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Index Page spkezp_c
Table of contents
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
       spkezp_c ( S/P Kernel, easy position )

       void spkezp_c ( SpiceInt            targ,
                       SpiceDouble         et,
                       ConstSpiceChar    * ref,
                       ConstSpiceChar    * abcorr,
                       SpiceInt            obs,
                       SpiceDouble         ptarg[3],
                       SpiceDouble       * lt        )
#### Abstract
       Return the position of a target body relative to an observing
       body, optionally corrected for light time (planetary aberration)
       and stellar aberration.
#### Required_Reading
       SPK
       NAIF_IDS
       FRAMES
       TIME
#### Keywords
       EPHEMERIS
#### Brief_I/O
       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       targ       I   Target body NAIF ID code.
       et         I   Observer epoch.
       ref        I   Reference frame of output position vector.
       abcorr     I   Aberration correction flag.
       obs        I   Observing body NAIF ID code.
       ptarg      O   Position of target.
       lt         O   One way light time between observer and target.
#### Detailed_Input
       targ        is the NAIF ID code for a target body. The target
                   and observer define a position vector which points
                   from the observer to the target.

       et          is the ephemeris time, expressed as seconds past
                   J2000 TDB, at which the position of the target body
                   relative to the observer is to be computed. `et'
                   refers to time at the observer's location.

       ref         is the name of the reference frame relative to which
                   the output position vector should be expressed. This
                   may be any frame supported by the SPICE system,
                   including built-in frames (documented in the Frames
                   Required Reading) and frames defined by a loaded
                   frame kernel (FK).

                   When `ref' designates a non-inertial frame, the
                   orientation of the frame is evaluated at an epoch
                   dependent on the selected aberration correction. See
                   the description of the output position vector `ptarg'
                   for details.

       abcorr      indicates the aberration corrections to be applied to
                   the position of the target body to account for
                   one-way light time and stellar aberration. See the
                   discussion in the -Particulars section for
                   recommendations on how to choose aberration
                   corrections.

                   `abcorr' may be any of the following:

                      "NONE"     Apply no correction. Return the
                                 geometric position of the target body
                                 relative to the observer.

                   The following values of `abcorr' apply to the
                   "reception" case in which photons depart from the
                   target's location at the light-time corrected epoch
                   et-lt and *arrive* at the observer's location at `et':

                      "LT"       Correct for one-way light time (also
                                 called "planetary aberration") using a
                                 Newtonian formulation. This correction
                                 yields the position of the target at
                                 the moment it emitted photons arriving
                                 at the observer at `et'.

                                 The light time correction uses an
                                 iterative solution of the light time
                                 equation (see -Particulars for details).
                                 The solution invoked by the "LT" option
                                 uses one iteration.

                      "LT+S"     Correct for one-way light time and
                                 stellar aberration using a Newtonian
                                 formulation. This option modifies the
                                 position obtained with the "LT" option
                                 to account for the observer's velocity
                                 relative to the solar system
                                 barycenter. The result is the apparent
                                 position of the target---the position
                                 as seen by the observer.

                      "CN"       Converged Newtonian light time
                                 correction. In solving the light time
                                 equation, the "CN" correction iterates
                                 until the solution converges (three
                                 iterations on all supported platforms).
                                 Whether the "CN+S" solution is
                                 substantially more accurate than the
                                 "LT" solution depends on the geometry
                                 of the participating objects and on the
                                 accuracy of the input data. In all
                                 cases this routine will execute more
                                 slowly when a converged solution is
                                 computed. See the -Particulars section
                                 below for a discussion of precision of
                                 light time corrections.

                      "CN+S"     Converged Newtonian light time
                                 correction and stellar aberration
                                 correction.

                   The following values of `abcorr' apply to the
                   "transmission" case in which photons *depart* from
                   the observer's location at `et' and arrive at the
                   target's location at the light-time corrected epoch
                   et+lt:

                      "XLT"      "Transmission" case: correct for
                                 one-way light time using a Newtonian
                                 formulation. This correction yields the
                                 position of the target at the moment it
                                 receives photons emitted from the
                                 observer's location at `et'.

