Skip to main content
SpringerLink
Log in
Book cover

Lecture Notes on Newtonian Mechanics pp 191–207Cite as

Central Forces and Kepler’s Laws

  • Chapter
  • First Online:

  • 3046 Accesses

Part of the book series: Undergraduate Lecture Notes in Physics ((ULNP))

Abstract

From the historical perspective, the derivation of three Kepler’s laws in Classical Mechanics is one of the most relevant calculations which were ever done. We shall present this calculation in details and also give a simple treatment of the effect of Precession of Perihelion for a nearly circular orbit for a weakly non-Newtonian gravitational force. This problem has very special importance in General Relativity due to the Precession of Perihelion for the Mercury and some other relativistic tests.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    Let us remember that a central force field is characterized by the spherical symmetry about the origin (force acts in the radial direction and its modulus is independent of angular coordinates). The gravitational field generated by a spherically symmetric distribution is a central field.

References

  1. R. Abraham, J.E. Marsden, Foundations of Mechanics (AMS Chelsea, Providence, 2008)

    Google Scholar 

  2. G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists (Academic, San Diego, 1995)

    Google Scholar 

  3. V.I. Arnold, Mathematical Methods of Classical Mechanics (Springer, New York, 1989)

    Google Scholar 

  4. V.I. Arnold, Ordinary Differential Equations, 3rd edn. (Springer, 1997)

    Google Scholar 

  5. J. Barcelos Neto, Mecânica Newtoniana, Lagrangiana & Hamiltoniana (Editora Livraria da Física, S\(\tilde{\mathrm{a}}\)o Paulo, 2004)

    Google Scholar 

  6. G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge Mathematical Library, Cambridge University Press,Cambridge/New York, 2000)

    Google Scholar 

  7. M. Braun, Differential Equations and Their Applications: An Introduction to Applied Mathematics. Texts in Applied Mathematics, vol. 11, 4th edn. (Springer, New York, 1992)

    Google Scholar 

  8. H.C. Corben, P. Stehle, Classical Mechanics (Dover, New York, 1994)

    Google Scholar 

  9. E.A. Desloge, Classical Mechanics, vols. 1 and 2 (Wiley, New York, 1982)

    Google Scholar 

  10. F.R. Gantmacher, Lectures in Analytical Mechanics (Mir Publications, Moscow, 1975)

    Google Scholar 

  11. H. Goldstein, C.P. Poole, J.L. Safko, Classical Mechanics, 3rd edn. (Addison Wesley, San Francisco, 2001)

    Google Scholar 

  12. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, 7th edn. (Elsevier, Burlington, 2007)

    Google Scholar 

  13. R.A. Granger, Fluid Mechanics. Dover Books on Physics (Dover, New York, 1995)

    Google Scholar 

  14. D. Gregory, Classical Mechanics (Cambridge University Press, Cambridge, 2006)

    Google Scholar 

  15. W. Greiner, Classical Mechanics: Point Particles and Relativity. Classical Theoretical Physics (Springer, New York/London, 2003)

    Google Scholar 

  16. I.E. Irodov, Mechanics. Basic Laws. (in Russian) (Nauka, 6 Ed., 2002); I.E. Irodov, Problems in General Physics (Mir Publications, 1988 and GK Publisher, 2008)

    Google Scholar 

  17. J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1998)

    Google Scholar 

  18. J.V. José, E.J. Saletan, Classical Dynamics: A Contemporary Approach (Cambridge University Press, Cambridge/New York, 1998)

    Google Scholar 

  19. T.W.B. Kibble, F.H. Berkshire, Classical Mechanics (World Scientific, River Edge, 2004)

    Google Scholar 

  20. C. Lanczos, The Variational Principles of Mechanics (Dover, New York, 1970)

    Google Scholar 

  21. L.D. Landau, E.M. Lifshits, Course of Theoretical Physics: Mechanics, 3rd edn. (Butterworth-Heinemann, 1982)

    Google Scholar 

  22. L.D. Landau, E.M. Lifshitz, Hydrodynamics. Course of Theoretical Physics Series, vol. 6, 2nd edn. (Butterworth-Heinemann, 1987)

    Google Scholar 

  23. L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields. Course of Theoretical Physics Series, vol. 2

    Google Scholar 

  24. N.A. Lemos, Mecânica Analítica, 2nd edn. (Livaria da Física, 2007)

    Google Scholar 

  25. Y.-K. Lim, Problems and Solutions on Mechanics: Major American Universities Ph.D. Qualifying Questions and Solutions (World Scientific, Singapore/River Edge, 1994)

    Google Scholar 

  26. J.B. Marion, S.T. Thornton, Classical Dynamics of Particle and Systems (Harcourt, Fort Worth, 1995)

    Google Scholar 

  27. D. Morin, Introduction to Classical Mechanics with Problems and Solutions (Cambridge University Press, Cambridge/New York, 2008)

    Google Scholar 

  28. P.M. Morse, H. Fishbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953)

    Google Scholar 

  29. I.L. Shapiro, Lecture Notes on Vector and Tensor Algebra and Analysis (CBPF, Rio de Janeiro, 2003)

    Google Scholar 

  30. A. Sommerfeld, Mechanics. Lectures on Theoretical Physics, vol. 1 (Academic, New York, 1970)

    Google Scholar 

  31. K. Symon, Mechanics, 3rd edn. (Addison Wesley, Reading, 1971)

    Google Scholar 

  32. J.R. Taylor, Classical Mechanics (University Science Books, Sausalito, 2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Fisica – ICE, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil

    Ilya L. Shapiro & Guilherme de Berredo-Peixoto

  2. Tomsk State Pedagogical University, Tomsk, Russia

    Ilya L. Shapiro

Authors
  1. Ilya L. Shapiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guilherme de Berredo-Peixoto
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Shapiro, I.L., de Berredo-Peixoto, G. (2013). Central Forces and Kepler’s Laws. In: Lecture Notes on Newtonian Mechanics. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7825-6_9

Download citation

Publish with us

Policies and ethics

Search

Navigation