Moment of inertia factor


In planetary sciences, the moment of inertia factor or normalized polar moment of inertia is a dimensionless quantity that characterizes the radial distribution of mass inside a planet or satellite.

For a planetary body with principal moments of inertia A<B<C, the moment of inertia factor is defined as shown here.

Solar System values

Ganymede has the lowest moment of inertia factor among solid bodies in the Solar System because of its fully differentiated interior, a result in part of tidal heating due to the Laplace resonance, as well as its substantial component of low density water ice. Saturn has the lowest value among the gas giants in part because it has the lowest bulk density. The Sun has by far the lowest value of all, in part because it has by far the highest central density.


The polar moment of inertia is traditionally determined by combining measurements of spin quantities (spin precession rate or obliquity) and gravity quantities (coefficients in a spherical harmonics representation of the gravity field).


For bodies in hydrostatic equilibrium, the Darwin–Radau relation can provide estimates of the moment of inertia factor on the basis of shape, spin, and gravity quantities.

Role in interior models

The moment of inertia factor provides an important constraint for models representing the interior structure of a planet or satellite. At a minimum, acceptable models of the density profile must match the volumetric mass density and moment of inertia factor of the body.

Related formulas


Ifmoment of inertia factor (dimensionless)
Cpolar moment of inertia of the body (kg*m2)
Mmass of the body (kg)
Rmean radius of the body (m)