                      "XLT+S"    "Transmission" case: correct for one-way
                                 light time and stellar aberration using a
                                 Newtonian formulation. This option
                                 modifies the position obtained with the
                                 "XLT" option to account for the observer's
                                 velocity relative to the solar system
                                 barycenter. The computed target position
                                 indicates the direction that photons
                                 emitted from the observer's location must
                                 be "aimed" to hit the target.

                      "XCN"      "Transmission" case: converged
                                 Newtonian light time correction.

                      "XCN+S"    "Transmission" case: converged Newtonian
                                 light time correction and stellar
                                 aberration correction.

                   Neither special nor general relativistic effects are
                   accounted for in the aberration corrections applied
                   by this routine.

                   Case and blanks are not significant in the string
                   `abcorr'.

       obs         is the NAIF ID code for the observing body.
#### Detailed_Output
       ptarg       is a Cartesian 3-vector representing the position of
                   the target body relative to the specified observer.
                   `ptarg' is corrected for the specified aberrations, and
                   is expressed with respect to the reference frame
                   specified by `ref'. The three components of `ptarg'
                   represent the x-, y- and z-components of the target's
                   position.

                   `ptarg' points from the observer's location at `et' to
                   the aberration-corrected location of the target.
                   Note that the sense of this position vector is
                   independent of the direction of radiation travel
                   implied by the aberration correction.

                   Units are always km.

                   Non-inertial frames are treated as follows: letting
                   `ltcent' be the one-way light time between the observer
                   and the central body associated with the frame, the
                   orientation of the frame is evaluated at et-ltcent,
                   et+ltcent, or `et' depending on whether the requested
                   aberration correction is, respectively, for received
                   radiation, transmitted radiation, or is omitted.
                   `ltcent' is computed using the method indicated by
                   `abcorr'.

       lt          is the one-way light time between the observer and
                   target in seconds. If the target position is corrected
                   for aberrations, then `lt' is the one-way light time
                   between the observer and the light time corrected
                   target location.
#### Parameters
       None.
#### Exceptions
       1)  If name of target or observer cannot be translated to its NAIF
           ID code, the error SPICE(IDCODENOTFOUND) is signaled by a
           routine in the call tree of this routine.

       2)  If the reference frame `ref' is not a recognized reference
           frame, the error SPICE(UNKNOWNFRAME) is signaled by a routine
           in the call tree of this routine.

       3)  If the loaded kernels provide insufficient data to compute the
           requested position vector, an error is signaled by a routine
           in the call tree of this routine.

       4)  If an error occurs while reading an SPK or other kernel file,
           the error is signaled by a routine in the call tree of this
           routine.

       5)  If any of the required attributes of the reference frame `ref'
           cannot be determined, the error SPICE(UNKNOWNFRAME2) is
           signaled by a routine in the call tree of this routine.

       6)  If any of the `ref' or `abcorr' input string pointers is null,
           the error SPICE(NULLPOINTER) is signaled.

       7)  If any of the `ref' or `abcorr' input strings has zero length,
           the error SPICE(EMPTYSTRING) is signaled.
#### Files
       This routine computes positions using SPK files that have been
       loaded into the SPICE system, normally via the kernel loading
       interface routine furnsh_c. See the routine furnsh_c and the SPK
       and KERNEL Required Reading for further information on loading
       (and unloading) kernels.

       If the output position `ptarg' is to be expressed relative to a
       non-inertial frame, or if any of the ephemeris data used to
       compute `ptarg' are expressed relative to a non-inertial frame in
       the SPK files providing those data, additional kernels may be
       needed to enable the reference frame transformations required to
       compute the position. These additional kernels may be C-kernels, PCK
       files or frame kernels. Any such kernels must already be loaded
       at the time this routine is called.
#### Particulars
       This routine is part of the user interface to the SPICE ephemeris
       system. It allows you to retrieve position information for any
       ephemeris object relative to any other in a reference frame that
       is convenient for further computations.

