The Earth's equatorial principal axes and moments of inertia

Let the Earth's equatorial principal moments of inertia be A and B, where A < B, and the corresponding principal axes be a and b. Explicit formulae are here derived for determining the orientation of a and b axes and the difference B − A using C22 and S22, the two gravitational harmonic coefficients of degree 2 and order 2. For the Earth, the a axis lies along the (14.93°W, 165.07°E) diameter, and the b axis lies perpendicular to it along the (75.07°E, 104.93°W) diameter. The difference B − A is 7.260 × 10−6MR2. These quantities for other planets are contrasted, and geophysical implications are discussed.