Planetary impact probabilities for long-period comets

Planetary impact probabilities for long-period (near-parabolic) comets are determined by averaging Öpik's equations over inclination and perihelion distance for each planet. These averaged values compare well with the results of more elaborate Monte Carlo calculations. The impact probabilities are proportional to the square of the normalized capture radius of each planet, which in turn is a function of the planet's radius and mass, so that the major planets have the highest impact probabilities. Encounter velocities have an average value of $\text{3}\text{1}\text{2}$ times the planetary orbital velocity but the most probable encounter velocities are slightly higher than this for the terrestrial planets and slightly lower for the major planets. Comparison of the impact probabilities with the cratering record, corrected for gravity and velocity effects, indicates that long-period comets may account for 3 to 9% of the observed large crattes (diameter > 10 km) on the terrestrial planets. The inclination and perihelion properties of the impact probabilities obtained from numerical averaging provide a simple method for determining the impact probabilities for nonuniform distributions. The perihelion distribution of long period comets from J. A. Fernandez ((1981) Astron. Astrophys.96, 26–35) results in a crater production rate quite similar throughout the solar system, unlike that of a uniform perihelion distribution.