Editing Clairaut's theorem (gravity) (section)

==Geodesy==
{{see also|Theoretical gravity}}
The spheroidal shape of the Earth is the result of the interplay between [[gravity]] and [[centrifugal force]] caused by the Earth's rotation about its axis.<ref name=Vinti>{{cite book |title=Orbital and Celestial Mechanics |series=Progress in astronautics and aeronautics, v. 177 |author1=John P. Vinti |author2=Gim J. Der |author3=Nino L. Bonavito |page=171 |url=https://books.google.com/books?id=-dXzdYHvPgMC&dq=Earth+spheroid+centrifugal+date:1990-2008&pg=PA171 |isbn=1-56347-256-2 |year=1998 |publisher=[[American Institute of Aeronautics and Astronautics]]}}</ref><ref name=Webster>{{cite book |title=The Dynamics of Particles and of Rigid, Elastic, and Fluid Bodies: being lectures on mathematical physics |author=Arthur Gordon Webster |year=1904 |publisher=[[B.G. Teubner]] |url=https://archive.org/details/dynamicsparticl03websgoog |page=[https://archive.org/details/dynamicsparticl03websgoog/page/n488 468] }}</ref> In his ''Principia'', [[Isaac Newton|Newton]] proposed the equilibrium shape of a homogeneous rotating Earth is a rotational ellipsoid with a flattening ''f'' given by 1/230.<ref name=Newton>Isaac Newton: ''Principia'' Book III Proposition XIX Problem III, p. 407 in Andrew Motte translation.</ref><ref name="Principia">{{Cite book |last=Newton |first=Isaac |url=https://archive.org/details/newtonspmathema00newtrich |title=Newton's Principia : the mathematical principles of natural philosophy |last2=Chittenden |first2=N. W. (Life of Sir Isaac Newton) |last3=Adee publ. |first3=Daniel |last4=Motte transl. |first4=Andrew |last5=Hill |first5=Theodore Preston |date= |publisher=Early American mathematics books CU-BANC |others=University of California Libraries |year=1846 |location=New York}}</ref>  As a result, gravity increases from the equator to the poles. By applying Clairaut's theorem, [[Pierre-Simon Laplace|Laplace]] found from 15 gravity values that ''f'' = 1/330: ''g''<sub>NP</sub>/''G''<sub>eq</sub> − 1 = 5.6‰. A modern estimate is 1:298.25642.<ref>[https://tai.bipm.org/iers/convupdt/chapter1/icc1.pdf IERS Numerical Standards (2003)] ''tai.bipm.org'' Table 1.1</ref> See [[Figure of the Earth]] for more detail.

For a detailed account of the construction of the [[Reference ellipsoid|reference Earth model]] of geodesy, see Chatfield.<ref name=Chatfield>{{cite book |title= Fundamentals of High Accuracy Inertial Navigation |url=https://books.google.com/books?id=2hJTDpT2U1UC&dq=frame+coordinate+%22state+of+motion%22&pg=PA7
|isbn=1-56347-243-0 |year=1997 |author=Averil B. Chatfield |publisher=American Institute of Aeronautics and Astronautics  |series=Volume 174 in ''Progress in Astronautics and Aeronautics'' |no-pp= true |pages= Chapter 1, Part VIII p. 7  }}</ref>