Why are asteroids with circular orbits rare?
Orbital eccentricities cannot be normally distributed around zero, since the minimum eccentricity is zero.
Thus, in the same way that the Maxwell-Boltzmann distribution for particle speeds is zero at zero speed and peaks at finite speed, then no asteroids have exactly zero eccentricity and we would expect a peak at higher eccentricities.
The analogy can be extended further by asking what distribution might be expected for a &quot;thermal distribution&quot; of eccentricities - a distribution where the energies of the orbits follow the Boltzmann distribution and have been allowed to randomise by some unspecified dynamical or formation processes (e.g. Geller et al.
2019 ). In those case the density of eccentricities should go as
$$n(e) \propto e^2$$
and there should be more high eccentricity objects than low eccentricity objects.
Of course asteroids are not expected to be represented by this random distribution, since their dynamical histories likely have them being perturbed away from very low eccentricity orbits induced by the drag of a gas/dust disc in the early solar system.
Nevertheless, any initial perturbation moves them away from zero eccentricity and subsequent random perturbations might be expected to make them head towards the thermal distribution. I would guess that objects in the top end of the thermal distribution must also then just get selected out - falling into the Sun, hitting planets or getting ejected out of the main asteroid belt.