Many used the same ellipsoid, but the ellipsoid was “fixed” to different places on Earth. References that share the same ellipsoid could have a pair of coordinates spaced hundreds of meters apart on the ground. These older references such as NAD27 and ED50 have a fundamental or origin point. A relaxed ellipsoid, i.e. in hydrostatic equilibrium, has a flattening axe – b directly proportional to its average density and radius. Ellipsoids with a differentiated interior – that is, a nucleus denser than the mantle – have less flattening than a homogeneous body. Overall, the ratio (ay–b)/(ax−b) is about 0.25, although this decreases with rapidly rotating bodies. [4] An Earth erdellipsoid or spheroid is a mathematical number that approximates the shape of the Earth and is used as a frame of reference for calculations in geodesy, astronomy and Earth sciences. Various ellipsoids were used as approximations. In general, an ellipsoid not necessarily oriented towards the axis is defined by the equation The North American date of 1983 (NAD 83) included another national adjustment, necessitated in part by the introduction of a new ellipsoid, called GRS 80. Unlike Clarke 1866, GRS 80 is a global ellipsoid focused on the center of mass of the Earth. GRS 80 essentially corresponds to WGS 84, the global ellipsoid on which the global positioning system is based. NAD 27 and NAD 83 align the grids of coordinate systems with ellipsoids.
They simply differ in that they refer to different ellipsoids. Because Clarke 1866 and GRS 80 differ slightly in the shape and position of their centers, the adjustment from NAD 27 to NAD 83 resulted in a change in the geographic coordinate grid. As a variety of references continue to be used, geospatial experts need to understand this change and how data is transformed between horizontal references. Introduction. The geoid-ellipsoid separation, N, should be evaluated so that “h” is the ellipsoidal height. of GPS can be converted to “II”, the orthometric altitude used in surveying and mapping. This can be done either by the single point (or absolute) approach, where II = h ·N. An ellipsoid is a three-dimensional geometric figure that resembles a sphere, but whose equatorial axis (a in Figure 2.15.1 above) is slightly longer than its polar axis (b).
The equatorial axis of the 1984 Global Geodetic System, for example, is about 22 kilometers longer than the polar axis, a part very similar to the flattened spheroid of planet Earth. Ellipsoids are often used as substitutes for geoids to simplify the mathematics associated with linking a coordinate system grid to a model of the shape of the Earth. Ellipsoids are good, but not perfect, approaches to the geoid. The map in Figure 2.15.2 below shows the differences in altitude between a geoid model called GEOID96 and the WGS84 ellipsoid. The surface of GEOID96 rises up to 75 meters above the WGS84 ellipsoid over New Guinea (where the map is colored red). In the Indian Ocean (where the map is colored purple), the surface of GEOID96 falls about 104 meters below the ellipsoid surface. The above statement remains true, although NAD 83 will soon be abandoned as part of the ongoing modernization of the U.S. National Spatial Reference System by the National Geodetic Survey. The transition from an ellipsoid-based “passive” reference system to a GPS-based dynamic system was planned for 2022, but has since been postponed to 2024 or -25. Visit the National Geodetic Survey for the latest information. If the three rays are equal, the solid body is a sphere; When two rays are equal, the ellipsoid is a spheroid: in the 19th and 20th centuries, different ellipsoids were adopted in different parts of the world.
Surveys have been conducted on different continents. Each survey revealed different ellipsoidal parameters. Many ellipsoids are used worldwide. (Wikipedia presents a list in its entry on erdellipsoids) Local ellipsoids minimize the differences between the geoid and the ellipsoid for individual countries or continents. The Clarke 1866 ellipsoid, for example, minimizes deviations in North America. The North American date of 1927 (NAD 27) connects the grid of geographic coordinates to the Clarke 1866 ellipsoid. NAD 27 involved adjusting the latitude and longitude coordinates of approximately 25,000 geodetic checkpoints in the United States. The national adjustment began with an initial checkpoint at Meades Ranch, Kansas, and was intended to close the gaps between the many local and regional control investigations that preceded it.
By themselves, ellipsoidal models are primarily used to measure distances across the Earth`s surface when miles and miles, rather than inches and centimeters, make the difference. For example, surveys in Australia revealed the “best” ellipsoid, which differed from South America and Asia. There was no unifying global ellipsoid. Each continental survey was isolated with its own ellipsoid parameters. Geodesists use reference ellipsoids to specify point coordinates such as latitude (north/south), longitude (east/west), and altitude (altitude). Scalene ellipsoids and cuboids rotate stably along their main or secondary axis, but not along their midline. This can be seen experimentally by throwing an eraser with a little rotation. In addition, moment of inertia considerations mean that rotation along the main axis is more easily disturbed than rotation along the secondary axis. A practical effect of this is that astronomical bodies, like scales, usually rotate along their secondary axes (as well as the Earth, which is simply flattened); In addition, Scalene moons orbit their main axis radially to their planet in synchronous orbits such as Saturn`s due to tidal locking. The most common reference ellipsoid in cartography and surveying is the World Geodetic System (WGS84).
Clarke`s ellipsoid of 1866 was recalculated for the North American date of 1927 (NAD27). The geoid is defined as the surface of the Earth`s gravity field approaching mean sea level. It is perpendicular to the direction of gravity. As the mass of the Earth is not uniform in all respects, the size of gravity varies and the shape of the geoid is irregular. Click on the link below to access a National Oceanographic & Atmospheric Administration (NOAA) website. The website contains links to images that show interpretations of the geoid in North America. NOAA Geoid IndexTo simplify the model, various spheroids or ellipsoids have been developed. These terms are used interchangeably. For the rest of this article, the term spheroid is used. A spheroid is a three-dimensional shape created from a two-dimensional ellipse. The ellipse is an oval with a main axis (the longest axis) and a secondary axis (the shortest axis). If you rotate the ellipse around one of its axes, the shape of the rotated figure is a spheroid.
Ellipsoids can also be defined in higher dimensions, such as images of spheres under invertible linear transformations.