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. Technical book.
Format: 170 x 240 x 8 mm. Weight: 283 g. Paperback.

Released: October 2022
Status: available
Expert literature
Price: 899,00 € + shipping


    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
  12. Polynomial Form of the Besselian Elements

    Lunar Eclipses

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

  26. Supplements

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

Sample page: Click to enlarge