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cspice_spkez

Table of contents
Abstract
I/O
Parameters
Examples
Particulars
Exceptions
Files
Restrictions
Required_Reading
Literature_References
Author_and_Institution
Version
Index_Entries

Abstract


   CSPICE_SPKEZ returns the state (position and velocity) of a target body
   relative to an observing body, optionally corrected for light
   time (planetary aberration) and stellar aberration.

I/O


   Given:

      targ     the NAIF ID code for a target body.

               [1,1] = size(targ); int32 = class(targ)

               The target and observer define a state vector whose
               position component points from the observer to the target.

      et       the ephemeris time, expressed as seconds past J2000 TDB, at
               which the state of the target body relative to the observer
               is to be computed.

               [1,1] = size(et); double = class(et)

               `et' refers to time at the observer's location.

      ref      the name of the reference frame relative to which the output
               state vector should be expressed.

               [1,c1] = size(ref); char = class(ref)

                  or

               [1,1] = size(ref); cell = class(ref)

               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 state vector `starg'
               for details.

      abcorr   indicates the aberration corrections to be applied to the
               state of the target body to account for one-way light time
               and stellar aberration.

               [1,c2] = size(abcorr); char = class(abcorr)

                  or

               [1,1] = size(abcorr); cell = class(abcorr)

               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 state 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 state 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
                             state obtained with the 'LT' option to
                             account for the observer's velocity
                             relative to the solar system
                             barycenter. The result is the apparent
                             state of the target---the position and
                             velocity 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
                             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
                             state 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
                             state obtained with the 'XLT' option to
                             account for the observer's velocity
                             relative to the solar system
                             barycenter. The position component of
                             the computed target state 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      the NAIF ID code for an observing body.

               [1,1] = size(obs); int32 = class(obs)

   the call:

      [starg, lt] = cspice_spkez( targ, et, ref, abcorr, obs )

   returns:

      starg    a Cartesian state vector representing the position and
               velocity of the target body relative to the specified
               observer.

               [6,1] = size(starg); double = class(starg)

               `starg' is corrected for the specified aberrations, and is
               expressed with respect to the reference frame specified by
               `ref'. The first three components of `starg' represent the
               x-, y- and z-components of the target's position; the last
               three components form the corresponding velocity vector.

               Units are always km and km/sec.

               The position component of `starg' points from the
               observer's location 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.

               The velocity component of `starg' is the derivative
               with respect to time of the position component of
               `starg.'

               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       the one-way light time between the observer and target in
               seconds.

               [1,1] = size(lt); double = class(lt)

               If the target state is corrected for aberrations, then 'lt'
               is the one-way light time between the observer and the light
               time corrected target location.

Parameters


   None.

Examples


   Any numerical results shown for this example may differ between
   platforms as the results depend on the SPICE kernels used as input
   and the machine specific arithmetic implementation.

   1) Load a planetary ephemeris SPK, then look up a series of
      geometric states 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.


      function spkez_ex1()

         ABCORR = 'NONE';
         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.
         %
         SPK = 'de421.bsp';

         %
         % ET0 represents the date 2000 Jan 1 12:00:00 TDB.
         %
         ET0 = 0.0;

         %
         % Use a time step of 1 hour; look up 4 states.
         %
         STEP   = 3600.0;
         MAXITR = 4;

         %
         % The NAIF IDs of the earth and moon are 399 and 301
         % respectively.
         %
         OBSERVER = 399;
         TARGET   = 301;

         %
         % Load the spk file.
         %
         cspice_furnsh( SPK );

         %
         % Step through a series of epochs, looking up a state vector
         % at each one.
         %
         for i=0:MAXITR-1

            et =  ET0 + i*STEP;

            [state, lt] = cspice_spkez( TARGET,  et,     ...
                                        FRAME,   ABCORR, ...
                                        OBSERVER         );

            fprintf( '\n' )
            fprintf( 'et = %20.10f\n', et )
            fprintf( '\n' )
            fprintf( 'J2000 x-position (km):   %20.10f\n', state(1) )
            fprintf( 'J2000 y-position (km):   %20.10f\n', state(2) )
            fprintf( 'J2000 z-position (km):   %20.10f\n', state(3) )
            fprintf( 'J2000 x-velocity (km/s): %20.10f\n', state(4) )
            fprintf( 'J2000 y-velocity (km/s): %20.10f\n', state(5) )
            fprintf( 'J2000 z-velocity (km/s): %20.10f\n', state(6) )

         end

         %
         % It's always good form to unload kernels after use,
         % particularly in Matlab due to data persistence.
         %
         cspice_kclear