       Aberration corrections
       ======================

       In space science or engineering applications one frequently
       wishes to know where to point a remote sensing instrument, such
       as an optical camera or radio antenna, in order to observe or
       otherwise receive radiation from a target. This pointing problem
       is complicated by the finite speed of light: one needs to point
       to where the target appears to be as opposed to where it actually
       is at the epoch of observation. We use the adjectives
       "geometric," "uncorrected," or "true" to refer to an actual
       position or state of a target at a specified epoch. When a
       geometric position or state vector is modified to reflect how it
       appears to an observer, we describe that vector by any of the
       terms "apparent," "corrected," "aberration corrected," or "light
       time and stellar aberration corrected." The SPICE Toolkit can
       correct for two phenomena affecting the apparent location of an
       object: one-way light time (also called "planetary aberration")
       and stellar aberration.

       One-way light time
       ------------------

       Correcting for one-way light time is done by computing, given an
       observer and observation epoch, where a target was when the observed
       photons departed the target's location. The vector from the
       observer to this computed target location is called a "light time
       corrected" vector. The light time correction depends on the motion
       of the target relative to the solar system barycenter, but it is
       independent of the velocity of the observer relative to the solar
       system barycenter. Relativistic effects such as light bending and
       gravitational delay are not accounted for in the light time
       correction performed by this routine.

       Stellar aberration
       ------------------

       The velocity of the observer also affects the apparent location
       of a target: photons arriving at the observer are subject to a
       "raindrop effect" whereby their velocity relative to the observer
       is, using a Newtonian approximation, the photons' velocity
       relative to the solar system barycenter minus the velocity of the
       observer relative to the solar system barycenter. This effect is
       called "stellar aberration." Stellar aberration is independent
       of the velocity of the target. The stellar aberration formula
       used by this routine does not include (the much smaller)
       relativistic effects.

       Stellar aberration corrections are applied after light time
       corrections: the light time corrected target position vector is
       used as an input to the stellar aberration correction.

       When light time and stellar aberration corrections are both
       applied to a geometric position vector, the resulting position
       vector indicates where the target "appears to be" from the
       observer's location.

       As opposed to computing the apparent position of a target, one
       may wish to compute the pointing direction required for
       transmission of photons to the target. This also requires correction
       of the geometric target position for the effects of light time
       and stellar aberration, but in this case the corrections are
       computed for radiation traveling *from* the observer to the target.
       We will refer to this situation as the "transmission" case.

       The "transmission" light time correction yields the target's
       location as it will be when photons emitted from the observer's
       location at `et' arrive at the target. The transmission stellar
       aberration correction is the inverse of the traditional stellar
       aberration correction: it indicates the direction in which
       radiation should be emitted so that, using a Newtonian
       approximation, the sum of the velocity of the radiation relative
       to the observer and of the observer's velocity, relative to the
       solar system barycenter, yields a velocity vector that points in
       the direction of the light time corrected position of the target.

       One may object to using the term "observer" in the transmission
       case, in which radiation is emitted from the observer's location.
       The terminology was retained for consistency with earlier
       documentation.

       Below, we indicate the aberration corrections to use for some
       common applications:

          1) Find the apparent direction of a target. This is
             the most common case for a remote-sensing observation.

                Use "LT+S" or "CN+S": apply both light time and stellar
                aberration corrections.

             Note that using light time corrections alone ("LT") is
             generally not a good way to obtain an approximation to an
             apparent target vector: since light time and stellar
             aberration corrections often partially cancel each other,
             it may be more accurate to use no correction at all than to
             use light time alone.

          2) Find the corrected pointing direction to radiate a signal
             to a target. This computation is often applicable for
             implementing communications sessions.

                Use "XLT+S" or "XCN+S": apply both light time and stellar
                aberration corrections for transmission.

          3) Compute the apparent position of a target body relative
             to a star or other distant object.

