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Index Page spkapo_c

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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

       spkapo_c ( S/P Kernel, apparent position only )

       void spkapo_c ( SpiceInt               targ,
                       SpiceDouble            et,
                       ConstSpiceChar       * ref,
                       ConstSpiceDouble       sobs[6],
                       ConstSpiceChar       * abcorr,
                       SpiceDouble            ptarg[3],
                       SpiceDouble          * lt        )

#### Abstract

       Return the position of a target body relative to an observer,
       optionally corrected for light time and stellar aberration.

#### Required_Reading

       SPK

#### Keywords

       EPHEMERIS

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       targ       I   Target body.
       et         I   Observer epoch.
       ref        I   Inertial reference frame of observer's state.
       sobs       I   State of observer wrt. solar system barycenter.
       abcorr     I   Aberration correction flag.
       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 inertial reference frame with respect to which
                   the observer's state `sobs' is expressed. `ref' must be
                   recognized by the SPICE Toolkit. The acceptable
                   frames are listed in the Frames Required Reading.

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

       sobs        is the geometric (uncorrected) state of the observer
                   relative to the solar system barycenter at epoch et.
                   `sobs' is a 6-vector:  the first three components of
                   `sobs' represent a Cartesian position vector; the last
                   three components represent the corresponding velocity
                   vector. `sobs' is expressed relative to the inertial
                   reference frame designated by `ref'.

                   Units are always km and km/sec.

       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 involves
                                 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
                                 of the target 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 of
                                 spkezr_c 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 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'.

#### 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 specified inertial
                   reference frame. The components of `ptarg' represent
                   the x-, y- and z-components of the target's position.

                   Units are always km.

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

       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 the value of `abcorr' is not recognized, the error
           SPICE(SPKINVALIDOPTION) is signaled by a routine in the call
           tree of this routine.

       2)  If the reference frame requested is not a recognized
           inertial reference frame, the error SPICE(BADFRAME) is
           signaled by a routine in the call tree of this routine.

       3)  If the position of the target relative to the solar system
           barycenter cannot be computed, an error is signaled by a
           routine in the call tree of this routine.

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

       5)  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. Application programs typically load
       kernels once before this routine is called, for example during
       program initialization; kernels need not be loaded repeatedly.
       See the routine furnsh_c and the SPK and KERNEL Required Reading
       for further information on loading (and unloading) kernels.

       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 `ptarg'. Normally
       these additional kernels are PCK files or frame kernels. Any
       such kernels must already be loaded at the time this routine is
       called.

#### Particulars

       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. 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, 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.

       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 motion of the target. The stellar aberration formula used
       by this routine is non- relativistic.

       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 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.

       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.

       The traditional aberration corrections applicable to observation
       and those applicable to transmission are related in a simple way:
       one may picture the geometry of the "transmission" case by
       imagining the "observation" case running in reverse time order,
       and vice versa.

       One may reasonably 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 state vector derived directly from
             data in an SPK file.

                Use "NONE".

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

                Use "NONE".

          6) While this routine cannot perform the relativistic
             aberration corrections required to compute states
             with the highest possible accuracy, it can supply the
             geometric states 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
       ==============

          spkapo_c begins by computing the geometric position targ(et) of
          the target body relative to the solar system barycenter (SSB).
          Subtracting the geometric position of the observer obs(et) gives
          the geometric position of the target body relative to the
          observer. The one-way light time, `lt', is given by

                   | targ(et) - obs(et) |
             lt = ------------------------
                             C

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

              SSB ---> obs(et)
               |      /
               |     /
               |    /
               |   /  targ(et) - obs(et)
               V  V
             targ(et)

          The returned position vector is

             targ(et) - obs(et)

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

          When any of the options "LT", "CN", "LT+S", "CN+S" are
          selected, spkapo_c computes the position of the target body at
          epoch et-lt, where `lt' is the one-way light time. Let targ(t)
          and obs(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

                   | targ(et-lt) - obs(et) |
             lt = ---------------------------                         (1)
                               C

          The ratio

              | targ(et) - obs(et) |
             ------------------------                                 (2)
                        C

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

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

               SSB ---> obs(et)
                | \       |
                |  \      |
                |   \     | targ(et-lt) - obs(et)
                |    \    |
                |     \   |
                |      \  |
                V       V V
             targ(et)   targ(et-lt)

          The light-time corrected position is the vector

             targ(et-lt) - obs(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 magnitude of the rotation
          depends on the magnitude of the observer's velocity relative
          to the solar system barycenter and the angle between
          this velocity and the observer-target vector. 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" are
          selected, spkapo_c computes the position of the target body at
          epoch et+lt, where `lt' is the one-way light time.  `lt' is the
          solution of the light-time equation

                   | targ(et+lt) - obs(et) |
             lt = ---------------------------                         (3)
                               C

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

                         SSB --> obs(et)
                        / |    *
                       /  |  *  targ(et+lt) - obs(et)
                      /   |*
                     /   *|
                    V  V  V
             targ(et+lt)  targ(et)

          The light-time corrected position is

             targ(et+lt) - obs(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 magnitude of the
          rotation depends on the magnitude of the velocity and the
          angle between the velocity and the observer-target vector.
          The rotation is computed as in the reception case, but the
          sign of the rotation angle is negated.

