# Why are asteroids with circular orbits rare?

Regarding this excellent question by Swike: Why are asteroids with zero orbital inclination rare?, I recently proposed that orbits with zero inclination are rare as a natural result of the statistical distribution of orbital revolution axes extended onto the celestial sphere.

In the below graph we see a similar sparsity of orbital eccentricities near zero. If asteroid orbital eccentricities were normally distributed about zero, wouldn't we expect them to be densest here? What is the explanation?

The analogy can be extended further by asking what distribution might be expected for a "thermal distribution" 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.