### moment of inertia factor

(characterization of mass distribution within a planet)

A body's **moment of inertia factor**
(short for **polar moment of inertia factor**, the one of interest)
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 |

Earth | 0.3307 |

Moon | 0.3929 |

Mars | 0.3662 |

Jupiter | 0.254 |

Saturn | 0.210 |

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 number 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

- C - polar moment of inertia.
- M - object's mass.
- R - object's radius.

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.
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 of C:

- C - moment of inertia.
- L - angular momentum.
- ω - angular velocity.
- τ - torque.
- α - angular acceleration.

The less-specific term, **moment of inertia**
includes all the information to characterize an object's
resistance to torque along any axis through its center of mass,
i.e., the force it would take to
change its rotation (much like the way mass determines what
linear acceleration results from a given force).
A single scalar is insufficient to hold all this information,
which is generally represented as a 3×3 matrix,
specifically a 3×3 **tensor**.

(*physics,measure*)
**Further reading:**

http://en.wikipedia.org/wiki/Moment_of_inertia_factor

http://en.wikipedia.org/wiki/Moment_of_inertia

https://geo.libretexts.org/Courses/University_of_California_Davis/UCD_GEL_56_-_Introduction_to_Geophysics/Geophysics_is_everywhere_in_geology.../03%3A_Planetary_Geophysics/3.02%3A_Layered_Structure_of_a_Planet

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