From d54fe7c1f704a63824c5bfa0ece65245572e9b27 Mon Sep 17 00:00:00 2001 From: Joseph Hunkeler Date: Wed, 4 Mar 2015 21:21:30 -0500 Subject: Initial commit --- src/slalib/sun67.htx/node211.html | 232 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 232 insertions(+) create mode 100644 src/slalib/sun67.htx/node211.html (limited to 'src/slalib/sun67.htx/node211.html') diff --git a/src/slalib/sun67.htx/node211.html b/src/slalib/sun67.htx/node211.html new file mode 100644 index 0000000..2a8cbee --- /dev/null +++ b/src/slalib/sun67.htx/node211.html @@ -0,0 +1,232 @@ + + + + +Mean Place Transformations + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: Mean Place to Apparent Place +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Different Sorts of Mean Place +

+

+

+Mean Place Transformations +

+Figure 1 is based upon three varieties of mean $[\,\alpha,\delta\,]$ all of which are +of practical significance to observing astronomers in the present era: + +The figure outlines the steps required to convert positions in +any of these systems to a J2000 $[\,\alpha,\delta\,]$ for the current +epoch, as might be required in a telescope-control +program for example. +Most of the steps can be carried out by calling a single +SLALIB routines; there are other SLALIB routines which +offer set-piece end-to-end transformation routines for common cases. +Note, however, that SLALIB does not set out to provide the capability +for arbitrary transformations of star-catalogue data +between all possible systems of mean $[\,\alpha,\delta\,]$.Only in the (common) cases of FK4, equinox and epoch B1950, +to FK5, equinox and epoch J2000, and vice versa are +proper motion, parallax and radial velocity transformed +along with the star position itself, the +focus of SLALIB support. +

+As an example of using SLALIB to transform mean places, here is +a program which implements the top-left path of Figure 1. +An FK4 $[\,\alpha,\delta\,]$ of arbitrary equinox and epoch and with +known proper motion and +parallax is transformed into an FK5 J2000 $[\,\alpha,\delta\,]$ for the current +epoch. As a test star we will use $\alpha=$$16^{h}\,09^{m}\,55^{s}.13$,$\delta=$$-75^{\circ}\,59^{'}\,27^{''}.2$, equinox 1900, epoch 1963.087, +$\mu_\alpha=$$-0^{\rm s}\hspace{-0.3em}.0312$/y, $\mu_\delta=$ $+0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.103$ /y, +parallax = + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.062$ , radial velocity = -34.22 km/s. The +epoch of observation is 1994.35. +

+            IMPLICIT NONE
+            DOUBLE PRECISION AS2R,S2R
+            PARAMETER (AS2R=4.8481368110953599D-6,S2R=7.2722052166430399D-5)
+            INTEGER J,I
+            DOUBLE PRECISION R0,D0,EQ0,EP0,PR,PD,PX,RV,EP1,R1,D1,R2,D2,R3,D3,
+           :                 R4,D4,R5,D5,R6,D6,EP1D,EP1B,W(3),EB(3),PXR,V(3)
+            DOUBLE PRECISION sla_EPB,sla_EPJ2D
+
+      *  RA, Dec etc of example star
+            CALL sla_DTF2R(16,09,55.13D0,R0,J)
+            CALL sla_DAF2R(75,59,27.2D0,D0,J)
+            D0=-D0
+            EQ0=1900D0
+            EP0=1963.087D0
+            PR=-0.0312D0*S2R
+            PD=+0.103D0*AS2R
+            PX=0.062D0
+            RV=-34.22D0
+            EP1=1994.35D0
+
+      *  Epoch of observation as MJD and Besselian epoch
+            EP1D=sla_EPJ2D(EP1)
+            EP1B=sla_EPB(EP1D)
+
+      *  Space motion to the current epoch
+            CALL sla_PM(R0,D0,PR,PD,PX,RV,EP0,EP1B,R1,D1)
+
+      *  Remove E-terms of aberration for the original equinox
+            CALL sla_SUBET(R1,D1,EQ0,R2,D2)
+
+      *  Precess to B1950
+            R3=R2
+            D3=D2
+            CALL sla_PRECES('FK4',EQ0,1950D0,R3,D3)
+
+      *  Add E-terms for the standard equinox B1950
+            CALL sla_ADDET(R3,D3,1950D0,R4,D4)
+
+      *  Transform to J2000, no proper motion
+            CALL sla_FK45Z(R4,D4,EP1B,R5,D5)
+
+      *  Parallax
+            CALL sla_EVP(sla_EPJ2D(EP1),2000D0,W,EB,W,W)
+            PXR=PX*AS2R
+            CALL sla_DCS2C(R5,D5,V)
+            DO I=1,3
+               V(I)=V(I)-PXR*EB(I)
+            END DO
+            CALL sla_DCC2S(V,R6,D6)
+             :
+
+

+It is interesting to look at how the $[\,\alpha,\delta\,]$ changes during the +course of the calculation: +


+		 16 09 55.130 -75 59 27.20 		 		 original equinox and epoch
+		 16 09 54.155 -75 59 23.98 		 		 with space motion
+		 16 09 54.229 -75 59 24.18 		 		 with old E-terms removed
+		 16 16 28.213 -76 06 54.57 		 		 precessed to 1950.0
+		 16 16 28.138 -76 06 54.37 		 		 with new E-terms
+		 16 23 07.901 -76 13 58.87 		 		 J2000, current epoch
+		 16 23 07.907 -76 13 58.92 		 		 including parallax
+
+

+Other remarks about the above (unusually complicated) example: +

+
+ +next + +up + +previous +
+ Next: Mean Place to Apparent Place +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Different Sorts of Mean Place +

+

+

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +
+ + -- cgit