Mathematics – Differential Geometry
Scientific paper
Oct 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978avest..12..107g&link_type=abstract
(Astronomicheskii Vestnik, vol. 12, Apr.-June 1978, p. 107-119.) Solar System Research, vol. 12, no. 2, Oct. 1978, p. 90-102. Tr
Mathematics
Differential Geometry
1
Differential Geometry, Optical Reflection, Pageos Satellite, Specular Reflection, Convexity, Diffuse Radiation, High Altitude Balloons, Illuminance, Optical Properties, Surface Geometry
Scientific paper
Extensive research has been undertaken to determine the shape and the variations therein of the PAGEOS balloon satellite. In this article, exact formulas are derived which describe specular reflection of light from a section of a convex regular surface that may consist of elliptical, parabolic, or flat points. Four systems of equations which completely characterize the reflection geometry are obtained and used to solve specific problems. A general formula for illuminance is derived, and it is shown that a mutually unique and continuous correspondence between points of the reflecting surface and points of the source or parts thereof exists for convex surfaces. An attempt is made to illustrate some practical applications of the theory.
Grigorevskii V. M.
Kolesnik Ia. S.
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