                Use one of "LT", "CN", "LT+S", or "CN+S" as needed to match
                the correction applied to the position of the distant
                object. For example, if a star position is obtained from a
                catalog, the position vector may not be corrected for
                stellar aberration. In this case, to find the angular
                separation of the star and the limb of a planet, the vector
                from the observer to the planet should be corrected for
                light time but not stellar aberration.

          4) Obtain an uncorrected position vector derived directly from
             data in an SPK file.

                Use "NONE".

          5) Use a geometric position vector as a low-accuracy estimate
             of the apparent position for an application where execution
             speed is critical.

                Use "NONE".

          6) While this routine cannot perform the relativistic
             aberration corrections required to compute positions
             with the highest possible accuracy, it can supply the
             geometric positions required as inputs to these computations.

                Use "NONE", then apply relativistic aberration
                corrections (not available in the SPICE Toolkit).

       Below, we discuss in more detail how the aberration corrections
       applied by this routine are computed.

          Geometric case
          ==============

          spkezp_c begins by computing the geometric position T(et) of the
          target body relative to the solar system barycenter (SSB).
          Subtracting the geometric position of the observer O(et) gives
          the geometric position of the target body relative to the
          observer. The one-way light time, `lt', is given by

                    | T(et) - O(et) |
             lt = -------------------
                            c

          The geometric relationship between the observer, target, and
          solar system barycenter is as shown:

             SSB ---> O(et)
              |      /
              |     /
              |    /
              |   /  T(et) - O(et)
              V  V
             T(et)

          The returned position is

             T(et) - O(et)

          Reception case
          ==============

          When any of the options "LT", "CN", "LT+S", "CN+S" is selected
          for `abcorr', spkezp_c computes the position of the target body at
          epoch et-lt, where `lt' is the one-way light time. Let T(t) and
          O(t) represent the positions of the target and observer
          relative to the solar system barycenter at time t; then `lt' is
          the solution of the light-time equation

                    | T(et-lt) - O(et) |
             lt = ------------------------                            (1)
                             c

          The ratio

              | T(et) - O(et) |
            ---------------------                                     (2)
                      c

          is used as a first approximation to `lt'; inserting (2) into the
          right hand side of the light-time equation (1) yields the
          "one-iteration" estimate of the one-way light time ("LT").
          Repeating the process until the estimates of `lt' converge yields
          the "converged Newtonian" light time estimate ("CN").

          Subtracting the geometric position of the observer O(et) gives
          the position of the target body relative to the observer:
          T(et-lt) - O(et).

             SSB ---> O(et)
              | \     |
              |  \    |
              |   \   | T(et-lt) - O(et)
              |    \  |
              V     V V
             T(et)  T(et-lt)

          The light time corrected position vector is

             T(et-lt) - O(et)

          If correction for stellar aberration is requested, the target
          position is rotated toward the solar system
          barycenter-relative velocity vector of the observer. The
          rotation is computed as follows:

             Let r be the light time corrected vector from the observer
             to the object, and v be the velocity of the observer with
             respect to the solar system barycenter. Let w be the angle
             between them. The aberration angle phi is given by

                sin(phi) = v sin(w) / c

             Let h be the vector given by the cross product

                h = r X v

             Rotate r by phi radians about h to obtain the apparent
             position of the object.

          Transmission case
          ==================

          When any of the options "XLT", "XCN", "XLT+S", "XCN+S" is
          selected, spkezp_c computes the position of the target body T at
          epoch et+lt, where `lt' is the one-way light time. `lt' is the
          solution of the light-time equation

                    | T(et+lt) - O(et) |
             lt = ------------------------                            (3)
                              c

          Subtracting the geometric position of the observer, O(et),
          gives the position of the target body relative to the
          observer: T(et-lt) - O(et).

                     SSB --> O(et)
                    / |    *
                   /  |  *  T(et+lt) - O(et)
                  /   |*
                 /   *|
                V  V  V
            T(et+lt)  T(et)

          The position component of the light-time corrected position
          is the vector

             T(et+lt) - O(et)

          If correction for stellar aberration is requested, the target
          position is rotated away from the solar system barycenter-
          relative velocity vector of the observer. The rotation is
          computed as in the reception case, but the sign of the
          rotation angle is negated.

