The Besselian Elements

Mathematical Basics for Solar und Lunar Eclipses


  Anybody who wants to calculate the course of a solar eclipse needs the so-called "Besselian Elements". These are a set of eight variables obtained from the ephemeris (astronomical data for positions) of the Sun and Moon.

This book provides the mathematical tools to compute the visibility conditions of an eclipse for any place on Earth, e.g. widths of the lunar shadow, contact times or magnitude. The formulae are an integral part of computer algorithms nowadays, however, only few really understand in detail what happens in a simulation. In addition to solar eclipses, the book deals with lunar eclipses and the tolerance limits for the occurrence of an obscuration. Sample calculations demonstrate the working method. It is a step-by-step guide to getting started with the basics of eclipse theory.

The work is a supplement to the author's Habilitation at the University of Heidelberg. A German version is also available. 		The Besselian Elements
 
Author: Emil Khalisi
© October 2022. Galaktarium.
ISBN 978-3-9822794-5-9
107 pages, 34 images, 9 tables, paperback.

Released: October 2022
Status: available		 Expert literature
Price: 799,00 € + shipping 		Order:
Galaktarium


Contents:

    Introduction
    List of Symbols


    Solar Eclipses

  1. Basic Concept
  2. Projection on the Fundamental Plane
  3. Rotation of the Coordinate System
  4. Time Stamps on the Celestial Sphere
  5. The Shadow Cones
  6. Ellipticity of the Earth
  7. Postion P in the Fundamental System
  8. The Deceleration of Earth's Rotation -- Delta-T
  9. Checking the Local Circumstances
  10. Occultation Quantities
    11. Example: Partial Solar Eclipse 2053 in Juba
    Example: Total Eclipse of 1999 in Stuttgart
    Example: 15 April 136 BCE in Babylon
  11. Polynomial Form of the Besselian Elements


    Lunar Eclipses

  12. Methodological Differences to Solar Eclipses
  13. The Concept for Lunar Eclipses
  14. The Elements of a Lunar Eclipse
  15. Position of the Moon in the Earth's Shadow
  16. Width of the Shadow Zones
  17. Optical Path through the Earth's Atmosphere
  18. Contact points at the Shadow Boundaries
  19. The Middle of the Eclipse
  20. Times of Entry and Exit at the Shadow Boundaries
  21. Re-Adjustment
  22. Lunar Eclipse Magnitude
    23. Example: Partial Eclipse of 26 June 2048
    Example: Total Lunar Eclipse of 28 September 2015
  23. Hierarchical Eclipses


    24. Supplements

  24. Global Course of a Solar Eclipse
    25. Example: Contacts of the Solar Eclipse of 1999
  25. Visibility Maps
  26. The Eclipse Boundaries (Tolerance Limits)
  27. The Gamma Value
  28. Historical Development of the Method
    29. Habilitation, Abstracts from Papers, The Geogonic Year
    Acknowledgements, Image Credits
    Bibliography, Index

Sample page: Click to enlarge