A theory of dust comets. I. Model and equations

Surface densities in the tail of Comet Arend-Roland 1956h are calculated using the theory of Paper I. The distributions of surface density are compared with measured distributions of light intensity from which the dust and head-gas emission rates as functions of time, the distribution of dust-particle sizes, and the emission velocity from the inner head region as a function of particle size and time are deter- mined essentially for the first time Dust-particle diameters on the order of 1 .~ are found, consistent with previous estimates. The deduced particle-size distribution is qualitatively similar to those found for the interplanetary dust particles from studies of the zodiacal light and to one suggested from an analysis of the continuous spectra from the heads of Comets Arend-Roland and Mrkos. For Comet Arend-Roland, near its perihelion, dust emission rates `--`7 5 X 1O~ g sec' and gas emission rates c~.'1 5 X 1030 molecules sec' are found, confirming previous estimates An outburst in the dust emission is deduced to have occurred in Comet Arend-Roland on April 2, 1957, about 6 days before perihelion, and the "forward spike" of this comet is found to consist of particles emitted between February 6 and March 1, 1957. As a general property of dust-rich comets, it is suggested that they emit larger amounts of dust during their approach to the Sun than during recession