Changeset 3772 for trunk/doc/pslib/psLibADD.tex
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- Apr 27, 2005, 9:59:04 AM (21 years ago)
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trunk/doc/pslib/psLibADD.tex (modified) (17 diffs)
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trunk/doc/pslib/psLibADD.tex
r3721 r3772 1 %%% $Id: psLibADD.tex,v 1.7 2 2005-04-19 23:44:43eugene Exp $1 %%% $Id: psLibADD.tex,v 1.73 2005-04-27 19:59:04 eugene Exp $ 2 2 \documentclass[panstarrs]{panstarrs} 3 3 … … 14 14 \project{Pan-STARRS Image Processing Pipeline} 15 15 \organization{Institute for Astronomy} 16 \version{1 0}16 \version{11} 17 17 \docnumber{PSDC-430-006} 18 18 … … 41 41 09 & 2005 Feb 14 & Frozen for Cycle 5 \\ \hline 42 42 10 & 2005 Apr 19 & Frozen for Cycle 6 \\ \hline 43 11 & 2005 Apr 27 & Update for Cycle 6 \\ \hline 43 44 \RevisionsEnd 44 45 … … 1553 1554 the quarternion for this transformation. 1554 1555 1555 \tbd{can we drop this, since we do this with the quaternion?}1556 1557 1556 The relevant trigonometric relationships are: 1558 1557 % … … 1611 1610 \phi_p & = & 90^\circ + 0^\circ.6406161\, T + 0^\circ.0003041\, T^2 + 0^\circ.0000051\, T^3 1612 1611 \end{eqnarray} 1613 where $T$ is $($MJD$_{\rm out} -$ MJD$_{\rm in})/36525$ is the difference1614 between the two epochs, in Julian centuries. 1615 1612 where $T$ is $($MJD$_{\rm out} -$ MJD$_{\rm in})/36525$ is the 1613 difference between the two epochs, in Julian centuries. This 1614 precession form shall be used to implement \code{PS_PRECESS_ROUGH}. 1616 1615 1617 1616 \subsubsection{Suggested test cases} … … 1648 1647 There are two reference implementatins for the code to account for the 1649 1648 motion of the Earth in space. The first are the sample routines 1650 provided by the IERS to accompany chaper 5 of IERS Bulletin 32. This 1651 document and the code can be downloaded from 1652 http://maia.usno.navy.mil/conv2003.html . The second reference 1653 implementation is the SOFA software package managed by the IAU and 1654 available at http://www.iau-sofa.rl.ac.uk Only the 2003-04-29 version 1655 of SOFA should be used. The IERS code requires a few of the rotation 1656 matrix utility routines from SOFA. 1649 provided by the IERS to accompany chaper 5 of IERS Bulletin 1650 32.\footnote{http://maia.usno.navy.mil/conv2003.html} The second 1651 reference implementation is the SOFA software package managed by the 1652 IAU.\footnote{http://www.iau-sofa.rl.ac.uk} Only the 2003-04-29 1653 version of SOFA should be considered. The IERS code requires a few of 1654 the rotation matrix utility routines from SOFA. 1657 1655 1658 1656 Both implementations are in FORTRAN 77. The SOFA code has a more … … 1663 1661 reference for psLib should be the IERS code. Note that the IERS code 1664 1662 calculates the transform from terrestrial to celestial coordinates, 1665 while the SOFA code calculates its inverse. 1663 while the SOFA code calculates its inverse. This code may be using as 1664 a comparison for testing purposes. 1666 1665 1667 1666 \subsubsection{Coordinate Systems} … … 1711 1710 1712 1711 The X axes of the intermediate coordinate systems are known as the 1713 Celestial and Terrestrial Ephemeris Origins. (CEO and TEO). Both are defined1714 to be non-rotating origins. A non-rotating origin is a point on the equator 1715 whose instantaneous motion is always orthogonal to the equator 1716 (Kaplan 2003 IAU XXV Joint Discussion 16 1717 \footnote{http://aa.usno.navy.mil/kaplan/NROs\%5BJD16proc\%5D.pdf}).1718 Thus the CEO is defined by its position in the GCRS at some epoch and by the1719 motion of the CIP in the GCRS since that date. Similarly the TEO is 1720 defined by its position in the ITRS at some epoch and the motion ofthe1721 CIP in the ITRS since that date.1712 Celestial and Terrestrial Ephemeris Origins. (CEO and TEO). Both are 1713 defined to be non-rotating origins. A non-rotating origin is a point 1714 on the equator whose instantaneous motion is always orthogonal to the 1715 equator (Kaplan 2003 IAU XXV Joint Discussion 1716 16\footnote{http://aa.usno.navy.mil/kaplan/NROs\%5BJD16proc\%5D.pdf}). 