Diffuse Reflection by Planetary Atmospheres.

An attempt is made to interpret quantitatively the photometric observations which have been made of the planets by using the laws of diffuse reflection recently derived by Chandrasekhar. The basic problem is presented in Section 1. Consider a planet at a particular phase. By assuming a certain law of reflection, we can compute the intensity at any point on the disk of the planet. The limb darkening readily follows; however, in order to compute the magnitude of the planet, it is necessary to perform an integration over the visible crescent. This can be accomplished by using an appropriate cubature formula. The problem then consists in finding a law of diffuse reflection which will "predict" the magnitude and limb-darkening observations of a planet. The laws of diffuse reflection are summarized in Section II. The geometry of the problem is discussed and certain necessary formulae derived in Sections III and IV. The observational data are briefly discussed in Section V. The results of the computations aregiven in the last section. The observations of Saturn can be represented by a semi-infinite atmosphere characterized by a forward-throwing type of phase function. This phase function has the form 0.985(1 + 0.9 cos 0) for yellow light and 0.925(1 + 0.65 cos 0) for blue light. The visual phase-curve is computed, and the albedo is found to be 0.70. The visual and photographic phase-curves of Venus can be represented by known laws of diffuse reflection for a < 130 . At larger phase angles the planet is much too bright. Isotropic scattering with o= 0.95 appears to give the closest agreement in both the visual and the photographic cases. The limb darkening in yellow light can also be represented fairly well by isotropic scattering with o = 0.95. Polarization computations show that the polarization of the Venus atmosphere is not due to Rayleigh scattering.