Darwin–Radau equation
In astrophysics, the Darwin–Radau equation gives an approximate relation between the moment of inertia factor of a planetary body and its rotational speed and shape. The moment of inertia factor is directly related to the largest principal moment of inertia, C. It is assumed that the rotating body is in hydrostatic equilibrium and is an ellipsoid of revolution. The Darwin–Radau equation states
where M and Re represent the mass and mean equatorial radius of the body. Here λ is the d'Alembert parameter and the Radau parameter η is defined as
where q is the geodynamical constant
and ε is the geometrical flattening
where Rp is the mean polar radius and Re is the mean equatorial radius.
For Earth, and, which yields, a good approximation to the measured value of 0.3307.
