Themean radius inastronomy is a measure for the size ofplanets andsmall Solar System bodies. Alternatively, the closely relatedmean diameter (${\displaystyle D}$), which is twice the mean radius, is also used. For a non-spherical object, the meanradius (denoted${\displaystyle R}$ or${\displaystyle r}$) is defined as the radius of thesphere that would enclose the samevolume as the object.^[1] In the case of a sphere, the mean radius is equal to the radius.

For any irregularly shaped rigid body, there is a uniqueellipsoid with the same volume andmoments of inertia.^[2] In astronomy, thedimensions of an object are defined as theprincipal axes of that special ellipsoid.^[3]

The dimensions of aminor planet can be uni-, bi- or tri-axial, depending on what kind of ellipsoid is used to model it. Given the dimensions of an irregularly shaped object, one can calculate its mean radius:

Anoblate spheroid, bi-axial, orrotational ellipsoid with axes${\displaystyle a}$ and${\displaystyle c}$ has a mean radius of${\displaystyle R=(a^2\cdot c{)}^{1/3}}$.^[4]

Atri-axial ellipsoid with axes${\displaystyle a}$,${\displaystyle b}$ and${\displaystyle c}$ has mean radius${\displaystyle R=(a\cdot b\cdot c{)}^{1/3}}$.^[1] The formula for a rotational ellipsoid is the special case where${\displaystyle a=b}$.

For a sphere, which is uni-axial (${\displaystyle a=b=c}$), this simplifies to${\displaystyle R=a}$.

Planets anddwarf planets are nearly spherical if they are not rotating. A rotating object that is massive enough to be inhydrostatic equilibrium will be close in shape to an ellipsoid, with the details depending on the rate of the rotation. At moderate rates, it will assume the form of either a bi-axial (Maclaurin) or tri-axial (Jacobi) ellipsoid. At faster rotations, non-ellipsoidal shapes can be expected, but these are not stable.^[5]

• For planetEarth, which can be approximated as an oblate spheroid with radii6378.1 km and6356.8 km, the mean radius is${\displaystyle R={\left((6378.1\text{km}{)}^2\cdot 6356.8\text{km}\right)}^{1/3}=6371.0\text{km}}$. The equatorial and polar radii of a planet are often denoted${\displaystyle r_e}$ and${\displaystyle r_p}$, respectively.^[4]
• Theasteroid511 Davida, which is close in shape to a tri-axial ellipsoid with dimensions360 km × 294 km × 254 km, has a mean diameter of${\displaystyle D=(360\text{km}\cdot 294\text{km}\cdot 254\text{km}{)}^{1/3}=300\text{ km}}$.^[6]
• Assuming it is in hydrostatic equilibrium, the dwarf planetHaumea has dimensions 2,100 × 1,680 × 1,074 km,^[7] resulting in a mean diameter of${\displaystyle D={\left(2100\text{km}\cdot 1680\text{km}\cdot 1074\text{km}\right)}^{1/3}=1559\text{km}}$. Therotational physics ofdeformable bodies predicts that over as little as a hundred days, a body rotating as rapidly as Haumea will have been distorted into the equilibrium form of a tri-axial ellipsoid.^[8]

• Earth ellipsoid
• Geoid
• Geometric mean
• Planetary radius

• Radii
• Units of measurement in astronomy

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