Acknowledgements 1. Introduction 2. Electromagnetic wave propagation 3. The absorption of light 4. Specular reflection 5. Single particle scattering: perfect spheres 6. Single particle scattering: irregular particles 7. Propagation in a nonuniform medium: the equation of radiative transfer 8. The bidirectional reflectance of a semi-infinite medium 9. The opposition effect 10. A miscellany of bidirectional reflectances and related quantities 11. Integrated reflectances and planetary photometry 12. Photometric effects of large scale roughness 13. Polarization 14. Reflectance spectroscopy 15. Thermal emission and emittance spectroscopy 16. Simultaneous transport of energy by radiation and conduction Appendix A. A brief review of vector calculus Appendix B. Functions of a complex variable Appendix C. The wave equation in spherical coordinates Appendix D. Fraunhoffer diffraction by a circular hole Appendix E. Table of symbols Bibliography Index.

Theory of Reflectance and Emittance Spectroscopy

A model for colliding objects in the asteroidal belt is formulated. An integro-differential equation describing the evolution of a system of particles undergoing inelastic collisions and fragmentation is derived and solved for steady-state conditions. It is found that the number density of particles per unit volume in the mass range m to m + dm is Am−a dm, where A and α are constants (provided that certain conditions are satisfied). The population index α can then be derived theoretically; for asteroids and their debris, α = 1.837, in agreement with an empirical fit to the observed distribution. Various statistical properties of the distribution can be derived from the model. It is found that, for asteroidal objects, catastrophic collisions constitute the most important physical process determining particle lifetimes and the form of the particle distribution for particles sufficiently large that radiation effects are unimportant. The lifetime of the largest asteroids is found to be of the same order of magnitude as the probable lifetime of the solar system; therefore, some of the largest asteroids may have survived since the time of creation, whereas most smaller ones have not and are collisional fragments, according to the present model.

/pdf/collisional-model-of-asteroids-and-their-debris-2modxcvzc6.pdf

Collisional model of asteroids and their debris

The mass of extraterrestrial material accreted by the Earth as submillimeter particles has not previously been measured with a single direct and precise technique that samples the particle sizes representing most of that mass. The flux of meteoroids in the mass range 10(-9) to 10(-4) grams has now been determined from an examination of hypervelocity impact craters on the space-facing end of the Long Duration Exposure Facility satellite. The meteoroid mass distribution peaks near 1.5 x 10(-5) grams (200 micrometers in diameter), and the small particle mass accretion rate is (40 +/- 20) x 106 kilograms per year, higher than previous estimates but in good agreement with total terrestrial mass accretion rates found by geochemical methods. This mass input is comparable with or greater than the average contribution from extraterrestrial bodies in the 1-centimeter to 10-kilometer size range.

https://science.sciencemag.org/content/sci/262/5133/550.full.pdf

A direct measurement of the terrestrial mass accretion rate of cosmic dust.

As Voyager 1 flew through the Saturn system it returned photographs revealing many new and surprising characteristics of this complicated community of bodies. Saturn's atmosphere has numerous, low-contrast, discrete cloud features and a pattern of circulation significantly different from that of Jupiter. Titan is shrouded in a haze layer that varies in thickness and appearance. Among the icy satellites there is considerable variety in density, albedo, and surface morphology and substantial evidence for endogenic surface modification. Trends in density and crater characteristics are quite unlike those of the Galilean satellites. Small inner satellites, three of which were discovered in Voyager images, interact gravitationally with one another and with the ring particles in ways not observed elsewhere in the solar system. Saturn's broad A, B, and C rings contain hundreds of "ringlets," and in the densest portion of the B ring there are numerous nonaxisymmetric features. The narrow F ring has three components which, in at least one instance, are kinked and crisscrossed. Two rings are observed beyond the F ring, and material is seen between the C ring and the planet.

