oblate spheroids
An oblate spheroid is a rotationally symmetric ellipsoid having a polar axis shorter than the diameter of the equatorial circle whose plane bisects it. An M&M's candy (plain) (US) or Smartie (Canada, UK and Europe) is an approximate example of an oblate spheroid
It can be formed by rotating an ellipse about its minor axis, forming an equator with the end points of the major axis. As with all ellipsoids, it can also be described by the lengths of three mutually perpendicular principal axes, which are in this case two arbitrary equatorial semi-major axes and one semi-minor axis.
The opposite of oblate is prolate.
For a discussion of the physics that determines the shape of a spinning celestial body, see Equatorial bulge
The aspect ratio, b:a, is the ratio of the polar to equatorial lengths[citation needed], while the flattening (also called oblateness), f, is the ratio of the equatorial-polar length difference to the equatorial length:
These are just two of several different parameters used to define an ellipse and its solid body counterparts, all of which are ultimately trigonometric functions of the ellipse's modular angle, or angular eccentricity.
The oblate spheroid is interesting because it is the approximate shape of many planets and celestial bodies, including most notably Saturn and Altair, but also to a lesser extent the Earth (with a = 6378.137 km and b ≈ 6356.752 km, providing an aspect ratio of 0.99664717 and inverse flattening of 298.2572 [1]). It is therefore the geometric figure most used for defining reference ellipsoids, upon which cartographic and geodetic systems are based.
An oblate spheroid is a rotationally symmetric ellipsoid having a polar axis shorter than the diameter of the equatorial circle whose plane bisects it. An M&M's candy (plain) (US) or Smartie (Canada, UK and Europe) is an approximate example of an oblate spheroid
It can be formed by rotating an ellipse about its minor axis, forming an equator with the end points of the major axis. As with all ellipsoids, it can also be described by the lengths of three mutually perpendicular principal axes, which are in this case two arbitrary equatorial semi-major axes and one semi-minor axis.
The opposite of oblate is prolate.
For a discussion of the physics that determines the shape of a spinning celestial body, see Equatorial bulge
The aspect ratio, b:a, is the ratio of the polar to equatorial lengths[citation needed], while the flattening (also called oblateness), f, is the ratio of the equatorial-polar length difference to the equatorial length:
These are just two of several different parameters used to define an ellipse and its solid body counterparts, all of which are ultimately trigonometric functions of the ellipse's modular angle, or angular eccentricity.
The oblate spheroid is interesting because it is the approximate shape of many planets and celestial bodies, including most notably Saturn and Altair, but also to a lesser extent the Earth (with a = 6378.137 km and b ≈ 6356.752 km, providing an aspect ratio of 0.99664717 and inverse flattening of 298.2572 [1]). It is therefore the geometric figure most used for defining reference ellipsoids, upon which cartographic and geodetic systems are based.
Comment