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大地坐标系 - Wikipedia

大地坐标系

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大地坐标系
大地坐标系

-{T|zh-cn:大地坐标系;zh-tw:大地座標系}- -{A|zh-cn:大地坐标系;zh-tw:大地座標系}-系由大地经度和大地纬度构成的坐标系。

由右图所示,P点的子午面NPS与起始子午面NGS所构成的二面角L,叫做P点的大地经度,由起始子午面起算,向东为正,叫东经(0度~180度),向西为负,叫西经(0度~180度)。P点的法线Pn与赤道面的夹角B,叫做P点的大地纬度,由赤道面起算,向北为正,叫北纬(0度~90度),向南为负,叫南纬(0度~90度)。在该坐标系中,P点的位置用L,B表示,如果点不再椭球面上,表示点的位置除L,B外,还要附加另一个参数——大地高H。


  • 大地坐标系和子午面直角坐标系的关系
    • x=\frac{acosB}{\sqrt{1-e^{2}sin^{2}B}}
    • y=\frac{a(1-e^{2})sinB}{\sqrt{1-e^{2}sin^{2}B}}

式中,a为地球椭球的长半轴,e为地球椭球的第一偏心率 e=\frac{\sqrt{a^{2}-b^{2}}}{a},B为大地纬度。

  • 大地坐标系和空间直角坐标系的关系
    • X=\frac{acosB}{\sqrt{1-e^{2}sin^{2}B}}cosL
    • Y=\frac{acosB}{\sqrt{1-e^{2}sin^{2}B}}sinL
    • Z=\frac{bsinB}{\sqrt{1+e'^{2}cos^{2}B}}

e'为椭圆的第二偏心率 e'=\frac{\sqrt{a^{2}-b^{2}}}{b},B为大地纬度,L为大地经度,a、b为地球椭球的长、短半轴。

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