Discussing disturbed circular orbits: a pedagogical approach to the Bertrand's theorem for the high school

Authors

  • Rafael de Sousa Dutra Instituto Federal de Educação, Ciência e Tecnologia do Rio de Janeiro https://orcid.org/0000-0002-1897-2313
  • Tainá de Azevedo Instituto Federal de Educação, Ciência e Tecnologia
  • Vinícius Lopes Instituto Federal de Educação, Ciência e Tecnologia

DOI:

https://doi.org/10.26512/rpf.v6i1.39503

Keywords:

Newtonian gravitation. Bertrand's theorem. TICs.

Abstract

This work proposes to bring to high school physics classes the discussion of the
stability of planetary orbits during Newtonian gravitation classes. For this, we
present a didactic proposal for discussing Bertrand's theorem, using basic elements
of physics and mathematics from high school, as well as computer simulations, using
the free Modellus software, to illustrate the conclusions obtained during the
discussions.

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References

NEWTON, I. Philosophiae Naturalis Principia Mathematica (Royal Society, London, 1687). Traduzido para o Inglês por A. Motte e revisado por F. Cajori (University of California Press, Berkeley, 1962)

BERTRAND, J. C. R. Acad. Sci. Paris 77, p. 849-853, (1873).

ZARMI, Y. The Bertrand theorem revisited. American Journal of Physics, v. 70, n. 4, p. 446-449, (2002).

SANTOS, F. C.; SOARES, V. & TORT A. C.: Uma tradução da demonstração original do teorema de Bertrand. Revista Brasileira de História da Ciência. 4 n.1 92-97 (2011).

GOLDSTEIN, H.; POOLE, C. & SAFKO, J.: Classical Mechanics 3 a ed. Addison-Wesley, New York (2002).

NUSSENZVEIG, H. M. Física Básica: vol. 1. São Paulo, Edgard Blucher, (1981).

RAMALHO, NICOLAU. TOLEDO. Os fundamentos da física, v. 2, Moderna, (2015).

Published

2022-04-16

How to Cite

DE SOUSA DUTRA, Rafael; DE AZEVEDO SILVA, Tainá; LOPES DE ARAUJO DA SILVA, Vinicius. Discussing disturbed circular orbits: a pedagogical approach to the Bertrand’s theorem for the high school. Journal of the Physics Teacher, [S. l.], v. 6, n. 1, p. 69–77, 2022. DOI: 10.26512/rpf.v6i1.39503. Disponível em: https://periodicos.unb.br/index.php/rpf/article/view/39503. Acesso em: 22 dec. 2024.

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