       Precision of light time corrections
       ===================================

          Corrections using one iteration of the light time solution
          ----------------------------------------------------------

          When the requested aberration correction is "LT", "LT+S",
          "XLT", or "XLT+S", only one iteration is performed in the
          algorithm used to compute `lt'.

          The relative error in this computation

             | LT_ACTUAL - LT_COMPUTED |  /  LT_ACTUAL

          is at most

              (V/C)**2
             ----------
              1 - (V/C)

          which is well approximated by (V/C)**2, where V is the
          velocity of the target relative to an inertial frame and C is
          the speed of light.

          For nearly all objects in the solar system V is less than 60
          km/sec. The value of C is ~300000 km/sec. Thus the
          one-iteration solution for `lt' has a potential relative error
          of not more than 4e-8. This is a potential light time error of
          approximately 2e-5 seconds per astronomical unit of distance
          separating the observer and target. Given the bound on V cited
          above:

             As long as the observer and target are separated by less
             than 50 astronomical units, the error in the light time
             returned using the one-iteration light time corrections is
             less than 1 millisecond.

             The magnitude of the corresponding position error, given
             the above assumptions, may be as large as (V/C)**2 * the
             distance between the observer and the uncorrected target
             position: 300 km or equivalently 6 km/AU.

          In practice, the difference between positions obtained using
          one-iteration and converged light time is usually much smaller
          than the value computed above and can be insignificant. For
          example, for the spacecraft Mars Reconnaissance Orbiter and
          Mars Express, the position error for the one-iteration light
          time correction, applied to the spacecraft-to-Mars center
          vector, is at the 1 cm level.

          Comparison of results obtained using the one-iteration and
          converged light time solutions is recommended when adequacy of
          the one-iteration solution is in doubt.

          Converged corrections
          ---------------------

          When the requested aberration correction is "CN", "CN+S",
          "XCN", or "XCN+S", as many iterations as are required for
          convergence are performed in the computation of `lt'. Usually
          the solution is found after three iterations. The relative
          error present in this case is at most

              (V/C)**4
             ----------
              1 - (V/C)

          which is well approximated by (V/C)**4.

             The precision of this computation (ignoring round-off
             error) is better than 4e-11 seconds for any pair of objects
             less than 50 AU apart, and having speed relative to the
             solar system barycenter less than 60 km/s.

             The magnitude of the corresponding position error, given
             the above assumptions, may be as large as (V/C)**4 * the
             distance between the observer and the uncorrected target
             position: 1.2 cm at 50 AU or equivalently 0.24 mm/AU.

          However, to very accurately model the light time between
          target and observer one must take into account effects due to
          general relativity. These may be as high as a few hundredths
          of a millisecond for some objects.

       Relativistic Corrections
       =========================

       This routine does not attempt to perform either general or
       special relativistic corrections in computing the various
       aberration corrections. For many applications relativistic
       corrections are not worth the expense of added computation
       cycles. If however, your application requires these additional
       corrections we suggest you consult the astronomical almanac (page
       B36) for a discussion of how to carry out these corrections.
#### Examples
       The numerical results shown for this example 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) Load a planetary ephemeris SPK, then look up a series of
          geometric positions of the Moon relative to the Earth,
          referenced to the J2000 frame.

          Use the SPK kernel below to load the required Earth and
          Moon ephemeris data.

             de421.bsp

          Example code begins here.

