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Index Page spkaps_c

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Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

       spkaps_c ( SPK, apparent state )

       void spkaps_c ( SpiceInt           targ,
                       SpiceDouble        et,
                       ConstSpiceChar   * ref,
                       ConstSpiceChar   * abcorr,
                       ConstSpiceDouble   stobs [6],
                       ConstSpiceDouble   accobs[3],
                       SpiceDouble        starg [6],
                       SpiceDouble      * lt,
                       SpiceDouble      * dlt      )

#### Abstract

       Return the state (position and velocity) of a target body
       relative to an observer specified by its state and
       acceleration relative to the solar system barycenter. The
       returned state may be optionally corrected for light time
       and stellar aberration. All input and output vectors are
       expressed relative to an inertial reference frame.

       This routine supersedes spkapp_c.

       SPICE users normally should call the high-level API routines
       spkezr_c or spkez_c rather than this routine.

#### Required_Reading

       SPK

#### Keywords

       EPHEMERIS

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       targ       I   Target body.
       et         I   Observer epoch.
       ref        I   Inertial reference frame of output state.
       abcorr     I   Aberration correction flag.
       stobs      I   State of the observer relative to the SSB.
       accobs     I   Acceleration of the observer relative to the SSB.
       starg      O   State of target.
       lt         O   One way light time between observer and target.
       dlt        O   Derivative of light time with respect to time.

#### 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 inertial reference frame with respect to which
                   the input state `stobs', the input acceleration `accobs',
                   and the output state `starg' are expressed. `ref' must be
                   recognized by the SPICE Toolkit. The acceptable
                   frames are listed in the Frames Required Reading, as
                   well as in the CSPICE routine chgirf_.

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

       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 of spkezr_c 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 of
                                 spkezr_c for a discussion of precision of
                                 light time corrections.

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

                   The following values of `abcorr' apply to the
                   "transmission" case in which photons *depart* from
                   the observer's location at `et' and arrive at the
                   target's location at the light-time corrected epoch
                   et+lt:

                      "XLT"      "Transmission" case: correct for
                                 one-way light time using a Newtonian
                                 formulation. This correction yields the
                                 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'.

       stobs       is the geometric state of the observer relative
                   to the solar system barycenter at `et'. The
                   target and observer define a state vector whose
                   position component points from the observer to the
                   target. `stobs' is expressed relative to the reference
                   frame designated by `ref'.

       accobs      is the geometric acceleration of the observer
                   relative to the solar system barycenter at `et'. This
                   is the derivative with respect to time of the
                   velocity portion of `stobs'. `accobs' is expressed
                   relative to the reference frame designated by `ref'.

                   `accobs' is used for computing stellar aberration
                   corrected velocity. If stellar aberration corrections
                   are not specified by `abcorr', `accobs' is ignored; the
                   caller need not provide a valid input value in this
                   case.

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

                   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.

                   Units are always km and km/sec.

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

       dlt         is the derivative with respect to barycentric
                   dynamical time of the one way light time between
                   target and observer:

                      dlt = d(lt)/d(et)

                   `dlt' can also be described as the rate of change of
                   one way light time. `dlt' is unitless, since `lt' and
                   `et' both have units of TDB seconds.

                   If the observer and target are at the same position,
                   then `dlt' is set to zero.

#### Parameters

       None.

#### Exceptions

       1)  If the value of `abcorr' is not recognized, an error is signaled
           by a routine in the call tree of this routine.

       2)  If `abcorr' calls for stellar aberration but not light
           time corrections, the error SPICE(NOTSUPPORTED) is
           signaled by a routine in the call tree of this routine.

       3)  If `abcorr' calls for relativistic light time corrections, the
           error SPICE(NOTSUPPORTED) is signaled by a routine in the call
           tree of this routine.

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

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

       6)  If the observer and target are at the same position,
           then `dlt' is set to zero. This situation could arise,
           for example, when the observer is Mars and the target
           is the Mars barycenter.

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

       8)  If any of the `ref' or `abcorr' input strings has zero length,
           the error SPICE(EMPTYSTRING) is signaled.

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

       If any of the ephemeris data used to compute `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.

#### Particulars

       This routine supports higher-level SPK API routines that can
       perform both light time and stellar aberration corrections.

