Index Page spkez_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 spkez_c ( SpiceInt            targ,
                      SpiceDouble         et,
                      ConstSpiceChar     *ref,
                      ConstSpiceChar     *abcorr,
                      SpiceInt            obs,
                      SpiceDouble         starg[6],
                      SpiceDouble        *lt        )

#### Abstract

       Return the state (position and velocity) 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.
       et         I   Observer epoch.
       ref        I   Reference frame of output state vector.
       abcorr     I   Aberration correction flag.
       obs        I   Observing body.
       starg      O   State 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 state vector whose position
                   component points from the observer to the target.

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

       ref         is the name of the reference frame relative to which
                   the output state 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 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. 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         is the NAIF ID code for an observing body.

#### Detailed_Output

       starg       is a Cartesian state vector representing the position
                   and velocity of the target body relative to the
                   specified observer. `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          is the one-way light time between the observer and
                   target in seconds. 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.

#### Exceptions

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

       2) If the loaded kernels provide insufficient data to
          compute the requested state vector, the deficiency will
          be diagnosed 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  will be diagnosed by a routine in the call tree
          of this routine.

#### Files

       This routine computes states 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 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. 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 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
          ==============

          spkez_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 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', spkez_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 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, spkez_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 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.

#### Examples

       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.

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

           int main()
           {

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

              /.
              The name of the SPK file shown here is fictitious;
              you must supply the name of an SPK file available
              on your own computer system.
              ./
              #define        SPK           "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    state [6];

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

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

                 spkez_c ( TARGET,    et,     FRAME,  ABCORR,
                           OBSERVER,  state,  &lt             );

                 printf( "\net = %20.10f\n\n",                 et       );
                 printf( "J2000 x-position (km):   %20.10f\n", state[0] );
                 printf( "J2000 y-position (km):   %20.10f\n", state[1] );
                 printf( "J2000 z-position (km):   %20.10f\n", state[2] );
                 printf( "J2000 x-velocity (km/s): %20.10f\n", state[3] );
                 printf( "J2000 y-velocity (km/s): %20.10f\n", state[4] );
                 printf( "J2000 z-velocity (km/s): %20.10f\n", state[5] );
              }

              return ( 0 );
           }

#### Restrictions

       None.

#### Literature_References

       SPK Required Reading.

#### Author_and_Institution

       C.H. Acton      (JPL)
       W.L. Taber      (JPL)
       N.J. Bachman    (JPL)
       J.E. McLean     (JPL)
       H.A. Neilan     (JPL)
       M.J. Spencer    (JPL)
       I.M. Underwood  (JPL)

#### Version

       -CSPICE Version 3.0.1, 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 3.0.0, 27-DEC-2007 (NJB)

           This routine was upgraded to more accurately compute
           aberration-corrected velocity, and in particular, make it
           more consistent with observer-target positions.

           When light time corrections are used, the derivative of light
           time with respect to time is now accounted for in the
           computation of observer-target velocities. When the reference
           frame associated with the output state is time-dependent, the
           derivative of light time with respect to time is now accounted
           for in the computation of the rate of change of orientation of
           the reference frame.

           When stellar aberration corrections are used, velocities
           now reflect the rate of range of the stellar aberration
           correction.

       -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, 28-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 1.1.0, 08-FEB-1998 (NJB)

           References to C2F_CreateStr_Sig were removed; code was
           cleaned up accordingly. String checks are now done using
           the macro CHKFSTR.

       -CSPICE Version 1.0.0, 25-OCT-1997 (NJB)

           Based on SPICELIB Version 3.1.0, 09-JUL-1996 (WLT)

#### 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

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

    Wed Apr  5 17:54:43 2017