Foundations of Celestial Mechanics

This book provides an introduction to classical celestial mechanics. It is based on lectures delivered by the authors over many years at both Padua University (MC) and V.N. Karazin Kharkiv National University (EB). The book aims to provide a mathematical description of the gravitational interaction of celestial bodies. The approach to the problem is purely formal. It allows the authors to write equations of motion and solve them to the greatest degree possible, either exactly or by approximate techniques, when there is no other way. The results obtained provide predictions that can be compared with the observations. Five chapters are supplemented by appendices that review certain mathematical tools, deepen some questions (so as not to interrupt the logic of the mainframe with heavy technicalities), give some examples, and provide an overview of special functions useful here, as well as in many other fields of physics. The authors also present the original investigation of torus potential. This book is aimed at senior undergraduate students of physics or astrophysics, as well as graduate students undertaking a master’s degree or Ph.D.

1. N -body problem.- 2. Two-body problem.- 3. Three-body problem.- 4. Analytical mechanics.- 5. Gravitational potential.- Appendix.

Elena Bannikova is Ukrainian Astrophysicists. She is working as Leading Scientific Researcher in the Institute of Radio Astronomy of the National Academy of Sciences of Ukraine. She is also Professor of the Department of Astronomy and Space Informatics (the Faculty of Physics) of V.N.Karazin Kharkiv National University where she is lecturing courses on Celestial Mechanics, Cosmology, Gravity: from Aristotle to black holes. Her fields of research are active galactic nuclei, gravitational potential, N-body simulations, gravitational lensing. She is co-investigator of some national projects including the recent one on “Astrophysical Relativistic Galactic Objects (ARGO): the life cycle of active nucleus”. In 2021 she has been awarded the title of “Knight” by the President of the Italian Republic.

Massimo Capaccioli is Italian Astrophysicist. He has served as Professor of astronomy at the Universities of Padua and then of Naples Federico II, where he is currently Emeritus. The resultsof his studies, dealing mainly with the dynamics and evolution of stellar systems and the observational cosmology, are presented in over 550 scientific articles in international journals. For a long time director of the Capodimonte Astronomical Observatory in Naples, he has conceived and managed, in synergy with the European Southern Observatory (ESO), the construction of the VLT Survey Telescope (VST), one of the largest reflectors fully dedicated to astronomical surveys. He has chaired the Italian Astronomical Society (SAIt) for a decade and for a three-year turn the National Society of Sciences, Letters, and Arts in Naples. He has collaborated with various Italian newspapers and with the national public broadcasting company of Italy (RAI). He has authored both university manuals and popular books. The list of his honors includes the title of Commander of the Italian Republic for scientific merits (2005), the honorary professorship granted by the University of Moscow Lomonosov in 2010, the honorary doctor-degrees by the Universities of Dubna (Russia, 2015), Kharkiv (Ukraine, 2017), and Pyatigorsk (Russia, 2019), and the medals Struve (2010; Russian Academy of Sciences), Tacchini (2013; SAIt), Karazin (2019; Karazin University, Kharkiv, Ukraine), and Gamov (2019: University of Odessa, Ukraine). He is Member of some academies in Italy and of the Academia Europaea, and since 2021 foreign Member of the National Academy of Sciences of Ukraine.