COLLISION PROBABILITIES WITH THE PLANETS AND THE DISTRIBUTION OF INTERPLANETARY MATTER

FORMULAE for the probability of collision with a planet of a particle crossing the orbit of the planet are derived and applied to various objects. The secular advance of the perihelion with respect to the node renders collisions possible in all cases of a favourable distance range. The rOle of perturbations at close encounters is also considered. In the solar system there are known at present 28 cases of objects crossing the orbit of only one planet; these are Pluto with respect to Neptune, all the remaining being asteroids with respect to Mars. The expectation of life with respect to collisionrs for these objects ranges from 2 x 109 to 3 X 101 years. All the other cases of crossings in the inner portions of the solar system are multiple crossings and refer to objects moving in orbits of large eccentricity but small inclination suggestive of results of close -ncounters, such as the short-period comets, some meteor showers, and the Apollo-Adonis group; they are short-lived, of the order of 108 years, and can be only transient members of the inner portions of the solar system; this group is called "zodiacal particles." The actual stability of the Trojan group of planets against perturbations for time intervals of the order of the' age of the solar system is proved by their mere existence, as otherwise they would have been destroyed by physical collisions with Jupiter in about 106 years. The ecliptical portions of the zodiacal light may be chiefly due to the zodiacal particles ; an interstellar photometric component of the zodiacal light can be calculated from the absorption coefficient of galactic space without any other specific' assumptions and is found close to the yalue determined photoelectrically at the McDonald Observatory for the pole of the ecliptic. A planetoidal component of large particles (r > 100cm) wlth small eccentricities and inclinations, unaffected by the Poynting-Robertson effect, is definitely absent or photometrically inconspicuous in the portions of the zodiacal light inside the orbit of Mars.