| radrec |
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Table of contents
Procedure
RADREC ( Range, RA and DEC to rectangular coordinates )
SUBROUTINE RADREC ( RANGE, RA, DEC, RECTAN )
Abstract
Convert from range, right ascension, and declination to
rectangular coordinates.
Required_Reading
None.
Keywords
CONVERSION
COORDINATES
Declarations
IMPLICIT NONE
DOUBLE PRECISION RANGE
DOUBLE PRECISION RA
DOUBLE PRECISION DEC
DOUBLE PRECISION RECTAN ( 3 )
Brief_I/O
VARIABLE I/O DESCRIPTION
-------- --- ---------------------------------------------------
RANGE I Distance of a point from the origin.
RA I Right ascension of point in radians.
DEC I Declination of point in radians.
RECTAN O Rectangular coordinates of the point.
Detailed_Input
RANGE is the distance of the point from the origin. Input
should be in terms of the same units in which the
output is desired.
RA is the right ascension of the point. This is the angular
distance measured toward the east from the prime
meridian to the meridian containing the input point.
The direction of increasing right ascension is from
the +X axis towards the +Y axis.
The range (i.e., the set of allowed values) of
RA is unrestricted. Units are radians.
DEC is the declination of the point. This is the angle from
the XY plane of the ray from the origin through the
point.
The range (i.e., the set of allowed values) of
DEC is unrestricted. Units are radians.
Detailed_Output
RECTAN is the array containing the rectangular coordinates of
the point.
The units associated with RECTAN are those
associated with the input RANGE.
Parameters
None.
Exceptions
Error free.
Files
None.
Particulars
This routine converts the right ascension, declination, and range
of a point into the associated rectangular coordinates.
The input is defined by a distance from a central reference point,
an angle from a reference meridian, and an angle above the equator
of a sphere centered at the central reference point.
Examples
The numerical results shown for these examples may differ across
platforms. The results depend on the SPICE kernels used as
input, the compiler and supporting libraries, and the machine
specific arithmetic implementation.
1) Convert to the J2000 frame the right ascension and declination
of an object initially expressed with respect to the B1950
reference frame.
Example code begins here.
PROGRAM RADREC_EX1
IMPLICIT NONE
C
C SPICELIB functions.
C
DOUBLE PRECISION DPR
DOUBLE PRECISION RPD
C
C Local variables
C
DOUBLE PRECISION DECB
DOUBLE PRECISION DECJ
DOUBLE PRECISION MTRANS ( 3, 3 )
DOUBLE PRECISION R
DOUBLE PRECISION RAB
DOUBLE PRECISION RAJ
DOUBLE PRECISION V1950 ( 3 )
DOUBLE PRECISION V2000 ( 3 )
C
C Set the initial right ascension and declination
C coordinates of the object, given with respect
C to the B1950 reference frame.
C
RAB = 135.88680896D0
DECB = 17.50151037D0
C
C Convert RAB and DECB to a 3-vector expressed in
C the B1950 frame.
C
CALL RADREC ( 1.D0, RAB * RPD(), DECB * RPD(), V1950 )
C
C We use the SPICELIB routine PXFORM to obtain the
C transformation matrix for converting vectors between
C the B1950 and J2000 reference frames. Since
C both frames are inertial, the input time value we
C supply to PXFORM is arbitrary. We choose zero
C seconds past the J2000 epoch.
C
CALL PXFORM ( 'B1950', 'J2000', 0.D0, MTRANS )
C
C Transform the vector to the J2000 frame.
C
CALL MXV ( MTRANS, V1950, V2000 )
C
C Find the right ascension and declination of the
C J2000-relative vector.
C
CALL RECRAD ( V2000, R, RAJ, DECJ )
C
C Output the results.
C
WRITE(*,*) 'Right ascension (B1950 frame): ', RAB
WRITE(*,*) 'Declination (B1950 frame) : ', DECB
WRITE(*,*) 'Right ascension (J2000 frame): ',
. RAJ * DPR()
WRITE(*,*) 'Declination (J2000 frame) : ',
. DECJ * DPR()
END
When this program was executed on a Mac/Intel/gfortran/64-bit
platform, the output was:
Right ascension (B1950 frame): 135.88680896000000
Declination (B1950 frame) : 17.501510369999998
Right ascension (J2000 frame): 136.58768235448090
Declination (J2000 frame) : 17.300442748830637
2) Define a set of 15 right ascension-declination data pairs for
the Earth's pole at different ephemeris epochs, convert them
to rectangular coordinates and compute the angular separation
between these coordinates and the IAU_EARTH pole given by a
PCK kernel.
Use the PCK kernel below to load the required triaxial
ellipsoidal shape model and orientation data for the Earth.
pck00010.tpc
Example code begins here.
PROGRAM RADREC_EX2
IMPLICIT NONE
C
C SPICELIB functions.
