spkezp_c

Index Page spkezp_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 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).

                                 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 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 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.

       obs         is the NAIF ID code for an 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.

                   Units are always km.

                   '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.

                   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.

       2) If the reference frame 'ref' is not a recognized reference
          frame the error SPICE(UNKNOWNFRAME) is signaled.

       3) If the loaded kernels provide insufficient data to
          compute the requested position vector, the deficiency will
          be diagnosed 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  will be diagnosed by a routine 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. 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":  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":  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 "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.

          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 4*10**-8.  This is a potential light time error
          of approximately 2*10**-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.

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

          When the requested aberration correction is "CN", "CN+S",
          "XCN", or "XCN+S", three iterations are performed in the
          computation of 'lt'.  The relative error present in this
          solution is at most

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

          which is well approximated by (V/C)**4.  Mathematically the
          precision of this computation is better than a nanosecond for
          any pair of objects in the solar system.

          However, to model the actual 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.

          When one considers the extra time required to compute the
          converged Newtonian light time (the state of the target relative
          to the solar system barycenter is looked up three times instead
          of once) together with the real gain in accuracy, it seems
          unlikely that you will want to request either the "CN" or "CN+S"
          light time corrections.  However, these corrections can be useful
          for testing situations where high precision (as opposed to
          accuracy) is required.

       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
       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.

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

           void 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           "planetary_spk.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 100 states.
              ./
              #define        STEP          3600.0
              #define        MAXITR        100

              /.
              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] );
              }
           }
#### Restrictions
       None.
#### Literature_References
       SPK Required Reading.
#### Author_and_Institution
       C.H. Acton      (JPL)
       B.V. Semenov    (JPL)
       N.J. Bachman    (JPL)
       W.L. Taber      (JPL)
#### Version
       -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
       get target 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

    Thu Apr 16 08:59:12 2009