Index Page spkapo_c
A B C D E F G H I J K L M N O P Q R S T U V W X
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
       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, as
                   well as in the CSPICE routine chgirf_.

                   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).

                                 The "CN" correction typically does not
                                 substantially improve accuracy because
                                 the errors made by ignoring
                                 relativistic effects may be larger than
                                 the improvement afforded by obtaining
                                 convergence of the light time solution.
                                 The "CN" correction computation also
                                 requires a significantly greater number
                                 of CPU cycles than does the
                                 one-iteration light time correction.

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

                   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 and stellar
                                 aberration corrections.

                   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.

       2) If the reference frame requested is not a recognized
          inertial reference frame the error SPICE(BADFRAME) is
          signaled.

       3) If the position of the target relative to the solar system
          barycenter cannot be computed, the error will be diagnosed
          by routines in the call tree of this routine.
#### 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 for a remote-sensing
             observation:

                Use "LT+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:

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

          3) Obtain an uncorrected position vector derived directly from
             data in an SPK file:

                Use "NONE".

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

                Use "LT" or "LT+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.

          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 high-accuracy 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 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 vector is

             T(et) - O(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 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
          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 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 is the vector

             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 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 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 light-time corrected position is

             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 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
       In the following code fragment, spkssb_c and spkapo_c are used
       to display the position of Io (body 501) as seen from the
       Voyager 2 spacecraft (Body -32) at a series of epochs.

       Normally, one would call the high-level reader spkpos_c to obtain
       position vectors.  The example below illustrates the interface
       of this routine, but is not intended as a recommendation on
       how to use the CSPICE SPK subsystem.

       The use of integer ID codes is necessitated by the low-level
       interface of this routine.

          #include <stdio.h>
          #include "SpiceUsr.h"
               .
               .
               .
          #define  IO          501
          #define  VGR2        -32

          while ( epoch <= end )
          {
             spkssb_c ( VGR2,  epoch,  "J2000", stvgr2                   );
             spkapo_c ( IO,    epoch,  "J2000", stvgr2, "LT", posio, &lt );
             recrad_c ( posio, &range, &ra,     &dec                     );

             printf ( "RA = %f   DEC = %f\n", ra*dpr_c(), dec*dpr_c() );

             epoch +=  delta;
          }
#### 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
       SPK Required Reading.
#### Author_and_Institution
       N.J. Bachman    (JPL)
       H.A. Neilan     (JPL)
       I.M. Underwood  (JPL)
       W.L. Taber      (JPL)
#### Version
       -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

    Wed Jun  9 13:05:29 2010