C
DOUBLE PRECISION DPR
DOUBLE PRECISION RPD
DOUBLE PRECISION VSEP
C
C Local parameters.
C
INTEGER NCOORD
PARAMETER ( NCOORD = 15 )
C
C Local variables
C
DOUBLE PRECISION DEC ( NCOORD )
DOUBLE PRECISION ET ( NCOORD )
DOUBLE PRECISION POLE ( 3 )
DOUBLE PRECISION MTRANS ( 3, 3 )
DOUBLE PRECISION RA ( NCOORD )
DOUBLE PRECISION V2000 ( 3 )
DOUBLE PRECISION Z ( 3 )
INTEGER I
C
C Define a set of 15 right ascension-declination
C coordinate pairs (in degrees) for the Earth's pole
C and the array of corresponding ephemeris times in
C J2000 TDB seconds.
C
DATA RA /
. 180.003739D0, 180.003205D0, 180.002671D0,
. 180.002137D0, 180.001602D0, 180.001068D0,
. 180.000534D0, 360.000000D0, 359.999466D0,
. 359.998932D0, 359.998397D0, 359.997863D0,
. 359.997329D0, 359.996795D0, 359.996261D0 /
DATA DEC /
. 89.996751D0, 89.997215D0, 89.997679D0,
. 89.998143D0, 89.998608D0, 89.999072D0,
. 89.999536D0, 90.000000D0, 89.999536D0,
. 89.999072D0, 89.998607D0, 89.998143D0,
. 89.997679D0, 89.997215D0, 89.996751D0 /
DATA ET / -18408539.52023917D0,
. -15778739.49107254D0, -13148939.46190590D0,
. -10519139.43273926D0, -7889339.40357262D0,
. -5259539.37440598D0, -2629739.34523934D0,
. 60.68392730D0, 2629860.71309394D0,
. 5259660.74226063D0, 7889460.77142727D0,
. 10519260.80059391D0, 13149060.82976055D0,
. 15778860.85892719D0, 18408660.88809383D0 /
DATA Z / 0.D0, 0.D0, 1.D0 /
C
C Load a PCK kernel.
C
CALL FURNSH ( 'pck00010.tpc' )
C
C Print the banner out.
C
WRITE(*,'(A)') ' ET Angular difference'
WRITE(*,'(A)') '------------------ ------------------'
DO I = 1, NCOORD
C
C Convert the right ascension and declination
C coordinates (in degrees) to rectangular.
C
CALL RADREC ( 1.D0, RA(I) * RPD(), DEC(I) * RPD(),
. V2000 )
C
C Retrieve the transformation matrix from the J2000
C frame to the IAU_EARTH frame.
C
CALL PXFORM ( 'J2000', 'IAU_EARTH', ET(I), MTRANS )
C
C Rotate the V2000 vector into IAU_EARTH. This vector
C should equal (round-off) the Z direction unit vector.
C
CALL MXV ( MTRANS, V2000, POLE )
C
C Output the ephemeris time and the angular separation
C between the rotated vector and the Z direction unit
C vector.
C
WRITE(*,'(F18.8,2X,F18.16)') ET(I),
. VSEP( POLE, Z ) * DPR()
END DO
END
When this program was executed on a Mac/Intel/gfortran/64-bit
platform, the output was:
ET Angular difference
------------------ ------------------
-18408539.52023917 0.0000001559918278
-15778739.49107254 0.0000000106799881
-13148939.46190590 0.0000001773517911
-10519139.43273926 0.0000003440236194
-7889339.40357262 0.0000004893045693
-5259539.37440598 0.0000003226327536
-2629739.34523934 0.0000001559609507
60.68392730 0.0000000107108706
2629860.71309394 0.0000001773826862
5259660.74226063 0.0000003440544891
7889460.77142727 0.0000004892736740
10519260.80059391 0.0000003226018712
13149060.82976055 0.0000001559300556
15778860.85892719 0.0000000107417474
18408660.88809383 0.0000001774135760
Restrictions
None.
Literature_References
[1] L. Taff, "Celestial Mechanics, A Computational Guide for the
Practitioner," Wiley, 1985
Author_and_Institution
C.H. Acton (JPL)
N.J. Bachman (JPL)
J. Diaz del Rio (ODC Space)
H.A. Neilan (JPL)
W.L. Taber (JPL)
Version
SPICELIB Version 1.1.0, 06-JUL-2021 (JDR)
Added IMPLICIT NONTE statement.
Edited the header to comply with NAIF standard. Removed
unnecessary $Revisions section.
Added complete code example based on existing code fragment
and a second example.
SPICELIB Version 1.0.2, 30-JUL-2003 (NJB) (CHA)
Various header changes were made to improve clarity. Some
minor header corrections were made.
SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)
Comment section for permuted index source lines was added
following the header.
SPICELIB Version 1.0.0, 31-JAN-1990 (HAN)
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Fri Dec 31 18:36:41 2021