  In this work, we analyse static spherically symmetric solutions in the
framework of mimetic gravity, an extension of general relativity where the
conformal degree of freedom of gravity is isolated in a covariant fashion. Here
we extend previous works by considering in addition a potential for the mimetic
field. An appropriate choice of such potential allows for the reconstruction of
a number of interesting cosmological and astrophysical scenarios. We explicitly
show how to reconstruct such a potential for a general static spherically
symmetric space-time. A number of applications and scenarios are then explored,
among which traversable wormholes. Finally, we analytically reconstruct
potentials which leads to solutions to the equations of motion featuring
polynomial corrections to the Schwarzschild spacetime. Accurate choices for
such corrections could provide an explanation for the inferred flat rotation
curves of spiral galaxies within the mimetic gravity framework, without the
need for particle dark matter.
