The magnitude distribution, perihelion distribution and flux of long-period comets

The mass distribution and perihelion distribution of long-period comets are re-assessed. The mass distribution index is found to be 1.598 +/-0.016, indicating that the distribution is somewhat steeper than was obtained by previous analyses of an amalgam of all the available historical data. The number of long-period comets that have orbital perihelion distances, q, that fall in a specific q to q + dq range is found to be independent of q. It is also noted that the flux of long-period comets to the inner Solar system has remained constant throughout recorded history. The number of long-period comets, Ar, per I-au interval of perihelion distance, per year, brighter than H, entering the inner Solar system is found to be given by log(10)N = -2.607 + 0.359H. It is therefore estimated that, for example, about 0.5, 30 and 2000 long-period comets with absolute magnitudes brighter than 0, 5 and 10 respectively pass the Sun on orbits with perihelion distances less than 2.0 au, every century.