1717 Thus the CEO is defined by its position in the GCRS at some epoch and 1718 by the motion of the CIP in the GCRS since that date. Similarly the 1719 TEO is defined by its position in the ITRS at some epoch and the 1720 motion of the CIP in the ITRS since that date. 1722 1721 1723 1722 \subsubsection{ICRS - GCRS} … … 1793 1792 1794 1793 This section is largely a summary of Chapter 5 of IERS Technical Note 1795 32 1794 32\footnote{http://maia.usno.navy.mil/conv2003.html} (hereafter 1796 1795 IERS32), which is a description of the implementation of the 1797 1796 Resoltions of the XXIVth General Assembly of the IAU, available from … … 1807 1806 accurate to the 0.2 mas level. For higher accuracy the user must 1808 1807 apply corrections to the model, which are tabulated by the IERS. 1808 1809 \subparagraph{IAU 200A Precession/Nutation Model : {\tt psEOC\_PrecessionModel}} 1809 1810 1810 1811 The IAU 2000A precession-nutation model may be calculated in the … … 1855 1856 The constants $p_j$, $w_{i,j,k}$, $(a_{{\rm s},j})_i$, and $(a_{{\rm c},j})_i$ 1856 1857 are given in the ASCII files: 1857 tab5.2a.txt 1858 tab5.2b.txt 1859 tab5.2c.txt 1858 tab5.2a.txt\footnote{http://maia.usno.navy.mil/conv2000/chapter5/tab5.2a.txt} (for $X$), 1859 tab5.2b.txt\footnote{http://maia.usno.navy.mil/conv2000/chapter5/tab5.2b.txt} (for $Y$), and 1860 tab5.2c.txt\footnote{http://maia.usno.navy.mil/conv2000/chapter5/tab5.2c.txt} (for $s+XY/2$). 1860 1861 Note that the expansion is given for $s+XY/2$, since this series converges 1861 1862 more rapidly than the one for $s$ alone. … … 1876 1877 1877 1878 A FORTRAN reference implementation for the precession/nutation model 1878 is available from the IERS 1879 \footnote{http://maia.usno.navy.mil/conv2000/chapter5/XYS2000A.f}. 1880 The psLib results should agree with the reference implementation to within 1881 the limits of numerical precision. 1882 1883 Next, corrections to $X$, and $Y$ may be obtained from the IERS as 1879 is available from the 1880 IERS.\footnote{http://maia.usno.navy.mil/conv2000/chapter5/XYS2000A.f} 1881 The psLib results should agree with the reference implementation to 1882 within the limits of numerical precision. 1883 1884 \subparagraph{Corrections to the Model : {\tt psEOC\_PrecessionCorr}} 1885 1886 Corrections to $X$, and $Y$ may be obtained from the IERS as 1884 1887 part of Bulletin A, or B. It is recommended to use the values 1885 1888 published daily by USNO in the table … … 1895 1898 the result as instantaneous values. 1896 1899 1897 The final step is to use $X$, $Y$, and $s$ to calculate the rotation 1898 matrix from the CIP/CEO system to the GCRS using IERS32 equation (10), 1899 reproduced below: 1900 1901 \begin{equation} 1900 \subparagraph{Spherical Rotation from Polar Coordinates : {\tt psSphereRot\_CEOtoGCRS}} 1901 1902 In order to relate the values $X$, $Y$, and $s$ to the rotation 1903 components, the rotation matrix below must be used. The definitions 1904 of $X$, $Y$, and $s$ transform from the CIP/CEO system to the GCRS 1905 using IERS32 equation (10), reproduced below: 1906 1907 \begin{equation} 1908 \label{CEOtoGCRS} 1902 1909 \begin{pmatrix}1-aX^2& -aXY& X\cr -aXY& 1-aY^2& Y\cr -X& -Y& 1903 1910 1-a(X^2+Y^2)\cr 1904 1911 \end{pmatrix} \cdot R_3(s), 1905 1912 \end{equation} 1906 where $R_3$ denotes a rotation about the Z axis, 1907 $a = 1/(1+\sqrt{1 - X^2 + Y^2})$, 1908 and $X$ and $Y$ are expressed in radians. 