| spkaps |
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Table of contents
Procedure
SPKAPS ( SPK, apparent state )
SUBROUTINE SPKAPS ( TARG, ET, REF, ABCORR,
. STOBS, ACCOBS, STARG, LT, 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.
SPICE users normally should call the high-level API routines
SPKEZR or SPKEZ rather than this routine.
Required_Reading
SPK
Keywords
EPHEMERIS
Declarations
IMPLICIT NONE
INCLUDE 'zzabcorr.inc'
INTEGER TARG
DOUBLE PRECISION ET
CHARACTER*(*) REF
CHARACTER*(*) ABCORR
DOUBLE PRECISION STOBS ( 6 )
DOUBLE PRECISION ACCOBS ( 3 )
DOUBLE PRECISION STARG ( 6 )
DOUBLE PRECISION LT
DOUBLE PRECISION DLT
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 SPICELIB 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 header of SPKEZR 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 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. STOBS is expressed
relative to the reference frame designated by REF.
The target and observer define a state vector whose
position component points from the observer to the
target.
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 aberrations, and is expressed with respect
to the inertial reference frame designated by REF.
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.
3) If ABCORR calls for relativistic light time corrections, the
error SPICE(NOTSUPPORTED) is signaled.
4) If the reference frame requested is not a recognized
inertial reference frame, the error SPICE(BADFRAME)
is signaled.
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.
Files
This routine computes states using SPK files that have been
loaded into the SPICE system, normally via the kernel loading
interface routine FURNSH. 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 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
SPKEZP
or the low-level, position-only analog of this routine
SPKAPO
In general, the position-only routines are more efficient.
See the header of the routine SPKEZR 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
IMPLICIT NONE
C
C Local constants
C
C The meta-kernel name shown here refers to a file whose
C contents are those shown above. This file and the kernels
C it references must exist in your current working
C directory.
C
CHARACTER*(*) META
PARAMETER ( META = 'spkaps_ex1.tm' )
C
C Use a time step of 1 hour; look up 5 states.
C
DOUBLE PRECISION STEP
PARAMETER ( STEP = 3600.0D0 )
INTEGER MAXITR
PARAMETER ( MAXITR = 5 )
C
C Local variables
C
DOUBLE PRECISION ACC ( 3 )
DOUBLE PRECISION DLT
DOUBLE PRECISION ET
DOUBLE PRECISION ET0
DOUBLE PRECISION LT
DOUBLE PRECISION STATE ( 6 )
DOUBLE PRECISION STATE0 ( 6 )
DOUBLE PRECISION STATE2 ( 6 )
DOUBLE PRECISION STOBS ( 6 )
DOUBLE PRECISION TDELTA
INTEGER I
C
C Load the SPK and LSK kernels via the meta-kernel.
C
CALL FURNSH ( META )
C
C Convert the start time to seconds past J2000 TDB.
C
CALL STR2ET ( '2000 JAN 1 12:00:00 TDB', ET0 )
C
C Step through a series of epochs, looking up a
C state vector at each one.
