= Solution
For an unperturbed <Kepler orbit>, successive revolutions advance the planet-relative orientation by $-n_pT_c$ modulo $2\pi$, where $T_c$ is the <comet>'s <orbital period>. An irrational period ratio makes these orientations dense; sufficiently distant <mean-motion resonance> and adequate observation time justify the corresponding <phase mixing> approximation.
At each radius between its <pericentre distance> and <apocentre distance>, the <comet> eventually visits every azimuth in the <rotating reference frame>. The spatial projection is therefore
$$
\boxed{q\leq r\leq Q,\quad 0\leq\theta<2\pi.}
$$
It is an <annulus>, with a nonuniform radial residence probability, rather than a uniformly filled area. Strictly, the full position-velocity <phase space> is not this <annulus>: at each radius the energy and angular momentum constrain the velocity, with inward and outward branches. The <annulus> is its position-space projection. This description assumes the <orbital elements> have not yet been substantially changed by <planetary scattering>.
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