## Mathematical Theory of Stellar EclipsesASTRONOMICAL ECLIPSE PHENOMENA In looking over the long history of human science from time immemorial to our own times, it is impossible to overestimate the role played in it by the phenomena of eclipses of the celestial bodies-both within our solar system as well as in the stellar universe at large. Not later than in the 4th century B. C. , the observed features of the shadow cast on the Moon by the Earth during eclipses led Aristotle (384-322 B. C. ) to formulate the first scientific proof worthy of that name of the spherical shape of the Earth; and only somewhat later, the eclipses of the Sun provided Aristarchos (in the early part of the 3rd century B. C. ) or Hipparchos (2nd half ofthe same century) with the geometric means to ascertain the distance which separates the Earth from the Sun. In the 17th century A. D. (in 1676, to be exact) the timings of the eclipses of the satellites of Jupiter by their central planet enabled Olaf Romer to discover that the velocity with which light propagates through space is finite. |

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### Contents

1 | |

LIGHT CHANGES DUE TO ECLIPSES | 10 |

LOSS OF LIGHT AS INTEGRAL TRANSFORMS | 41 |

THEORETICAL PHOTOMETRY OF DISTORTED | 69 |

SOLUTION FOR ELEMENTS | 97 |

INVERSE PROBLEM FOR DISTORTED ECLIPSING | 119 |

LABORATORY SIMULATIONS | 150 |

157 | |

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Algol analog computers analysis annular aperture arising associated o-functions astronomical Bessel functions celestial sphere Chapter close binary systems coefficients constant coordinates defined by Eq differential equation direction cosines discloses distortion distribution of brightness eclipse functions eclipse is partial eclipsing binary eclipsing star eclipsing systems eclipsing variables expansion expressed in terms fact finite foregoing equation Fourier transform fractional radius geometrical elements given by Eq Goodricke Hankel transform hypergeometric series imaginary unit integral Jacobi polynomials John Goodricke Kopal latter Legendre let us return light curves limb-darkening limits line of sight loss of light minima modulated moments A2m moreover numerical observed light changes obtained occultation oscillations parameters phenomena photometric effects photometric perturbations preceding equation problem proximity effects radial velocity recursion formula reduces represent respect rewritten right-hand side rotating shadow cylinder side of Eq side of Equation solution spherical stars star undergoing eclipse theorem type of eclipse values zero