Propriétés remarquables de la réfraction astronomique dans une atmosphère à symétrie sphérique
2023; Elsevier BV; Volume: 23; Issue: S1 Linguagem: Inglês
10.5802/crphys.113
ISSN1878-1535
Autores Tópico(s)Satellite Image Processing and Photogrammetry
ResumoThe general theoretical properties and various approximate formulas for the angle χ S of astronomical refraction at S are presented, beginning with its fundamental expression by the refraction integral and immediately leading to the Simpson formula. Assuming a spherically symmetric atmosphere, many additional results show up, starting with Oriani’s “theorem” and Bouguer’s equation. From these, an usual form of the refraction integral is derived. A fundamental approximation follows to deduce the Laplace formula, then the series expansions that generalize it but are divergent for an isothermal atmosphere—because of the approximation made. Two results, free from any approximation, exist and are presented: Biot’s and Biot–Sang–Meyer–Fraser–White’s theorems. It leads to an approximate link with extinction, as found by Laplace, and an approximation of the refraction χ Sh for points on the astronomical horizon. We compute the chromatic effects on χ S , χ Sh —and (in a document associated with this article) on various characteristics of optical ducts considered in air—and an original expression of the “local vertical angular distortion coefficient” on the horizon (in Annexe B).
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