Geometrical Approach to Kepler’s Laws of Planetary Motion


The elementary pen-and-string method to draw ellipsis has been devised to examine planetary orbits on the basis of the Kepler’s laws. Besides qualitative features of the orbits, quantitative dependence of the orbital shape on the quantities appearing in the Kepler’s laws can also be analyzed with simple geometrical procedures. The method thus provides a relevant intermediate step to students prior to the study of the rigorous theory of central force problems.

Share and Cite:

Yajima, Y. (2013). Geometrical Approach to Kepler’s Laws of Planetary Motion. Creative Education, 4, 6-8. doi: 10.4236/ce.2013.48A002.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Goldstein, H. (1980). Classical mechanics. Reading: Addison-Wesley.
[2] Goodstein, D. L., & Goodstein, J. R. (1999). Feynman’s lost lecture. New York: Norton.
[3] Okabe, Y., & Yajima, Y. (2004). A Note on the Feynman’s geometrical demonstration of elliptic motion of planets around the sun. Bulletin of the Faculty of Education Ibaraki University (Natuaral Sciences), 53, 81-86.
[4] Yajima, Y., & Okabe, Y. (2006). Wakuseikidou no Sakuzuhou (A method to construct planetary orbits). Butsuri Kyouiku (Physics Education), 54, 276-281.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.