On a correlation between the reciprocal of cometary semi-major axis and absolute brightness

An investigation is made as to whether there exists a correlation between 1/a (a denotes the semi-major axis) and H₁₀ (the absolute magnitude) of a comet. Adopting the original values of 1/a calculated by Marsden, Sekanina & Everhart and the numerical values of H₁₀ given by Vsekhsvyatskij and by Meisel & Morris, it is found that the increase in H₁₀ from nearly parabolic orbits (D) to orbits of P (period) ∼ 10²yr (B) is 1.6. On the other hand, the number of revolutions, N required for a comet to evolve from D to B orbits by planetary perturbations is calculated and it is found that $$N\simeq 700$$. On the icy nucleus model of comets, the original value of the nuclear radii can be estimated on the assumption that comets evolve from nearly parabolic to short periodic orbits. The radius so estimated is consistent with Roemer's and O'Dell's values for observed comets with nearly parabolic orbits. Thus, the process of dynamical diffusion is consistent with the observational results.