          /.
             Program spkezp_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main()
          {

             #define        ABCORR        "NONE"
             #define        FRAME         "J2000"

             /.
             The name of the SPK file shown here is fictitious;
             you must supply the name of an SPK file available
             on your own computer system.
             ./
             #define        SPK           "de421.bsp"

             /.
             ET0 represents the date 2000 Jan 1 12:00:00 TDB.
             ./
             #define        ET0           0.0

             /.
             Use a time step of 1 hour; look up 4 states.
             ./
             #define        STEP          3600.0
             #define        MAXITR        4

             /.
             The NAIF IDs of the earth and moon are 399 and 301
             respectively.
             ./
             #define        OBSERVER      399
             #define        TARGET        301

             /.
             Local variables
             ./
             SpiceInt       i;

             SpiceDouble    et;
             SpiceDouble    lt;
             SpiceDouble    pos [3];

             /.
             Load the spk file.
             ./
             furnsh_c ( SPK );

             /.
             Step through a series of epochs, looking up a position vector
             at each one.
             ./
             for ( i = 0;  i < MAXITR;  i++ )
             {
                et  =  ET0 + i*STEP;

                spkezp_c ( TARGET,    et,   FRAME,  ABCORR,
                           OBSERVER,  pos,  &lt             );

                printf( "\net = %20.10f\n\n",                 et     );
                printf( "J2000 x-position (km):   %20.10f\n", pos[0] );
                printf( "J2000 y-position (km):   %20.10f\n", pos[1] );
                printf( "J2000 z-position (km):   %20.10f\n", pos[2] );
             }

             return ( 0 );

          }

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

          et =         0.0000000000

          J2000 x-position (km):     -291608.3853096409
          J2000 y-position (km):     -266716.8329467875
          J2000 z-position (km):      -76102.4871467836

          et =      3600.0000000000

          J2000 x-position (km):     -289279.8983133120
          J2000 y-position (km):     -269104.1084289378
          J2000 z-position (km):      -77184.2420729120

          et =      7200.0000000000

          J2000 x-position (km):     -286928.0014055001
          J2000 y-position (km):     -271469.9902460162
          J2000 z-position (km):      -78259.9083077002

          et =     10800.0000000000

          J2000 x-position (km):     -284552.9026554719
          J2000 y-position (km):     -273814.3097527430
          J2000 z-position (km):      -79329.4060465982
#### Restrictions
       None.
#### Literature_References
       None.
#### Author_and_Institution
       C.H. Acton          (JPL)
       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       W.L. Taber          (JPL)
       E.D. Wright         (JPL)
#### Version
       -CSPICE Version 2.0.7, 05-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard. Added reference to the
           required SPK for the example code. Reduced the number of positions to be
           computed.

           Moved SPK required reading from -Literature_References to
           -Required_Reading section. Added entries #5, #6 and #7 to -Exceptions
           section.

       -CSPICE Version 2.0.6, 07-JUL-2014 (NJB)

           Discussion of light time corrections was updated. Assertions
           that converged light time corrections are unlikely to be
           useful were removed.

       -CSPICE Version 2.0.5, 04-APR-2008 (NJB)

           Corrected minor error in description of XLT+S aberration
           correction.

       -CSPICE Version 2.0.4, 17-APR-2005 (NJB)

           Error was corrected in example program: variable name `state'
           was changed to `pos' in printf calls.

       -CSPICE Version 2.0.3, 12-DEC-2004 (NJB)

           Minor header error was corrected.

       -CSPICE Version 2.0.2, 13-OCT-2003 (EDW)

           Various minor header changes were made to improve clarity.
           Added mention that 'lt' returns a value in seconds.

       -CSPICE Version 2.0.1, 29-JUL-2003 (NJB) (CHA)

           Various minor header changes were made to improve clarity.

       -CSPICE Version 2.0.0, 31-DEC-2001 (NJB)

           Updated to handle aberration corrections for transmission
           of radiation. Formerly, only the reception case was
           supported. The header was revised and expanded to explain
           the functionality of this routine in more detail.

       -CSPICE Version 1.0.0, 29-MAY-1999 (NJB) (WLT)
#### Index_Entries
       using body names get position relative to an observer
       get position relative observer corrected for aberrations
       read ephemeris data
       read trajectory data
#### Link to routine spkezp_c source file spkezp_c.c

    Fri Dec 31 18:41:12 2021