Earth science problems. . .

The geoid is an irregular closed surface formed by the static sea surface and extending to the mainland. It is the equipotential surface of gravity, that is, when an object moves along this surface, gravity does not do work (for example, water will not flow on this surface). Geoid is an important physical reference surface to describe the shape of the earth, and it is also the starting surface of altitude system. The determination of geoid is realized by determining the distance between it and the reference ellipsoid-geoid (for quasi-geoid, it is called elevation anomaly).

Earth ellipsoid is also called "Earth ellipsoid" and "Earth oblate sphere". A mathematical surface representing the size and shape of the earth. Expressed as long radius and oblateness. Because it is very close to the ellipsoid, the reference ellipsoid is usually used to represent the shape and size of the earth ellipsoid. A figure formed by an ellipse rotating around its short axis, which is similar to the geoid of the earth. The shape of the geoid is expressed by the deviation from the reference ellipsoid. Generally speaking, the shape and size of the earth are actually expressed by the semi-major diameter, semi-minor diameter and oblateness of the reference ellipsoid. The data recommended by the International Union of Geodesy and Geophysics in 1975 are: semi-long diameter 6378140m, semi-short diameter 6356755m, flatness 1∶298.257. Generally speaking, it is a smooth and regular globe formed by the rapid rotation of the earth around the short axis. It is a description of the shape of the earth and is defined for the calculation of measurement results and the needs of surveying and mapping.

To establish a parametric coordinate system, the following tasks need to be completed:

① Select or determine the geometric parameters (long radius and short radius) of the ellipsoid; ② Determine the center position (positioning) of the ellipsoid; ③ Determine the direction (orientation) of the short axis of the ellipsoid; (4) establish the origin of the earth.

To establish geodetic coordinate system (taking 80 Xi coordinate system as an example), we must first determine the geodetic origin and establish a reference ellipsoid. The origin of the earth is determined by various conditions, and it is usually chosen in the middle of the country, Yongle Town, Jingyang County, Xi. For the reference ellipsoid, the geometric parameters must be determined first. The geometric parameter of 80 Xi 'an coordinate system is 75 IUGG. The second is positioning. Positioning is determined by the position of the origin of the earth. Xi 'an coordinate system is multi-point, so the reference ellipsoid is not tangent to Xi 'an geodetic origin, but close to China territory. Thirdly, orientation is determined by the basic requirements of ellipsoid orientation.

After the reference ellipsoid is determined, the other parts of the country are projected onto the reference ellipsoid by Gaussian-Kruger projection method (if it is Gaussian projection), and then the coordinates of other points are obtained according to the position of the origin of the earth, and then the national geodetic coordinate system is established.

A, for 80 xi coordinate system:

1. Geometric parameters of ellipsoid:

The recommended value 1975 of the International Land Federation is selected, and its geometric parameters are: long radius A = 6 378 140m, flatness = 1: 298.247.

2. Multipoint positioning.

3. Clear direction:

The minor axis is parallel to the earth's center of mass and points to the origin 1968.0, and the initial geodetic meridian plane is parallel to the initial astronomical meridian plane of China, that is, ωx=ωy=ωz=0.

Second, the ellipsoid positioning orientation

1. Positioning and orientation conditions of reference ellipsoid:

The short axis of (1) ellipsoid is parallel to the earth rotation axis of the specified epoch, that is, ωx=0 and ωy=0.

(2) The earth's initial meridian plane is parallel to the astronomical initial meridian plane, that is, ωz=0 (the above two points are "clear orientation")

(3) In a certain area, the ellipsoid is the closest to the geoid, that is, σσN2 = min (mainly used for positioning, that is, to determine the position of the center of the ellipsoid).

2. About positioning:

(1) positioning methods can be divided into single-point positioning and multi-point positioning.

(2) Single point positioning: At the origin K of the earth, the normal direction of the ellipsoid coincides with the vertical direction, and the ellipsoid is tangent to the geoid. The result is often difficult to make ellipsoid and geoid fit well in a large range.

③ Multi-point positioning:

<1> definition: after the astronomical geodesy of a country or region is carried out or basically completed at a certain time, a new geocentric coordinate system is established by calculation according to the generalized arc measurement equation and the condition of = minimum value by using the measurement results of many Laplacian points (that is, the large places where astronomical longitude, astronomical latitude and astronomical azimuth are measured) and the existing ellipsoid parameters. This method is usually called multi-point positioning method because it contains many Laplacian points.

& lt2> Results: The ellipsoid is no longer tangent to the geoid of the origin of the earth, but it has the best fitting with the geoid within the data range of astronomical geodetic network.

Third, the origin of the earth

The origin of the earth is artificially determined, and it has many requirements. The following is what I picked from the Internet: "From 1975, I organized manpower, collected and analyzed a large amount of data, and conducted on-the-spot investigation and comprehensive analysis on the topography, geology, geotectonics, astronomy, gravity and geodesy of Zhengzhou, Wuhan, Xi and Lanzhou according to the requirements of the" origin ".

4. For the establishment of the classical parametric geodetic coordinate system, the positioning and orientation of the reference ellipsoid is realized by determining the initial data of the geodetic origin, and determining the initial data is the result of the positioning and orientation of the ellipsoid. No matter which positioning and orientation method is used to establish the national geodetic coordinate system, there must be one and only one geodetic origin, otherwise the positioning and orientation results will not be clearly displayed.

Therefore, a reference ellipsoid and a geodetic origin are calculated to determine a coordinate system. Usually, the establishment of reference ellipsoid and the initial data of the origin of the earth are used as signs for the establishment of parametric geodetic coordinate system.