Oblate ellipsoid in the context of "Geodesics on an ellipsoid"

Earth radius (denoted as R_🜨 or R_E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equatorial radius, denoted a) of about 6,378 km (3,963 mi) to a minimum (polar radius, denoted b) of nearly 6,357 km (3,950 mi).

A globally-average value is usually considered to be 6,371 kilometres (3,959 mi) with a 0.3% variability (±10 km) for the following reasons.The International Union of Geodesy and Geophysics (IUGG) provides three reference values: the mean radius (R₁) of three radii measured at two equator points and a pole; the authalic radius, which is the radius of a sphere with the same surface area (R₂); and the volumetric radius, which is the radius of a sphere having the same volume as the ellipsoid (R₃). All three values are about 6,371 kilometres (3,959 mi).

The Universal Transverse Mercator (UTM) is a projected coordinate system based on the transverse Mercator map projection of the Earth spheroid. As a map projection, it transforms geographic coordinates of locations on Earth's surface to assign plane coordinates to them. It is a horizontal position representation, which means it ignores altitude and treats the earth surface as an oblate ellipsoid. The system divides Earth into 60 zones and projects each to the plane as a basis for its coordinates. Specifying a location means specifying the zone and the x, y coordinate in that plane.

UTM parameter specifications vary by nation or region or mapping system. However, most zones in UTM span 6 degrees of longitude, and each has a designated central meridian. In each zone, the scale factor at the central meridian is specified to be 0.9996 of true scale (for most UTM systems in use). Therefore maps, atlases, and topographic grid systems built from an appropriate collection of UTM zones cover a region with planar maps with well-controlled, minimal distortion. For this reason, UTM coordinates are used in many nations and regions for topographic mapping, as well as more generally for pinpointing locations.