Editing Ellipsoid (section)

===Dynamical properties===
The [[mass]] of an ellipsoid of uniform [[density]] {{mvar|ρ}} is
:<math>m = V \rho = \tfrac{4}{3} \pi abc \rho.</math>

The [[Moment of Inertia|moments of inertia]] of an ellipsoid of uniform density are
:<math>\begin{align}
  I_\mathrm{xx} &= \tfrac{1}{5}m\left(b^2 + c^2\right), &
    I_\mathrm{yy} &= \tfrac{1}{5}m\left(c^2 + a^2\right), &
    I_\mathrm{zz} &= \tfrac{1}{5}m\left(a^2 + b^2\right), \\[3pt]
  I_\mathrm{xy} &=  I_\mathrm{yz} = I_\mathrm{zx} = 0.
\end{align}</math>

For {{math|1=''a'' = ''b'' = ''c''}} these moments of inertia reduce to those for a sphere of uniform density.

[[File:2003EL61art.jpg|right|thumb|Artist's conception of {{dp|Haumea}}, a Jacobi-ellipsoid [[dwarf planet]], with its two moons]]
Ellipsoids and [[cuboid]]s rotate stably along their major or minor axes, but not along their median axis. This can be seen experimentally by throwing an eraser with some spin. In addition, [[moment of inertia]] considerations mean that rotation along the major axis is more easily perturbed than rotation along the minor axis.<ref>Goldstein, H G (1980). ''Classical Mechanics'', (2nd edition) Chapter 5.</ref>

One practical effect of this is that scalene astronomical bodies such as {{dp|Haumea}} generally rotate along their minor axes (as does Earth, which is merely [[oblate spheroid|oblate]]); in addition, because of [[tidal locking]], moons in [[synchronous orbit]] such as [[Mimas (moon)|Mimas]] orbit with their major axis aligned radially to their planet.

A spinning body of homogeneous self-gravitating fluid will assume the form of either a [[Maclaurin spheroid]] (oblate spheroid) or [[Jacobi ellipsoid]] (scalene ellipsoid) when in [[hydrostatic equilibrium]], and for moderate rates of rotation.  At faster rotations, non-ellipsoidal [[:wikt:pyriform|piriform]] or [[oviform]] shapes can be expected, but these are not stable.