Encounter with Saturn: Voyager 1 imaging science results

The global hydrogen Lyman alpha, helium (584 angstroms), and molecular hydrogen band emissions from Saturn are qualitatively similar to those of Jupiter, but the Saturn observations emphasize that the H(2) band excitation mechanism is closely related to the solar flux. Auroras occur near 80 degrees latitude, suggesting Earth-like magnetotail activity, quite different from the dominant Io plasma torus mechanism at Jupiter. No ion emissions have been detected from the magnetosphere of Saturn, but the rings have a hydrogen atmosphere; atomic hydrogen is also present in a torus between 8 and 25 Saturn radii. Nitrogen emission excited by particles has been detected in the Titan dayglow and bright limb scans. Enhancement of the nitrogen emission is observed in the region of interaction between Titan's atmosphere and the corotating plasma in Saturn's plasmasphere. No particle-excited emission has been detected from the dark atmosphere of Titan. The absorption profile of the atmosphere determined by the solar occultation experiment, combined with constraints from the dayglow observations and temperature information, indicate that N(2) is the dominant species. A double layer structure has been detected above Titan's limb. One of the layers may be related to visible layers in the images of Titan.

https://science.sciencemag.org/content/sci/212/4491/206.full.pdf

Extreme ultraviolet observations from Voyager 1 encounter with Jupiter

Results of Pioneer 11 imaging photopolarimeter observations of Saturn, its rings, and Titan are presented. The imaging photopolarimeter is a pointable telescope with an aperture of 2.5 cm and passbands of 390 to 500 to 720 nm which uses the spin of the spacecraft to scan across an object. Images of the Saturn system and of the rings are presented, and the absence of a D ring, structures in the C, B and A rings and the Cassini division and the discoveries of the F ring and the provisionally named Pioneer division separating it from the A ring are reported. A mean particle size less than 15 meters is estimated from estimates of total ring mass and the optical depth of the B ring. The discovery of the satellite 1979 S 1 at 2.53 Saturn radii is also noted. Models of the vertical aerosol structure of Saturn's atmosphere are compared with the polarization data, and it is indicated that the density of cloud particles decreases with altitude with a scale height about one fourth that of the gas, and that an optical depth of one is to be found at 750 mbar.

https://science.sciencemag.org/content/sci/207/4429/434.full.pdf

Imaging photopolarimeter on pioneer saturn.

The Palomar-Leiden survey of faint minor planets

Survey of Asteroids.

In January 1991, the 0.9-m Spacewatch telescope made the first observation of an asteroid outside Earth's atmosphere but in the neighborhood of the Earth-moon system. Since then, more than 40 Earth-approaching asteroids have been discovered, including 13 smaller than 50 m. Using these data, one of us has shown that there is an excess of Earth-approaching asteroids with diameters less than 50 m, relative to the population inferred from the distribution of larger objects. Here we argue that these smaller objects - characterized by low eccentricities, widely ranging inclinations and unusual spectral properties - form a previously undetected asteroid belt concentrated near Earth. The recent discovery of additional small Earth-approaching asteroids supports this conclusion.

Evidence for a near-Earth asteroid belt

Polarimetric observations of 43 asteroids are presented. All objects show a well-developed negative polarization branch as an indicator of unconsolidated surface regoliths. The empirical slope-albedo law for diffusely reflecting solid surfaces is reexamined and used to compute polarimetric albedos and diameters for 30 asteroids. In many cases the results are in good agreement with infrared-radiometric diameters; the older visual diameter measurements were systematically too small. Radiometric albedos below 5%, however, are not confirmed by the polarimetry. Bimodal frequency distributions are noted for asteroid color, albedo, and the depth of the negative polarization branch. Correlations between B - V color and polarimetric parameters suggest that most of the asteroid population can be divided into silicaceous and carbonaceous opacity classes.

Tom Gehrels

Papers

Imaging photopolarimeter on pioneer saturn.

The Palomar-Leiden survey of faint minor planets

Survey of Asteroids.

Evidence for a near-Earth asteroid belt

Minor planets and related objects. XVI - Polarimetric diameters