       User applications normally will not need to call this routine
       directly. However, this routine can improve run-time efficiency
       in situations where many targets are observed from the same
       location at the same time. In such cases, the state and
       acceleration of the observer relative to the solar system
       barycenter need be computed only once per look-up epoch.

       When apparent positions, rather than apparent states, are
       required, consider using the high-level position-only API
       routines

          spkpos_c
          spkezp_c

       or the low-level, position-only analog of this routine

          spkapo_c

       In general, the position-only routines are more efficient.

       See the header of the routine spkezr_c for a detailed discussion
       of aberration corrections.

#### Examples

       The numerical results shown for this example may differ across
       platforms. The results depend on the SPICE kernels used as
       input, the compiler and supporting libraries, and the machine
       specific arithmetic implementation.

       1) Look up a sequence of states of the Moon as seen from the
          Earth. Use light time and stellar aberration corrections.
          Compute the first state for the epoch 2000 JAN 1 12:00:00 TDB;
          compute subsequent states at intervals of 1 hour. For each
          epoch, display the states, the one way light time between
          target and observer, and the rate of change of the one way
          light time.

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

             KPL/MK

             File name: spkaps_ex1.tm

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

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

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

                File name                     Contents
                ---------                     --------
                de418.bsp                     Planetary ephemeris
                pck00008.tpc                  Planet orientation and
                                              radii
                naif0008.tls                  Leapseconds

             \begindata

                KERNELS_TO_LOAD = ( 'de418.bsp',
                                    'pck00008.tpc',
                                    'naif0008.tls'  )

             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program spkaps_ex1
          ./

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

          int main()
          {
             /.
             Local constants

             The meta-kernel name shown here refers to a file whose contents
             are those shown above. This file and the kernels it references
             must exist in your current working directory.
             ./
             #define META                   "spkaps_ex1.tm"

             /.
             Use a time step of 1 hour; look up 5 states.
             ./
             #define STEP                   3600.0
             #define MAXITR                 5

             /.
             Local variables
             ./
             SpiceDouble             acc     [3];
             SpiceDouble             dlt;
             SpiceDouble             et;
             SpiceDouble             et0;
             SpiceDouble             lt;
             SpiceDouble             state   [6];
             SpiceDouble             state0  [6];
             SpiceDouble             state2  [6];
             SpiceDouble             stobs   [6];
             SpiceDouble             tdelta;

             SpiceInt                dim;
             SpiceInt                i;

             /.
             Load the SPK and LSK kernels via the meta-kernel.
             ./
             furnsh_c ( META );

             /.
             Convert the start time to seconds past J2000 TDB.
             ./
             str2et_c ( "2000 JAN 1 12:00:00 TDB", &et0 );

             /.
             Step through a series of epochs, looking up a
             state vector at each one.
             ./
             for ( i = 0;  i < MAXITR;  i++ )
             {
                et = et0 + i*STEP;

                /.
                Look up a state vector at epoch ET using the
                following inputs:

                   Target:                 Moon (NAIF ID code 301)
                   Reference frame:        J2000
                   Aberration correction:  Light time and stellar
                                           aberration ('LT+S')
                   Observer:               Earth (NAIF ID code 399)

                Before we can execute this computation, we'll need the
                geometric state and acceleration of the observer relative to
                the solar system barycenter at ET, expressed relative to the
                J2000 reference frame. First find the state:
                ./
                spkssb_c ( 399, et, "j2000", stobs );

                /.
                Next compute the acceleration. We numerically differentiate
                the velocity using a quadratic approximation.
                ./
                tdelta = 1.0;

                spkssb_c ( 399, et-tdelta, "j2000", state0 );
                spkssb_c ( 399, et+tdelta, "j2000", state2 );

                dim = 3;
                qderiv_c ( dim, state0+3, state2+3, tdelta, acc );

