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 Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input Detailed_Output Parameters Exceptions Files Particulars Examples Restrictions Literature_References Author_and_Institution Version Index_Entries

Procedure

```   radrec_c ( Range, RA and DEC to rectangular coordinates )

void radrec_c ( SpiceDouble range,
SpiceDouble ra,
SpiceDouble dec,
SpiceDouble rectan[3] )

```

Abstract

```   Convert from range, right ascension, and declination to
rectangular coordinates.
```

```   None.
```

Keywords

```   CONVERSION
COORDINATES

```

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.

/.
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables
./
SpiceDouble          decb;
SpiceDouble          decj;
SpiceDouble          mtrans [3][3];
SpiceDouble          r;
SpiceDouble          rab;
SpiceDouble          raj;
SpiceDouble          v1950  [3];
SpiceDouble          v2000  [3];

/.
Set the initial right ascension and declination
coordinates of the object, given with respect
to the B1950 reference frame.
./
rab  = 135.88680896;
decb =  17.50151037;

/.
Convert `rab' and `decb' to a 3-vector expressed in
the B1950 frame.
./
radrec_c ( 1.0, rab * rpd_c(), decb * rpd_c(), v1950 );

/.
We use the CSPICE routine pxform_c to obtain the
transformation  matrix for converting vectors between
the B1950 and J2000 reference frames.  Since
both frames are inertial, the input time value we
supply to pxform_c is arbitrary.  We choose zero
seconds past the J2000 epoch.
./
pxform_c ( "B1950", "J2000", 0.0, mtrans );

/.
Transform the vector to the J2000 frame.
./
mxv_c ( mtrans, v1950, v2000 );

/.
Find the right ascension and declination of the
J2000-relative vector.
./
recrad_c ( v2000, &r, &raj, &decj );

/.
Output the results.
./
printf( "Right ascension (B1950 frame): %f\n", rab );
printf( "Declination (B1950 frame)    : %f\n", decb );

printf( "Right ascension (J2000 frame): %f\n", raj * dpr_c() );
printf( "Declination (J2000 frame)    : %f\n", decj * dpr_c() );

return ( 0 );
}

When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:

Right ascension (B1950 frame): 135.886809
Declination (B1950 frame)    : 17.501510
Right ascension (J2000 frame): 136.587682
Declination (J2000 frame)    : 17.300443

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.

/.
./
#include <math.h>
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local parameters.
./
#define NCOORD       15

/.
Local variables
./
SpiceDouble          pole   [3];
SpiceDouble          mtrans [3][3];
SpiceDouble          v2000  [3];
SpiceInt             i;

/.
Define a set of 15 right ascension-declination
coordinate pairs (in degrees) for the Earth's pole
and the array of corresponding ephemeris times in
J2000 TDB seconds.
./
SpiceDouble          ra     [NCOORD] = { 180.003739, 180.003205,
180.002671, 180.002137,
180.001602, 180.001068,
180.000534, 360.000000,
359.999466, 359.998932,
359.998397, 359.997863,
359.997329, 359.996795,
359.996261 };

SpiceDouble          dec    [NCOORD] = { 89.996751, 89.997215,
89.997679, 89.998143,
89.998608, 89.999072,
89.999536, 90.000000,
89.999536, 89.999072,
89.998607, 89.998143,
89.997679, 89.997215,
89.996751 };

SpiceDouble          et     [NCOORD] = { -18408539.52023917,
-15778739.49107254,
-13148939.46190590,
-10519139.43273926,
-7889339.40357262,
-5259539.37440598,
-2629739.34523934,
60.68392730,
2629860.71309394,
5259660.74226063,
7889460.77142727,
10519260.80059391,
13149060.82976055,
15778860.85892719,
18408660.88809383 };

SpiceDouble          z      [3] = { 0.0, 0.0, 1.0 };

/.
Load a PCK kernel.
./
furnsh_c ( "pck00010.tpc" );

/.
Print the banner out.
./
printf( "       et           Angular difference\n" );
printf( "------------------  ------------------\n" );

for ( i = 0; i < NCOORD; i++ )
{

/.
Convert the right ascension and declination
coordinates (in degrees) to rectangular.
./
radrec_c ( 1.0, ra[i] * rpd_c(), dec[i] * rpd_c(), v2000 );

/.
Retrieve the transformation matrix from the J2000
frame to the IAU_EARTH frame.
./
pxform_c ( "J2000", "IAU_EARTH", et[i], mtrans );

/.
Rotate the `v2000' vector into IAU_EARTH. This vector
should equal (round-off) the Z direction unit vector.
./
mxv_c ( mtrans, v2000, pole );

/.
Output the ephemeris time and the angular separation
between the rotated vector and the Z direction unit
vector.
./
printf( "%18.8f  %17.16f\n",
et[i], vsep_c ( pole, z ) * dpr_c() );

}

return ( 0 );
}

When this program was executed on a Mac/Intel/cc/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

```   N.J. Bachman        (JPL)
J. Diaz del Rio     (ODC Space)
E.D. Wright         (JPL)
```

Version

```   -CSPICE Version 1.0.3, 10-AUG-2021 (JDR)

Edited the header to comply with NAIF standard. Added complete
code example based on existing code fragment and a second
example.

-CSPICE Version 1.0.2, 28-JUL-2003 (NJB)

-CSPICE Version 1.0.1, 13-APR-2000 (NJB)

Made some minor updates and corrections in the code example.

-CSPICE Version 1.0.0, 08-FEB-1998 (EDW)
```

Index_Entries

```   range ra and dec to rectangular coordinates
right_ascension and declination to rectangular
```
`Fri Dec 31 18:41:11 2021`