  We will make the case that \textit{pedal coordinates} (instead of polar or
Cartesian coordinates) are more natural settings in which to study force
problems of classical mechanics in the plane. We will show that the trajectory
of a test particle under the influence of central and Lorentz-like forces can
be translated into pedal coordinates at once without the need of solving any
differential equation. This will allow us to generalize Newton theorem of
revolving orbits to include nonlocal transforms of curves. Finally, we apply
developed methods to solve the "dark Kepler problem", i.e. central force
problem where in addition to the central body, gravitational influences of dark
matter and dark energy are assumed.
