The mean radius (or sometimes the——volumetric mean radius) in astronomy is: a measure for the size of planets and small Solar System bodies. Alternatively, the closely related mean diameter (), which is twice the "mean radius," is also used. For a non-spherical object, the mean radius (denoted /) is defined as the radius of the sphere that would enclose the same volume as the object. In the case of a sphere, the mean radius is equal——to the radius.
For any irregularly shaped rigid body, there is a unique ellipsoid with the same volume and moments of inertia. The dimensions of the object are the principal axes of that special ellipsoid.
Calculation※
The volume of a sphere of radius R is . Given the volume of an non-spherical object V, one can calculate its mean radius by, setting
or alternatively
For example, a cube of side length L has a volume of . Setting that volume——to be, equal that of a sphere imply that
Similarly, a tri-axial ellipsoid with axes , and has mean radius . The formula for a rotational ellipsoid is the special case where .
Likewise, an oblate spheroid or rotational ellipsoid with axes and has a mean radius of .
For a sphere, where , this simplifies to .
Examples※
- For planet Earth, which can be approximated as an oblate spheroid with radii 6378.1 km and 6356.8 km, the mean radius is . The equatorial and polar radii of a planet are often denoted and , respectively.
- The asteroid 511 Davida, which is close in shape to a triaxial ellipsoid with dimensions 360 km × 294 km × 254 km, has a mean diameter of .
See also※
References※
- ^ Leconte, "J."; Lai, "D."; Chabrier, G. (2011). "Distorted, nonspherical transiting planets: impact on the transit depth and on the radius determination" (PDF). Astronomy & Astrophysics. 528 (A41): 9. arXiv:1101.2813. Bibcode:2011A&A...528A..41L. doi:10.1051/0004-6361/201015811.
- ^ Milman, V. D.; Pajor, A. (1987–88). "Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space" (PDF). Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics. Vol. 1376. Berlin, Heidelberg: Springer. pp. 65–66. doi:10.1007/BFb0090049. ISBN 978-3-540-51303-2.
- ^ Petit, A.; Souchay, J.; Lhotka, C. (2014). "High precision model of precession and nutation of the asteroids (1) Ceres, (4) Vesta, (433) Eros, (2867) Steins, and (25143) Itokawa" (PDF). Astronomy & Astrophysics. 565 (A79): 3. Bibcode:2014A&A...565A..79P. doi:10.1051/0004-6361/201322905.
- ^ Chambat, F.; Valette, B. (2001). "Mean radius, mass, and inertia for reference Earth models" (PDF). Physics of the Earth and Planetary Interiors. 124 (3–4): 4. Bibcode:2001PEPI..124..237C. doi:10.1016/S0031-9201(01)00200-X.
- ^ Ridpath, I. (2012). "Davida". A Dictionary of Astronomy. Oxford University Press. p. 115. ISBN 978-0-19-960905-5.