                /.
                Now compute the desired state vector:
                ./
                spkaps_c ( 301,   et,  "j2000", "lt+s",
                           stobs, acc, state,   &lt,    &dlt );

                printf( "et = %20.6f\n",                        et       );
                printf( "J2000 x-position (km):   %20.8f\n",    state[0] );
                printf( "J2000 y-position (km):   %20.8f\n",    state[1] );
                printf( "J2000 z-position (km):   %20.8f\n",    state[2] );
                printf( "J2000 x-velocity (km/s): %20.12f\n",   state[3] );
                printf( "J2000 y-velocity (km/s): %20.12f\n",   state[4] );
                printf( "J2000 z-velocity (km/s): %20.12f\n",   state[5] );
                printf( "One-way light time (s):  %20.12f\n",   lt       );
                printf( "Light time rate:         %20.08e\n\n", dlt      );
             }
             return ( 0 );
          }

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

          et =             0.000000
          J2000 x-position (km):       -291584.61369498
          J2000 y-position (km):       -266693.40583163
          J2000 z-position (km):        -76095.65320924
          J2000 x-velocity (km/s):       0.643439157435
          J2000 y-velocity (km/s):      -0.666065873657
          J2000 z-velocity (km/s):      -0.301310063429
          One-way light time (s):        1.342310610325
          Light time rate:               1.07316909e-07

          et =          3600.000000
          J2000 x-position (km):       -289256.45942322
          J2000 y-position (km):       -269080.60545908
          J2000 z-position (km):        -77177.35277130
          J2000 x-velocity (km/s):       0.649970320169
          J2000 y-velocity (km/s):      -0.660148253293
          J2000 z-velocity (km/s):      -0.299630417907
          One-way light time (s):        1.342693954864
          Light time rate:               1.05652599e-07

          et =          7200.000000
          J2000 x-position (km):       -286904.89654240
          J2000 y-position (km):       -271446.41676468
          J2000 z-position (km):        -78252.96553362
          J2000 x-velocity (km/s):       0.656443883155
          J2000 y-velocity (km/s):      -0.654183552046
          J2000 z-velocity (km/s):      -0.297928532945
          One-way light time (s):        1.343071311734
          Light time rate:               1.03990457e-07

          et =         10800.000000
          J2000 x-position (km):       -284530.13302757
          J2000 y-position (km):       -273790.67111559
          J2000 z-position (km):        -79322.41170392
          J2000 x-velocity (km/s):       0.662859504730
          J2000 y-velocity (km/s):      -0.648172246851
          J2000 z-velocity (km/s):      -0.296204558469
          One-way light time (s):        1.343442689069
          Light time rate:               1.02330665e-07

          et =         14400.000000
          J2000 x-position (km):       -282132.37807792
          J2000 y-position (km):       -276113.20159697
          J2000 z-position (km):        -80385.61203056
          J2000 x-velocity (km/s):       0.669216846492
          J2000 y-velocity (km/s):      -0.642114815280
          J2000 z-velocity (km/s):      -0.294458644904
          One-way light time (s):        1.343808095656
          Light time rate:               1.00673404e-07

#### Restrictions

       1)  This routine should not be used to compute geometric states.
           Instead, use spkezr_c, spkez_c, or spkgeo_c. spkgeo_c, which is called
           by spkezr_c and spkez_c, introduces less round-off error when the
           observer and target have a common center that is closer to
           both objects than is the solar system barycenter.

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

       3)  Unlike most other SPK state computation routines, this
           routine requires that the output state be relative to an
           inertial reference frame.

#### Literature_References

       None.

#### Author_and_Institution

       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)

#### Version

       -CSPICE Version 1.1.0, 01-NOV-2021 (JDR)

           Fixed size of "accobs" argument: it was 6 when it should be 3.

           Edited the header and meta-kernel in -Examples section to comply with
           NAIF standard. Updated code example comments.

           Updated code example to use qderiv_c instead of f2c'ed routine.

       -CSPICE Version 1.0.1, 07-JUL-2014 (NJB)

           Descriptions of aberration correction choices that include
           stellar aberration were missing. These have been added.
           Erroneous claim that stellar aberration specifiers (instances
           of "+S") in `abcorr' are ignored was deleted.

           Discussion of light time corrections was updated. Assertions
           that converged light time corrections are unlikely to be
           useful were removed.

       -CSPICE Version 1.0.0, 11-JAN-2008 (NJB)

#### Index_Entries

       low-level aberration-corrected state computation
       low-level light time and stellar aberration correction

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

    Fri Dec 31 18:41:12 2021