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
where C is the polar moment of inertia of the body, M is the mass of the body, and R is the mean radius of the body. For a sphere with uniform density, C/MR2 = 0.4. For a differentiated planet or satellite, where there is an increase of density with depth, C/MR2 < 0.4. The quantity is a useful indicator of the presence and extent of a planetary core, because a greater departure from the uniform-density value of 0.4 conveys a greater degree of concentration of dense materials towards the center.
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).
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