1909 A FORTRAN reference implementation for this calculation is given 1910 by the IERS \footnote{http://maia.usno.navy.mil/conv2000/chapter5/BPN2000.f}. 1911 1912 Note that above we gave the expression for the transform toward celestial 1913 coordinates (upward in figure X), in order to match the IERS reference code. 1914 The inverse transform may be found byinverting the resulting rotation.1915 1916 \paragraph{ Rotation of the Earth}1913 where $R_3$ denotes a rotation about the Z axis, $a = 1/(1+\sqrt{1 - 1914 (X^2 + Y^2})$, and $X$ and $Y$ are expressed in radians. A FORTRAN 1915 reference implementation for this calculation is given by the 1916 IERS.\footnote{http://maia.usno.navy.mil/conv2000/chapter5/BPN2000.f} 1917 1918 Note that above we gave the expression for the transform toward 1919 celestial coordinates (upward in Figure~\ref{earthrot}), in order to 1920 match the IERS reference code. The inverse transform may be found by 1921 inverting the resulting rotation. 1922 1923 \paragraph{Earth Rotation} 1917 1924 1918 1925 The transform from the CIP/CEO to CIP/TEO coordinate systems is a … … 1931 1938 motion''. Similarly to precession/nutation, the instantaneous position 1932 1939 of the CIP in the ITRS is specified by the quantites $x_p$, and $y_p$, 1933 and a third quantity, $s'$, gives the position of the TEO with respect 1934 to the ITRS. The values of $x_p$ and $y_p$ are published daily by the 1935 IERS\footnote{http://maia.usno.navy.mil/ser7/finals2000A.daily}, with 1940 and a third quantity, $s'$, which give the position of the TEO with 1941 respect to the ITRS. The values of $x_p$ and $y_p$ are published 1942 daily by the 1943 IERS,\footnote{http://maia.usno.navy.mil/ser7/finals2000A.daily} with 1936 1944 a format described by their 1937 1945 \code{readme.finals2000A}\footnote{http://maia.usno.navy.mil/ser7/readme.finals2000A}. 1938 1946 The UT1$-$UTC, and the precession/nutation corrections (discussed 1939 1947 elsewhere in this document) come from this same source. 1948 1949 \subparagraph{Polar Motion from Bulletin : {\tt psEOC\_GetPolarMotion}} 1940 1950 1941 1951 The polar motion coordinates should be interpolated using a third … … 1953 1963 The tidal effects should be included by using the Ray tidal model 1954 1964 given in IERS Gazette \#13. The definition of this correction is 1955 provided below. 1965 provided below (Section~\ref{Raymodel}). 1966 1967 \subparagraph{Polar Motion Nutation Correction : {\tt psEOC\_NutationCorr}} 1956 1968 1957 1969 By definition of the CIP, nutation terms with periods less than 2 days … … 1966 1978 over this century by $s' = -4.7 \times 10^{-5} t$ in arcseconds. There 1967 1979 is no need to apply short timescale corrections to $s'$. 1980 1981 \subparagraph{Spherical Rotation from Polar Motion : {\tt psSphereRot\_ITRStoTEO}} 1968 1982 1969 1983 The transform from the ITRS to the CIP/TEO frame can be constructed by … … 2009 2023 correction from the Ray Tidal Model applied. 2010 2024 2011 \subsubsection{Ray Tidal Model }2025 \subsubsection{Ray Tidal Model : {\tt psEOC\_PolarTideCorr}} 2012 2026 2013 2027 The Ray Model tidal corrections to X, Y, and dT are given by the the
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