      When this program was executed on a Mac/Intel/Octave6.x/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
      J2000 x-velocity (km/s):         0.6435313868
      J2000 y-velocity (km/s):        -0.6660876862
      J2000 z-velocity (km/s):        -0.3013257043

      et =      3600.0000000000

      J2000 x-position (km):     -289279.8983133120
      J2000 y-position (km):     -269104.1084289378
      J2000 z-position (km):      -77184.2420729120
      J2000 x-velocity (km/s):         0.6500629244
      J2000 y-velocity (km/s):        -0.6601685834
      J2000 z-velocity (km/s):        -0.2996455351

      et =      7200.0000000000

      J2000 x-position (km):     -286928.0014055001
      J2000 y-position (km):     -271469.9902460162
      J2000 z-position (km):      -78259.9083077002
      J2000 x-velocity (km/s):         0.6565368360
      J2000 y-velocity (km/s):        -0.6542023962
      J2000 z-velocity (km/s):        -0.2979431229

      et =     10800.0000000000

      J2000 x-position (km):     -284552.9026554719
      J2000 y-position (km):     -273814.3097527430
      J2000 z-position (km):      -79329.4060465982
      J2000 x-velocity (km/s):         0.6629527800
      J2000 y-velocity (km/s):        -0.6481896017
      J2000 z-velocity (km/s):        -0.2962186180


Particulars


   This routine is part of the user interface to the SPICE ephemeris
   system. It allows you to retrieve state 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 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
      ==============

      cspice_spkez 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 state consists of the position vector

         T(et) - O(et)

      and a velocity obtained by taking the difference of the
      corresponding velocities. In the geometric case, the
      returned velocity is actually the time derivative of the
      position.


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

      When any of the options 'LT', 'CN', 'LT+S', 'CN+S' is selected
      for `abcorr', cspice_spkez 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 position component of the light time corrected state
      is the vector

         T(et-lt) - O(et)

      The velocity component of the light time corrected state
      is the difference

         T_vel(et-lt)*(1-d(lt)/d(et)) - O_vel(et)

      where T_vel and O_vel are, respectively, the velocities of the
      target and observer relative to the solar system barycenter at
      the epochs et-lt and `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.

      When stellar aberration corrections are used, the rate of change
      of the stellar aberration correction is accounted for in the
      computation of the output velocity.


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

      When any of the options 'XLT', 'XCN', 'XLT+S', 'XCN+S' is
      selected, cspice_spkez 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 state
      is the vector

         T(et+lt) - O(et)

      The velocity component of the light-time corrected state
      consists of the difference

         T_vel(et+lt)*(1+d(lt)/d(et)) - O_vel(et)

      where T_vel and O_vel are, respectively, the velocities of the
      target and observer relative to the solar system barycenter at
      the epochs et+lt and `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.

Exceptions


   1)  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.

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

   3)  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.

   4)  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.

   5)  If any of the input arguments, `targ', `et', `ref', `abcorr'
       or `obs', is undefined, an error is signaled by the Matlab
       error handling system.

   6)  If any of the input arguments, `targ', `et', `ref', `abcorr'
       or `obs', is not of the expected type, or it does not have the
       expected dimensions and size, an error is signaled by the Mice
       interface.

Files


   This routine computes states using SPK files that have been loaded into
   the SPICE system, normally via the kernel loading interface routine
   cspice_furnsh. See the routine cspice_furnsh and the SPK and KERNEL
   Required Reading for further information on loading (and unloading)
   kernels.

   If the output state `starg' is to be expressed relative to a
   non-inertial frame, or if any of the ephemeris data used to
   compute `starg' 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 state. Normally these additional kernels are PCK
   files or frame kernels. Any such kernels must already be loaded
   at the time this routine is called.

Restrictions


   None.

Required_Reading


   FRAMES.REQ
   MICE.REQ
   NAIF_IDS.REQ
   SPK.REQ
   TIME.REQ

Literature_References


   None.

Author_and_Institution


   J. Diaz del Rio     (ODC Space)

Version


   -Mice Version 1.0.0, 10-AUG-2021 (JDR)

Index_Entries


   using body codes get target state relative to an observer
   get state relative to observer corrected for aberrations
   read ephemeris data
   read trajectory data


Fri Dec 31 18:44:27 2021