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

#### 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) Compute the apparent position of the Moon relative to the
          Earth, corrected for one light-time and stellar aberration,
          given the geometric state of the Earth relative to the Solar
          System Barycenter, and the difference between the stellar
          aberration corrected and uncorrected position vectors, taking
          several steps.

          First, compute the light-time corrected state of the Moon body
          as seen by the Earth, using its geometric state. Then apply
          the correction for stellar aberration to the light-time
          corrected state of the target body.

          The code in this example could be replaced by a single call
          to spkpos_c:

             spkpos_c ( "MOON", et, "J2000", "LT+S", "EARTH", pos, &lt );

          Use the meta-kernel shown below to load the required SPICE
          kernels.

             KPL/MK

             File name: spkapo_ex1.tm

             This meta-kernel is intended to support operation of SPICE
             example programs. The kernels shown here should not be
             assumed to contain adequate or correct versions of data
             required by SPICE-based user applications.

             In order for an application to use this meta-kernel, the
             kernels referenced here must be present in the user's
             current working directory.

             The names and contents of the kernels referenced
             by this meta-kernel are as follows:

                File name                     Contents
                ---------                     --------
                de418.bsp                     Planetary ephemeris
                naif0009.tls                  Leapseconds

             \begindata

                KERNELS_TO_LOAD = ( 'de418.bsp',
                                    'naif0009.tls'  )

             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program spkapo_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main ()
          {

             /.
             Local variables.
             ./
             SpiceChar             * reffrm;
             SpiceChar             * utcstr;

             SpiceDouble             appdif [ 3 ];
             SpiceDouble             et;
             SpiceDouble             lt;
             SpiceDouble             pcorr  [ 3 ];
             SpiceDouble             pos    [ 3 ];
             SpiceDouble             sobs   [ 6 ];

             SpiceInt                idobs;
             SpiceInt                idtarg;

             /.
             Assign an observer, Earth, target, Moon, time of interest and
             reference frame for returned vectors.
             ./
             idobs  = 399;
             idtarg = 301;
             utcstr = "July 4 2004";
             reffrm = "J2000";

             /.
             Load the needed kernels.
             ./
             furnsh_c ( "spkapo_ex1.tm" );

             /.
             Convert the time string to ephemeris time, J2000.
             ./
             str2et_c ( utcstr, &et );

             /.
             Get the state of the observer with respect to the solar
             system barycenter.
             ./
             spkssb_c ( idobs,  et, reffrm, sobs );

             /.
             Get the light-time corrected position `pos' of the target
             body `idtarg' as seen by the observer.
             ./
             spkapo_c ( idtarg, et, reffrm, sobs, "LT", pos, &lt );

             /.
             Output the uncorrected vector.
             ./
             printf ( "Uncorrected position vector\n" );
             printf ( "   %18.6f %18.6f %18.6f\n", pos[0], pos[1], pos[2] );

             /.
             Apply the correction for stellar aberration to the
             light-time corrected position of the target body.
             ./
             stelab_c ( pos, sobs+3, pcorr );

             /.
             Output the corrected position vector and the apparent
             difference from the uncorrected vector.
             ./
             printf ( "\n" );
             printf ( "Corrected position vector\n" );
             printf ( "   %18.6f %18.6f %18.6f\n",
                       pcorr[0], pcorr[1], pcorr[2] );

             /.
             Apparent difference.
             ./
             vsub_c ( pos, pcorr, appdif );
             printf ( "\n" );
             printf ( "Apparent difference\n" );
             printf ( "   %18.6f %18.6f %18.6f\n",
                       appdif[0], appdif[1], appdif[2] );

             return ( 0 );
          }

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

          Uncorrected position vector
                  201738.725087     -260893.141602     -147722.589056

          Corrected position vector
                  201765.929516     -260876.818077     -147714.262441

          Apparent difference
                     -27.204429         -16.323525          -8.326615

#### Restrictions

       1)  The ephemeris files to be used by spkapo_c must be loaded
           (normally by the CSPICE kernel loader furnsh_c) before
           this routine is called.

       2)  Unlike most other SPK position computation routines, this
           routine requires that the input state be relative to an
           inertial reference frame. Non-inertial frames are not
           supported by this routine.

       3)  In a future version of this routine, the implementation
           of the aberration corrections may be enhanced to improve
           accuracy.

#### Literature_References

       None.

#### Author_and_Institution

       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       H.A. Neilan         (JPL)
       W.L. Taber          (JPL)
       I.M. Underwood      (JPL)
       E.D. Wright         (JPL)

#### Version

       -CSPICE Version 2.0.3, 10-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard. Moved SPK required
           reading from -Literature_References to -Required_Reading section.

           Added example's meta-kernel and problem statement. Created complete
           code example using the example from stelab_c.

           Added entries #4 and #5 in -Exceptions section.

       -CSPICE Version 2.0.2, 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 2.0.1, 13-OCT-2003 (EDW)

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

       -CSPICE Version 2.0.0, 19-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, 26-JUN-1999 (NJB) (HAN) (IMU) (WLT)

#### Index_Entries

       apparent position from SPK file
       get apparent position

#### Link to routine spkapo_c source file spkapo_c.c

    Fri Dec 31 18:41:12 2021