reference ellipsoid

[′ref·rəns i′lip‚sȯid]

(mapping)

A reference surface used to represent the size and shape of the earth for cartography.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Reference Ellipsoid

an earth ellipsoid with certain dimensions and a certain position in the body of the earth. It is used as an auxiliary mathematical surface to which the results of all geodetic measurements on the surface of the earth are referred and on which the points of a geodetic control network are thereby projected. Topographic surveys and maps compiled from such surveys are also referred to the surface of the reference ellipsoid. In order to refer geodetic measurements to the surface of the reference ellipsoid, we must know the height of the earth’s surface above the surface of the reference ellipsoid and the deflection of plumb line at all points at which the measurements are made. The height of the earth’s surface above the surface of the reference ellipsoid is determined by means of geometric and astronomical-gravimetric leveling. On topographic maps, however, the height of the earth’s surface is indicated with respect to sea level.

The dimensions of the reference ellipsoid are given in terms of its semimajor axis a and semiminor axis b or in terms of the semimajor axis and the flattening, or ellipticity, α, which is defined by the equation

The position of the reference ellipsoid within the earth is defined by what are called initial geodetic data, that is, the geodetic coordinates of the perpendicular projection of some point on the earth’s surface onto the reference ellipsoid, the geodetic azimuth of some direction from the point, and the height of the geoid above the reference ellipsoid at the point.

Different reference ellipsoids are used in geodetic and cartographic work in different countries. The USSR and other socialist countries use the Krasovskii ellipsoid as the reference ellipsoid. This ellipsoid is characterized by the quantities

a = 6, 378, 245 m

α = 1:298.3

The position, or orientation, of the Krasovskii ellipsoid within the earth is determined by the geodetic coordinates of the center of the Great Round Hall of the Pulkovo Observatory:

latitude B= 59°46ʹ18ʺ.55

longitude L = 30°19ʹ42ʺ.09

the azimuth to the control point Bugry is

A = 121°10ʹ38ʺ.79

The height of the geoid above the reference ellipsoid at Pulkovo is assumed equal to zero.

REFERENCES

Krasovskii, F. N. Rukovodstvo po vysshei geodezii, part 2. Moscow, 1942.
Izotov, A. A. “Novye iskhodnye geodezicheskie daty SSSR.” In Sbornik nauchno-tekhnicheskikh i proizvodstvennykh statei po geodezii, kartografii, topografii, aeros” emke i gravimetrii, fase. 17. Moscow, 1948.

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References in periodicals archive

Vertical velocity determined with the help of GNSS-measurements coincides with the normal line and is determined in accordance with the level-surface or reference ellipsoid. Non-parallelism of plumb line and normal of the Earth's surface is small and it does not affect the difference of velocity vectors which have been out of relative level surface or reference ellipsoid.

THE RESEARCH OF INTERRELATION BETWEEN SEISMIC ACTIVITY AND MODERN VERTICAL MOVEMENTS OF THE EUROPEAN PERMANENT GNSS-STATIONS

where a is the major semi-axis of the reference ellipsoid; f = (a - b)/a is the flattening of the ellipsoid; b is the minor semi-axis of the ellipsoid; [phi] is the geodetic latitude; m = [[omega].sup.2][a.sup.2]b/GM; [omega] is the angular velocity of the Earth's rotation and GM is the gravitational mass constant.

Precise levelling data processing near terraced landforms

With reference to Figure 3, we consider the projection of all sensed points within a finite region on the reference ellipsoid, centered on the ground track onto the map plane.

The space oblique conic projection

In the geometrical approach datum means the location and orientation of the reference ellipsoid in space.

On conformal geospatial transformations with complex polynomials/Konformsetest georuumilistest teisendustest komplekssete polunoomidega

Due to irregularities in mass distributions within the Earth, the geoidal heights undulate with respect to the reference ellipsoid. However, deviations of the two surfaces do not exceed [+ or -]100 m, globally.

Towards unification of terrestrial gravity data sets in Estonia/ Terrestriliste raskuskiirenduse andmete uhtlustamine Eestis

where GM is the geocentric gravitational constant; (r,l,q) the spherical coordinates of the computation point; g the normal gravity on the reference ellipsoid; a the equatorial radius of the earth; [P.sub.nm](sinq) the fully normalized associated Legendre functions for degree n and order m; [[DELTA][bar.C].sub.nm] and [[DELTA][bar.S].sub.nm] the normalized EGM-GGM harmonic coefficients, reduced for the even zonal harmonic for the ellipsoid and complete to degree and order [N.sub.max] = 360.

Accurate gravity anomaly interpolation: a case-study in Cameroon, Central Africa

Free-air anomaly is defined as the difference between the actual gravity (measured on the ground) and the normal gravity [gamma], whereas the latter is related to the normal height H (counted from the reference ellipsoid) of the survey point.

Effect of the GRACE satellite mission on gravity field studies in Fennoscandia and the Baltic Sea region/GRACE-satelliitide moju raskusjouvalja uuringutele Fennoskandia ja Balti mere piirkonnas

Thomas, P.D.: 1965, Geodesic arc length on the reference ellipsoid to second-order terms in the flattening.

Note on the direct computation of geodetic distances and azimuths on an ellipsoid of revolution

where W = [square root of (1 - [e.sup.2] [sin.sup.2] [[phi].sub.i])], [e.sup.2] is the eccentricity and f is the flattening of the reference ellipsoid.

Geoid determination for the area of Poland by the least squares modification of Stokes' formula

We symbolize [h.sub.i] as the ellipsoidal height of the GPS/leveling point i which is derived from processing of co-located GPS observations in ITRF with reference ellipsoid WGS84 and transferred to the Zero Tide System (Makinen et al.

Estimating the geopotential value [W.sub.0] of the local Geoid based on data from local and global normal heights of GPS/leveling points in Vietnam