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A computer model that accounts for the brightness of an eclipsed Moon based upon Sun-Earth-Moon geometry, as well as refraction, absorption, and focusing of sunlight by the Earth's atmosphere has been created. Visual magnitude estimates reported after 11 eclipses over the past 30 years fit well with the model in most cases. There have been 3 unusually dark eclipses, each of which followed a major volcanic eruption. The visual magnitude of the Moon fades from -12.7 outside of eclipse to -12.0 at first contact, then to -3.4 at second contact, and finally to +1.4 if the Moon is centered in the Earth's umbra at mid-eclipse. After volcanic eruptions totality may be up to 5 magnitudes fainter. The model can be used to determine whether historical eclipses were normal or unusually dark based on first hand descriptions of the Moon's visibility during totality, and knowledge of its position in the umbra.
In regard to Venus, the phase anomaly first reported by Schroter 200 years ago has been directly recorded on CCD imagery for the first time. The images show that the apparent illumination of Venus is about 2% less than predicted by the geometry of the Sun and Earth when Venus is about half illuminated. A computer model was created to test the hypothesis that Schroter's effect is due to scattering of sunlight in Venus' twilight atmosphere. The model is based on scattering from an optically thin atmosphere having a scale height of about 4 to 5 km. The computer model successfully reproduces the observed phase anomaly. In such an atmosphere the poles are brighter than the equator along the terminator. This is due to the greater optical depth for a view passing tangentially through the atmosphere at the poles versus obliquely at the equator. The result is an appearence that is slightly more crescent shaped than the prediction for geometrical factors alone.
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