Steady state populations of Apollo-Amor objects

Abstract

The steady-state distribution of orbits of Apollo-Amor objects is calculated for a variety of possible sources. These include asteroids near the inner edge of the belt, cometary orbits similar to Encke, and hypothetical extinct cometary orbits with perihelia larger than that of Encke. In all but one case, the steady-state distributions are similar for all these sources, and predict Amor/Apollo ratios of 1.5 to 3. These ratios are lower than those predicted by work in which the effects of the ν 6 secular resonance were not considered. These results are in general agreement with observation, although the higher (∼3) Amor/Apollo ratios found for many of the sources may turn out to be unacceptably high. The absolute number of Apollo-Amors observed is found to require an injection rate of ∼15 objects/(10 6 years). This rate is easily achieved if the present existence of Encke is assumed to be a reasonably probable event, and if Encke becomes a ∼1-km-diameter Apollo object following exhaustion of its volatile material; best estimates of the injection rate from the asteroid belt [∼1.5/(10 6 years)] are too low. Hence a dominant cometary component is suggested. The predicted number of Apollo objects in small ( q < 1.0 AU, a < 1.4 AU orbits is in agreement with observation. Predicted lunar and terrestrial cratering rates agree approximately with observation. An unexplained difference between the lunar and terrestrial results is probably caused by uncertainties in the scaling laws or crater counts used. This discrepancy precludes an exact test of these calculations using cratering data.