| spkapo |
|
Table of contents
Procedure
SPKAPO ( S/P Kernel, apparent position only )
SUBROUTINE SPKAPO ( TARG, ET, REF, SOBS, ABCORR, PTARG, LT )
Abstract
Return the position of a target body relative to an observer,
optionally corrected for light time and stellar aberration.
Required_Reading
SPK
Keywords
EPHEMERIS
Declarations
IMPLICIT NONE
INTEGER TARG
DOUBLE PRECISION ET
CHARACTER*(*) REF
DOUBLE PRECISION SOBS ( 6 )
CHARACTER*(*) ABCORR
DOUBLE PRECISION PTARG ( 3 )
DOUBLE PRECISION LT
Brief_I/O
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
TARG I Target body.
ET I Observer epoch.
REF I Inertial reference frame of observer's state.
SOBS I State of observer wrt. solar system barycenter.
ABCORR I Aberration correction flag.
PTARG O Position 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 position vector which points
from the observer to the target.
ET is the ephemeris time, expressed as seconds past
J2000 TDB, at which the position 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 observer's state SOBS is 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.
SOBS is the geometric (uncorrected) state of the observer
relative to the solar system barycenter at epoch ET.
SOBS is a 6-vector: the first three components of
SOBS represent a Cartesian position vector; the last
three components represent the corresponding velocity
vector. SOBS is expressed relative to the inertial
reference frame designated by REF.
Units are always km and km/sec.
ABCORR indicates the aberration corrections to be applied to
the position 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 position 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 position 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.
'LT+S' Correct for one-way light time and
stellar aberration using a Newtonian
formulation. This option modifies the
position obtained with the 'LT' option
to account for the observer's velocity
relative to the solar system
barycenter. The result is the apparent
position of the target---the position
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
position 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
position obtained with the 'XLT' option
to account for the observer's velocity
relative to the solar system
barycenter. The target position
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.
Detailed_Output
PTARG is a Cartesian 3-vector representing the position of
the target body relative to the specified observer.
PTARG is corrected for the specified aberrations, and
is expressed with respect to the specified inertial
reference frame. The components of PTARG represent
the x-, y- and z-components of the target's position.
The vector PTARG points from the observer's position
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.
LT is the one-way light time between the observer and
target in seconds. If the target position 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 value of ABCORR is not recognized, the error
SPICE(SPKINVALIDOPTION) is signaled.
2) If the reference frame requested is not a recognized
inertial reference frame, the error SPICE(BADFRAME) is
signaled.
3) If the position 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.
Files
This routine computes positions 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 PTARG 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 PTARG. 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
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. 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, 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.
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 motion of the target. The stellar aberration formula used
by this routine is non- relativistic.
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 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.
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.
The traditional aberration corrections applicable to observation
and those applicable to transmission are related in a simple way:
one may picture the geometry of the "transmission" case by
imagining the "observation" case running in reverse time order,
and vice versa.
One may reasonably 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 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' or 'CN')
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 '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 position vector as a low-accuracy estimate
of the apparent position for an application where execution
speed is critical:
Use 'NONE'.
6) While this routine cannot perform the relativistic
aberration corrections required to compute positions
with the highest possible accuracy, it can supply the
geometric positions required as inputs to these
computations:
Use 'NONE', then apply high-accuracy 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
==============
SPKAPO 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 position vector is
T(ET) - O(ET)
Reception case
==============
When any of the options 'LT', 'CN', 'LT+S', 'CN+S' are
selected, SPKAPO 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
RHS of the light-time equation (1) yields the "one-iteration"
estimate of the one-way light time. Repeating the process
until the estimates of LT converge yields the "converged
Newtonian" light time estimate.
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 light-time corrected position is the vector
T(ET-LT) - O(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 magnitude of the rotation
depends on the magnitude of the observer's velocity relative
to the solar system barycenter and the angle between
this velocity and the observer-target vector. 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.
Transmission case
==================
When any of the options 'XLT', 'XCN', 'XLT+S', 'XCN+S' are
selected, SPKAPO 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 light-time corrected position is
T(ET+LT) - O(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 magnitude of the
rotation depends on the magnitude of the velocity and the
angle between the velocity and the observer-target vector.
The rotation is computed as in the reception case, but the
sign of the rotation angle is negated.
Neither special nor general relativistic effects are accounted
for in the aberration corrections performed by this routine.
Examples
In the following code fragment, SPKSSB and SPKAPO are used
to display the position of Io (body 501) as seen from the
Voyager 2 spacecraft (Body -32) at a series of epochs.
Normally, one would call the high-level reader SPKPOS to obtain
position vectors. The example below illustrates the interface
of this routine, but is not intended as a recommendation on
how to use the SPICE SPK subsystem.
The use of integer ID codes is necessitated by the low-level
interface of this routine.
IO = 501
VGR2 = -32
DO WHILE ( EPOCH .LE. END )
CALL SPKSSB ( VGR2, EPOCH, 'J2000', STVGR2 )
CALL SPKAPO ( IO, EPOCH, 'J2000', STVGR2,
. 'LT+S', STIO, LT )
CALL RECRAD ( STIO, RANGE, RA, DEC )
WRITE (*,*) RA * DPR(), DEC * DPR()
EPOCH = EPOCH + DELTA
END DO
Restrictions
1) The ephemeris files to be used by SPKAPO must be loaded
(normally by the SPICELIB kernel loader FURNSH) before
this routine is called.
2) Unlike most other SPK position computation routines, this
routine requires that the input state be relative to an
inertial reference frame. Non-inertial frames are not
supported by this routine.
3) In a future version of this routine, the implementation
of the aberration corrections may be enhanced to improve
accuracy.
Literature_References
None.
Author_and_Institution
N.J. Bachman (JPL)
J. Diaz del Rio (ODC Space)
B.V. Semenov (JPL)
W.L. Taber (JPL)
E.D. Wright (JPL)
Version
SPICELIB Version 2.3.1, 28-APR-2021 (JDR)
Edited the header to comply with NAIF standard. Removed
unnecessary $Revisions section.
SPICELIB Version 2.3.0, 03-JUL-2014 (NJB) (BVS)
Discussion of light time corrections was updated. Assertions
that converged light time corrections are unlikely to be
useful were removed.
Last update was 21-SEP-2013 (BVS)
Updated to call LJUCRS instead of CMPRSS/UCASE.
SPICELIB Version 2.2.0, 17-MAY-2010 (NJB)
Bug fix: routine now returns immediately after
state lookup failure.
SPICELIB Version 2.1.0, 31-AUG-2005 (NJB)
Updated to remove non-standard use of duplicate arguments
in VSUB call.
SPICELIB Version 2.0.1, 20-OCT-2003 (EDW)
Added mention that LT returns in seconds.
Corrected spelling errors.
SPICELIB Version 2.0.0, 18-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.
SPICELIB Version 1.0.0, 03-MAR-1999 (WLT)
|
Fri Dec 31 18:36:50 2021