and density profiles, among those
considered, which are currently used for the description of galaxies and/or
dark matter haloes.
