The Earth's Dust Belt: Fact or fiction?: 1. Forces perturbing dust particle motion

Abstract

In this paper we have studied the forces influencing the motion of small dust particles orbiting near the earth and in interplanetary space. The predominant nongravitational force is that of sunlight whose effects may be quite varied depending on the shape, orientation, and constitution of a dust particle. Far from the earth the only other force that may be of significance is the Lorentz force, whereas near the earth all the usual forces included in analyzing satellite orbits become important. In the following papers in this series, combinations of forces that may contribute substantially to a concentration of such dust around the earth are also analyzed. These included gravitational focusing, Jacobi capture, ejection of dust from the moon via meteor impact, and the capture of dust into long-lifetime geocentric orbits through the combined action of air drag and sunlight pressure. Our calculations indicate that, sensibly defined, an increase in flux near the earth of only about a factor of 10 2 over the interplanetary value is understandable. Even this relatively modest factor depends vitally on the assumption that the major fraction of the dust at the boundary of the earth's sphere of influence has a speed on the order of 1 km/sec with respect to the earth. The more reasonable choice of 3 km/sec for this speed reduces the enhancement to a factor well less than 10. This result is to be contrasted with the widely accepted deduction, based on satellite experiments and zodiacal-cloud observations, that the enhancement is about 10 4 . Aside from questioning the data analysis, we are unable to offer any solution to this apparent paradox. We suspect, however, that when the experimental dust finally settles, the near-earth concentration will be found to fade almost imperceptibly into the interplanetary background. 1962]. Our first theoretical problem was to. decide where to start. The calculation of the distribution of particles near the earth depends importantly on the masses, densities, shapes,' orientations, crushing strengths, thermal properties, and complex indices of refraction of the dust. But none of these characteristics is well known, nor is the distribution of dust orbits in interplanetary space. We therefore began by studying the individual forces acting on a dust particle and their dependences on the physical properties and initial orbit of the particle. We considered the gravitational attraction of the 5695 5696 SHAPIRO, LAUTMAN, AND COLOMBO

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