C
DO I = 1, MAXITR
ET = ET0 + (I-1)*STEP
C
C Look up a state vector at epoch ET using the
C following inputs:
C
C Target: Moon (NAIF ID code 301)
C Reference frame: J2000
C Aberration correction: Light time and stellar
C aberration ('LT+S')
C Observer: Earth (NAIF ID code 399)
C
C Before we can execute this computation, we'll need the
C geometric state and acceleration of the observer
C relative to the solar system barycenter at ET,
C expressed relative to the J2000 reference frame. First
C find the state:
C
CALL SPKSSB ( 399, ET, 'J2000', STOBS )
C
C Next compute the acceleration. We numerically
C differentiate the velocity using a quadratic
C approximation:
C
TDELTA = 1.D0
CALL SPKSSB ( 399, ET-TDELTA, 'J2000', STATE0 )
CALL SPKSSB ( 399, ET+TDELTA, 'J2000', STATE2 )
CALL QDERIV ( 3, STATE0(4), STATE2(4), TDELTA, ACC )
C
C Now compute the desired state vector:
C
CALL SPKAPS ( 301, ET, 'J2000', 'LT+S',
. STOBS, ACC, STATE, LT, DLT )
WRITE (*,*) 'ET = ', ET
WRITE (*,*) 'J2000 x-position (km): ', STATE(1)
WRITE (*,*) 'J2000 y-position (km): ', STATE(2)
WRITE (*,*) 'J2000 z-position (km): ', STATE(3)
WRITE (*,*) 'J2000 x-velocity (km/s): ', STATE(4)
WRITE (*,*) 'J2000 y-velocity (km/s): ', STATE(5)
WRITE (*,*) 'J2000 z-velocity (km/s): ', STATE(6)
WRITE (*,*) 'One-way light time (s): ', LT
WRITE (*,*) 'Light time rate: ', DLT
WRITE (*,*) ' '
END DO
END
When this program was executed on a Mac/Intel/gfortran/64-bit
platform, the output was:
ET = 0.0000000000000000
J2000 x-position (km): -291584.61369497533
J2000 y-position (km): -266693.40583162551
J2000 z-position (km): -76095.653209237149
J2000 x-velocity (km/s): 0.64343915743508395
J2000 y-velocity (km/s): -0.66606587365741410
J2000 z-velocity (km/s): -0.30131006342946742
One-way light time (s): 1.3423106103251679
Light time rate: 1.0731690869897750E-007
ET = 3600.0000000000000
J2000 x-position (km): -289256.45942322229
J2000 y-position (km): -269080.60545907740
J2000 z-position (km): -77177.352771302132
J2000 x-velocity (km/s): 0.64997032016926526
J2000 y-velocity (km/s): -0.66014825329341664
J2000 z-velocity (km/s): -0.29963041790724715
One-way light time (s): 1.3426939548635302
Light time rate: 1.0565259895222426E-007
ET = 7200.0000000000000
J2000 x-position (km): -286904.89654239739
J2000 y-position (km): -271446.41676468350
J2000 z-position (km): -78252.965533623050
J2000 x-velocity (km/s): 0.65644388315539315
J2000 y-velocity (km/s): -0.65418355204586442
J2000 z-velocity (km/s): -0.29792853294482308
One-way light time (s): 1.3430713117337547
Light time rate: 1.0399045689875861E-007
ET = 10800.000000000000
J2000 x-position (km): -284530.13302756584
J2000 y-position (km): -273790.67111559171
J2000 z-position (km): -79322.411703917489
J2000 x-velocity (km/s): 0.66285950473048116
J2000 y-velocity (km/s): -0.64817224685146524
J2000 z-velocity (km/s): -0.29620455846903732
One-way light time (s): 1.3434426890693671
Light time rate: 1.0233066524342374E-007
ET = 14400.000000000000
J2000 x-position (km): -282132.37807791750
J2000 y-position (km): -276113.20159697317
J2000 z-position (km): -80385.612030562901
J2000 x-velocity (km/s): 0.66921684649247459
J2000 y-velocity (km/s): -0.64211481528028158
J2000 z-velocity (km/s): -0.29445864490384888
One-way light time (s): 1.3438080956559786
Light time rate: 1.0067340363005083E-007
Restrictions
1) This routine should not be used to compute geometric states.
Instead, use SPKEZR, SPKEZ, or SPKGEO. SPKGEO, which is called
by SPKEZR and SPKEZ, 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 must be loaded
(normally by the SPICELIB kernel loader FURNSH) 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
SPICELIB Version 1.2.0, 26-OCT-2021 (JDR) (NJB)
Edited the header to comply with NAIF standard. Updated
example's meta-kernel.
Bug fix: ABCORR now is parsed using ZZVALCOR. This improves
error checking. Removed unnecessary in-line error checking
now provided by ZZVALCOR.
SPICELIB Version 1.1.0, 04-JUL-2014 (NJB)
Discussion of light time corrections was updated. Assertions
that converged light time corrections are unlikely to be
useful were removed.
Last update was 15-APR-2014 (NJB)
Added a FAILED() call to prevent numeric problems
resulting from uninitialized values.
SPICELIB Version 1.0.0, 11-JAN-2008 (NJB)
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Fri Dec 31 18:36:50 2021