# Clairaut's theorem

## Description

Clairaut’s theorem is a general mathematical law applying to spheroids of revolution. The formula can be used to relate the gravity at any point on the Earth’s surface to the position of that point, allowing the ellipticity of the Earth to be calculated from measurements of gravity at different latitudes. Clairaut’s formula is giving the acceleration due to gravity g on the surface of a spheroid at latitude φ.

(The flattening of a meridian section of the earth is defining as the ratio of the difference between the semimajor axis and the semiminor axis to the semimajor axis f=(a-b)/a )

## Variables

g | The acceleration due to gravity (m/s^{2}) |

G | The value of the acceleration of gravity at the equator (m/s^{2}) |

m | The ratio of the centrifugal force to gravity at the equator (dimensionless) |

f | The flattening of a meridian section of the earth (dimensionless) |

ϕ | The latitude (degree) |