A simple mechanical model for the shape of the earth

Authors: Essén, H.
Document Type: Article
Pubstate: Published
Journal: European journal of physics
Volume: 17   131-135
Year: 1996


While it is well known that the rotation of the Earth causes it to be flattened at the poles, one rarely finds a quantitative treatment of this phenomenon in textbooks. Newton himself gave an approximate treatment of the amount of ellipticity and the problem is important in the history of science. Here the simplest model that can account for the phenomenon is considered. The planet is modelled by four bodies that attract gravitationally but are prevented from collapsing by elastic, spring forces. The rotating equilibrium of this system can be calculated exactly and by suitable interpretations one may compare the result with the observed ellipticity.