  We present an exact $\gamma=5/3$ spherical accretion solution which modifies
the Bondi boundary condition of $\rho \to const.$ as $r\to \infty$ to $\rho \to
0$ as $r \to \infty$. This change allows for simple power law solutions on the
density and infall velocity fields, ranging from a cold empty free-fall
condition where pressure tends to zero, to a hot hydrostatic equilibrium limit
with no infall velocity. As in the case of the Bondi solution, a maximum
accretion rate appears. As in the $\gamma=5/3$ case of the Bondi solution, no
sonic radius appears, this time however, because the flow is always
characterised by a constant Mach number. This number equals 1 for the case of
the maximum accretion rate, diverges towards the cold empty state, and becomes
subsonic towards the hydrostatic equilibrium limit. It can be shown that in the
limit as { $r \to 0$}, the Bondi solution tends to the new solution presented,
{ extending the validity of the Bondi accretion value to} cases where the
accretion density profile does not remain at a fixed constant value out to
infinity. We then explore small deviations from sphericity and the presence of
angular momentum through an analytic perturbative analysis. Such perturbed
solutions yield a rich phenomenology through density and velocity fields in
terms of Legendre polynomials, which we begin to explore for simple angular
velocity boundary conditions having zeros on the plane and pole. The new
solution presented provides complementary physical insight into accretion
problems in general.
