Les développements de Radau et leur divergence : commentaire historique

Abstract

In an award-winning 1882 article, Radau (1835–1911) takes stock of various expressions of refraction, including the power series of the tangent of the apparent zenith distance. We focus on the integral expression of its coefficients, on the fundamental approximation used to calculate them, and on the subsequent introduction (1906) for this purpose of multiple families of characteristic heights of the atmosphere. We comment on the divergence, due to the fundamental approximation, of the series obtained in the case of the isothermal atmosphere (therefore unlimited).

Keywords

• Série entière (développement en)
• Hauteur réduite
• Réfraction astronomique (approximation fondamentale pour la)
• Hauteurs caractéristiques relatives
• Moments réduits et relatifs
• Atmosphère isotherme
• Divergence des séries