| spkltc |
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Table of contents
Procedure
SPKLTC ( S/P Kernel, light time corrected state )
SUBROUTINE SPKLTC ( TARG, ET, REF, ABCORR,
. STOBS, STARG, LT, DLT )
Abstract
Return the state (position and velocity) of a target body
relative to an observer, optionally corrected for light time,
expressed relative to an inertial reference frame.
Required_Reading
FRAMES
SPK
Keywords
EPHEMERIS
Declarations
IMPLICIT NONE
INCLUDE 'zzabcorr.inc'
INTEGER TARG
DOUBLE PRECISION ET
CHARACTER*(*) REF
CHARACTER*(*) ABCORR
DOUBLE PRECISION STOBS ( 6 )
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.
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 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. See the discussion in the $Particulars
section for recommendations on how to choose
aberration corrections.
If ABCORR includes the stellar aberration correction
symbol '+S', this flag is simply ignored. Aside from
the possible presence of this symbol, 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 involves
iterative solution of the light time
equation (see $Particulars for details).
The solution invoked by the 'LT' option
uses one iteration.
'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.
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.
'XCN' "Transmission" case: converged
Newtonian light time 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 (uncorrected) state of the observer
relative to the solar system barycenter at epoch ET.
STOBS is a 6-vector: the first three components of
STOBS represent a Cartesian position vector; the last
three components represent the corresponding velocity
vector. STOBS is expressed relative to the inertial
reference frame designated by REF.
Units are always km and km/sec.
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) For the convenience of the caller, the input aberration
correction flag can call for stellar aberration correction via
inclusion of the '+S' suffix. This portion of the aberration
correction flag is ignored if present.
2) If the value of ABCORR is not recognized, an error
is signaled by a routine in the call tree of this
routine.
3) If the reference frame requested is not a recognized
inertial reference frame, the error SPICE(BADFRAME)
is signaled.
4) 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.
5) 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.
6) If a division by zero error would occur in the computation
of DLT, the error SPICE(DIVIDEBYZERO) 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. 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.
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 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: spkltc_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
--------- --------
de421.bsp Planetary ephemeris
pck00010.tpc Planet orientation and
radii
naif0010.tls Leapseconds
\begindata
KERNELS_TO_LOAD = ( 'de421.bsp',
'pck00010.tpc',
'naif0010.tls' )
\begintext
End of meta-kernel
Example code begins here.
PROGRAM SPKLTC_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 = 'spkltc_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 DLT
DOUBLE PRECISION ET
DOUBLE PRECISION ET0
DOUBLE PRECISION LT
DOUBLE PRECISION STATE ( 6 )
DOUBLE PRECISION STOBS ( 6 )
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 ('LT')
C Observer: Earth (NAIF ID code 399)
C
C Before we can execute this computation, we'll need the
C geometric state of the observer relative to the solar
C system barycenter at ET, expressed relative to the
C J2000 reference frame:
C
CALL SPKSSB ( 399, ET, 'J2000', STOBS )
C
C Now compute the desired state vector:
C
CALL SPKLTC ( 301, ET, 'J2000', 'LT',
. STOBS, 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): -291569.26516582817
J2000 y-position (km): -266709.18671506643
J2000 z-position (km): -76099.155290968716
J2000 x-velocity (km/s): 0.64353061395009092
J2000 y-velocity (km/s): -0.66608181647356979
J2000 z-velocity (km/s): -0.30132283137339932
One-way light time (s): 1.3423106103603615
Light time rate: 1.0731690854241060E-007
ET = 3600.0000000000000
J2000 x-position (km): -289240.78103223071
J2000 y-position (km): -269096.44111447036
J2000 z-position (km): -77180.899896450341
J2000 x-velocity (km/s): 0.65006211592321250
J2000 y-velocity (km/s): -0.66016273867753217
J2000 z-velocity (km/s): -0.29964267347917639
One-way light time (s): 1.3426939548981949
Light time rate: 1.0565259879591478E-007
ET = 7200.0000000000000
J2000 x-position (km): -286888.88711488992
J2000 y-position (km): -271462.30193841457
J2000 z-position (km): -78256.555851273239
J2000 x-velocity (km/s): 0.65653599225917958
J2000 y-velocity (km/s): -0.65419657625983696
J2000 z-velocity (km/s): -0.29794027264402967
One-way light time (s): 1.3430713117678452
Light time rate: 1.0399045674252711E-007
ET = 10800.000000000000
J2000 x-position (km): -284513.79148214310
J2000 y-position (km): -273806.60054129362
J2000 z-position (km): -79326.043350853026
J2000 x-velocity (km/s): 0.66295190125626391
J2000 y-velocity (km/s): -0.64818380654817442
J2000 z-velocity (km/s): -0.29621577893712070
One-way light time (s): 1.3434426891028646
Light time rate: 1.0233066508729246E-007
ET = 14400.000000000000
J2000 x-position (km): -282115.70342658088
J2000 y-position (km): -276129.16999696195
J2000 z-position (km): -80389.283131733537
J2000 x-velocity (km/s): 0.66930950447965998
J2000 y-velocity (km/s): -0.64212490750332751
J2000 z-velocity (km/s): -0.29446934292511795
One-way light time (s): 1.3438080956889309
Light time rate: 1.0067340347415892E-007
Restrictions
1) The routine SPKGEO should be used instead of this routine
to compute geometric states. SPKGEO introduces less
round-off error when the observer and target have common
center that is closer to both objects than is the solar
system barycenter.
2) The kernel files to be used by SPKLTC 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 2.0.1, 05-JUL-2021 (JDR)
Edited the header to comply with NAIF standards.
Added FRAMES to the list of $Required_Reading
SPICELIB Version 2.0.0, 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 02-MAY-2012 (NJB)
Updated to ensure convergence when CN or XCN light time
corrections are used. The new algorithm also terminates early
(after fewer than three iterations) when convergence is
attained.
Call to ZZPRSCOR was replaced by a call to ZZVALCOR.
SPICELIB Version 1.0.0, 11-JAN-2008 (NJB)
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Fri Dec 31 18:36:52 2021