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地心天球参考系到地球参考系转换（IERS96）
简述
从地心天球参考系（Geocentric Celestial Reference System）到国际地球参考系（International Terrestrial Reference System）有不同的版本，这里介绍 IERS96规范中的算法。IAU2000\IAU2006转换方法将在后续给出。
在IERS中称为从天球参考系（Celestial Reference System ）到协议地球参考系（Terrestrial Reference System）的转换。其转换过程为 \[{{\mathbf{r}}_{CRS}}{\mathbf{ = P}}\left( {\mathbf{t}} \right){\mathbf{N}}\left( {\mathbf{t}} \right){\mathbf{R}}\left( {\mathbf{t}} \right){\mathbf{W}}\left( {\mathbf{t}} \right){{\mathbf{r}}_{TRS}}\] 由于坐标转换矩阵为正交矩阵，其逆矩阵就是其转置。因此从TRS到CRS的转换过程就不再赘述。转换过程中的几个矩阵分别为岁差、章动、地球自转和极移矩阵。
岁差矩阵
历元时刻的平赤道平春分点相对于J2000平赤道平春分点由以下三个角度定义，即 \[\begin{gathered} \varsigma = 2306''.2182T + 0''.30188{T^2} + 0''.017998{T^3} \hfill \\ \vartheta = 2004''.3109T{\text{ }} - {\text{ }}0''.42665{T^2} - {\text{ }}0''.041833{T^3} \hfill \\ z = 2306''.2181T{\text{ }} + {\text{ }}1''.09468{T^2} + {\text{ }}0''.018203{T^3} \hfill \\ \end{gathered} \] 岁差矩阵为三个角度的旋转矩阵，即 \[{\mathbf{P}} = {{\mathbf{R}}_z}\left( { - z} \right){{\mathbf{R}}_y}\left( \vartheta \right){{\mathbf{R}}_z}\left( { - \varsigma } \right)\] 其中 \[T = \left( {J{D_{TT}} - 2451545.0} \right)/36525.0\] 为地球时从J2000TT时刻起算的儒略世纪数。章动矩阵
IAU1980章动理论是在一个刚体地球改进模型上建立的。其理论包含固体地核和流体外层地核和一些弹性模型。甚长基线干涉和激光测月表明， IAU1976岁差和IAU980章动模型理论存在毫秒量级的误差。因此提出了天极偏移量的改正。改正的模型增加修正项后为 \[\begin{gathered} \Delta \psi = \Delta {\psi _{IAU1980}} + \delta \Delta \psi \hfill \\ \Delta \varepsilon = \Delta {\varepsilon _{IAU1980}} + \delta \Delta \varepsilon \hfill \\ \end{gathered} \] 因此章动模型的改正式为（McCarthy 1996） \[{\mathbf{N}} = \left[ {\begin{array}{*{20}{c}} 1&{ - \delta \Delta \psi \cos {\varepsilon _t}}&{ - \delta \Delta \psi \sin {\varepsilon _t}} \\ {\delta \Delta \psi \cos {\varepsilon _t}}&1&{ - \delta \Delta {\varepsilon _t}} \\ {\delta \Delta \psi \sin {\varepsilon _t}}&{\delta \Delta {\varepsilon _t}}&1 \end{array}} \right]{{\mathbf{N}}_{IAU1980}}\] \[{\varepsilon _t} = {\varepsilon _A} + \Delta \varepsilon \] \[{\varepsilon _A} = {\text{ }}84381''.448{\text{ }} - {\text{ }}46''.8150T{\text{ }} - {\text{ }}0''.00059{T^2} + {\text{ }}0''.001813{T^3}\] \[{{\mathbf{N}}_{IAU1980}} = {{\mathbf{R}}_x}\left( { - {\varepsilon _A}} \right){{\mathbf{R}}_z}\left( {\Delta \psi } \right){{\mathbf{R}}_x}\left( {{\varepsilon _A} + \Delta \varepsilon } \right)\] \[\Delta \psi = \sum\limits_{i = 1}^{106} {\left( {{A_i} + A{'_i}t} \right)\sin \left( {AGUMEN{T_i}} \right)} \] \[\Delta \varepsilon = \sum\limits_{i = 1}^{106} {\left( {{B_i} + B{'_i}t} \right)\cos \left( {AGUMEN{T_i}} \right)} \] \[AGUMEN{T_i} = {p_{l,i}}l + {p_{l',i}}l' + {p_{F,i}}F + {p_{D,i}}D + {p_{\Omega ,i}}\Omega \] Delaunay幅角 \[\left\{ \begin{gathered} l = 134^\circ 57'46''.733 + {\text{ }}477198^\circ 52'02''33T + 31''310{T^2} + 0''.064{T^3} \hfill \\ l'{\text{ }} = 357^\circ 31'39''.804 + 35999^\circ 03101''.224T - 0''.577{T^2} - 0''.012{T^3} \hfill \\ F = 93^\circ 16'18''.877 + 483202^\circ 01'03''.137T - 13''.257{T^2} + 0''.011{T^3} \hfill \\ D = 297^\circ 51'01''.307 + 445267^\circ 06'41''.328T - 6''.891{T^2} + 0''.019{T^3} \hfill \\ Q = 125^\circ 02'40''.280 - 1934^\circ 08'10''.539T + 7''.455{T^2} + 0''.008{T^3} \hfill \\ \end{gathered} \right.\] 其中 \[{A_i},A{'_i},{B_i},B{'_i}{p_{l,i}},{p_{l',i}},{p_{F,i}},{p_{D,i}},{p_{\Omega ,i}}\] 由IAU1980章动模型给出。