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An astronomical body's moment of inertia factor (short for polar moment of inertia factor, the moment of inertia factor of interest regarding planets and stars) is a measure that characterizes the mass distribution within the body, of use in working out the dynamics of bodies' rotation, useful for objects such as stars, planets, and moons. It is independent of the object's mass and radius, and is a scalar within the range of 0 to 1. Example (polar) moment of inertia factor values:
| sphere of uniform density | 0.4 |
| sphere with higher density away from the axis | >0.4 |
| sphere with higher density nearer the axis | <0.4 |
| Sun | 0.070 |
| Mercury | 0.346 |
| Venus | 0.337 |
| Earth | 0.3307 |
| Moon | 0.3929 |
| Mars | 0.3644 |
| Jupiter | 0.2756 |
| Saturn | 0.22 |
| Uranus | 0.23 |
| Neptune | 0.23 |
A smaller number indicates more mass toward the axis, which is the case of a body with a dense "core", and a body's higher total mass and lower rigidity contribute to this. The most-direct measurement of a body's moment of inertia factor is non-trivial, generally computed from tracking data of orbits around the body and/or trajectories of close passes; in the above list, this has been done for Mercury, Venus, Earth, the Moon, and Mars. For other bodies, a value may be estimated based upon knowledge of the body's internal structure, which often is a rough model constructed from limited data. When it can be measured, it can help confirm such models.
The moment of inertia factor is of interest regarding the rotation-history of the object, such as the timescale necessary for tidal forces to produce tidal locking. A spherical object's polar moment of inertia factor is:
C/MR²
The object's polar moment of inertia (moment of inertia around its axis of rotation) is a scalar characterizing the object's implied resistance around its axis of rotation (analogous to how mass characterizes the linear acceleration from a given force). Such a moment of inertia of an object with respect to an axis is a measure of the ratio between a torque on the object with respect to that axis and the angular acceleration yielded by that torque:
C = L/ω or C = τ/α
For the axis being characterized:
If polar (or some other particular axis) is not specified or presumed, a single scalar is insufficient to characterize the object's resistance to torque that applies to any axis. For more generality, a 3×3 matrix (specifically a 3×3 tensor) can characterize all the objects' moments of inertia or moment of inertia factors for all possible axes through its center of mass.