文档介绍：会计学
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测绘学章地理基础
1、地球结构
We think of the
earth as a sphere ...
... when it is actually an ellipsoid, slightly larger in radius at the equator than at the poles.
椭圆Ellipse
An ellipse is defined by:
Focal length =
Flattening ratio: f = (a-b)/a
Distance F1-P-F2 is constant for all points P on ellipse
When = 0 then ellipse = circle
For the earth:
Major axis: a = 6378 km
Minor axis: b = 6357 km
Flattening ratio: f = 1/300
P
O
a
b
X
Z
F1
F2
P
地图数学基础
地球椭球体 : 地球是一个表面很复杂的球体，人们以假想的平均静止的海水面形成的“大地体”为参照，推求出近似的椭球体，理论和实践证明，该椭球体近似一个以地球短轴为轴的椭园而旋转的椭球面，这个椭球面可用数学公式表达，将自然表面上的点归化到这个椭球面上，就可以计算了。
常用的一些椭球及参数 海福特椭球(1910) 我国52年以前基准椭球 a=6378388m b= α=
克拉索夫斯基椭球(1940 Krassovsky) 北京54坐标系基准椭球 a=6378245m b= α= (国际大地测量协会1975) 西安80坐标系基准椭球 a=6378140m b= α=
WGS-84椭球(GPS全球定位系统椭球、17届国际大地测量协会) WGS-84 GPS 基准椭球 a=6378137m b= α=
地图数学基础
Name of ellipsoid
Earth’s axis (m)
Datum
Geodetic Reference System 1980 (GRS80)
6,378,137
World Geodetic System 1984
World Geodetic System 1972 (WGS72)
6,378,135
World Geodetic System 1972
Geodetic Reference System 1967
6,378,160
Australian Datum 1966
South American Datum 1969
Krassovski (1942)
6,378,245
Pulkovo Datum 1942
International (Hayford 1924)
6,378,388
European Datum 1950
Clark (1866)
6,378,206
North American Datum 1927
Bessel (1841)
6,377,397
German DHDN
椭圆体或回转椭圆体Ellipsoid or Spheroid
O
X
Z
Y
a
a
b
Rotational axis
Rotate an ellipse around one of its axis.
标准椭圆体Standard Ellipsoids
标准水平大地测量数据Standard Horizontal Geodetic Data
NAD27 (North American Datum of 1927) uses the Clarke (1866) ellipsoid.
NAD83 (North American Datum of 1983) uses the GRS80 ellipsoid.
WGS84 (World Geodetic System of 1984) uses GRS80.
地表Earth Surfaces
大地水准面是恒定重力的一个