Table of contents
MICE_SPKPOS returns the position of a target body relative
to an observing body, optionally corrected for light time
(planetary aberration) and stellar aberration.
Given:
targ the name of a target body.
[1,c1] = size(target); char = class(target)
or
[1,1] = size(target); cell = class(target)
Optionally, you may supply the integer ID code for the object
as an integer string, i.e. both 'MOON' and '301' are
legitimate strings that indicate the Moon is the target body.
The target and observer define a position vector
whose position component points from the observer
to the target.
et the ephemeris time(s), expressed as seconds past J2000
TDB, at which the position of the target body relative to
the observer is to be computed.
[1,n] = size(et); double = class(et)
`et' refers to time at the observer's location.
ref the name of the reference frame relative to which the output
position vector should be expressed.
[1,c2] = size(ref); char = class(ref)
or
[1,1] = size(ref); cell = class(ref)
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.
abcorr the aberration corrections to apply to the position of the
target body to account for one-way light time and stellar
aberration.
[1,c3] = size(abcorr); char = class(abcorr)
or
[1,1] = size(abcorr); cell = class(abcorr)
`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 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
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).
The 'CN' correction typically does not
substantially improve accuracy because
the errors made by ignoring
relativistic effects may be larger than
the improvement afforded by obtaining
convergence of the light time solution.
The 'CN' correction computation also
requires a significantly greater number
of CPU cycles than does the
one-iteration light time correction.
'CN+S' Converged Newtonian light time
and stellar aberration 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
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 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 and stellar
aberration corrections.
Neither special nor general relativistic effects are
accounted for in the aberration corrections applied
by this routine.
Neither letter case or embedded blanks are significant
in the `abcorr' string.
obs the name of a observing body.
[1,c4] = size(obs); char = class(obs)
or
[1,1] = size(obs); cell = class(obs)
Optionally, you may supply the integer ID code
for the object as an integer string, i.e. both
'MOON' and '301' are legitimate strings that
indicate the Moon is the observing body.
the call:
[ptarg] = mice_spkpos( targ, et, ref, abcorr, obs )
returns:
ptarg the structure(s) containing the results of the calculation.
[1,n] = size(ptarg); struct = class(ptarg)
Each structure consists of the fields:
pos the Cartesian state vector representing the
position of the target body relative
to the specified observer.
[3,1] = size(ptarg(i).pos);
double = class(ptarg(i).pos)
`pos' is corrected for the specified aberrations,
and is expressed with respect to the reference
frame specified by `ref'.
The position 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.
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 the value(s) of the one-way light time between the
observer and target in seconds.
[1,1] = size(ptarg(i).lt);
double = class(ptarg(i).lt)
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.
`ptarg' returns with the same vectorization measure (N) as
`et'.
None.
Any numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.
1) Load a planetary SPK, and look up the position of Mars
as seen from the Earth in the J2000 frame with aberration
corrections 'LT+S' (ligth time plus stellar aberration) at
different epochs.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File: spkpos_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
--------- --------
de430.bsp Planetary ephemeris
mar097.bsp Mars satellite ephemeris
naif0011.tls Leapseconds
\begindata
KERNELS_TO_LOAD = ( 'de430.bsp',
'mar097.bsp',
'naif0011.tls' )
\begintext
End of meta-kernel
Example code begins here.
function spkpos_ex1()
%
% Load a set of kernels: an SPK file, a PCK
% file and a leapseconds file. Use a meta
% kernel for convenience.
%
cspice_furnsh( 'spkpos_ex1.tm' )
%
% Define parameters for a position lookup:
%
% Return the position vector of Mars (499) as seen from
% Earth (399) in the J2000 frame
% using aberration correction LT+S (light time plus
% stellar aberration) at the epoch
% July 4, 2003 11:00 AM PST.
%
target = 'Mars';
epoch = 'July 4, 2003 11:00 AM PST';
frame = 'J2000';
abcorr = 'LT+S';
observer = 'Earth';
%
% Convert the epoch to ephemeris time.
%
et = cspice_str2et( epoch );
%
% Look-up the position for the defined parameters.
%
starg = mice_spkpos( target, et, frame, abcorr, observer);
%
% Output...
%
txt = sprintf( 'The position of : %s', target);
disp( txt )
txt = sprintf( 'As observed from : %s', observer );
disp( txt )
txt = sprintf( 'In reference frame : %s', frame );
disp( txt )
disp( ' ' )
txt = sprintf( 'Scalar' );
disp( txt )
utc_epoch = cspice_et2utc( et, 'C', 3 );
txt = sprintf( 'At epoch : %s', epoch );
disp( txt )
txt = sprintf( ' : i.e. %s', utc_epoch );
disp( txt )
txt = sprintf( ['R (kilometers) : ' ...
'%12.4f %12.4f %12.4f'], starg.pos );
disp( txt )
txt = sprintf( 'Light time (secs) : %12.7f', starg.lt );
disp( txt )
disp(' between observer' )
disp(' and target' )
disp( ' ' )
%
% Create a vector of et's, starting at `epoch'
% in steps of 100000 ephemeris seconds.
%
vec_et = [0:4]*100000. + et;
disp( 'Vector' )
vec_epoch = cspice_et2utc( vec_et, 'C', 3 );
%
% Look up the position vectors and light time values
% corresponding to the vector of input
% ephemeris time `vec_et'.
%
ptarg = mice_spkpos( target, vec_et, frame, abcorr, observer );
for i=1:5
txt = sprintf( 'At epoch (UTC) : %s', vec_epoch(i,:) );
disp( txt )
txt = sprintf( ['R (kilometers) : ' ...
'%12.4f %12.4f %12.4f'], ptarg(i).pos );
disp( txt )
txt = sprintf( 'Light time (secs) : %12.7f', ptarg(i).lt );
disp( txt )
disp(' between observer' )
disp(' and target' )
disp( ' ' )
end
%
% It's always good form to unload kernels after use,
% particularly in MATLAB due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
The position of : Mars
As observed from : Earth
In reference frame : J2000
Scalar
At epoch : July 4, 2003 11:00 AM PST
: i.e. 2003 JUL 04 19:00:00.000
R (kilometers) : 73822235.3312 -27127919.1784 -18741306.2848
Light time (secs) : 269.6898816
between observer
and target
Vector
At epoch (UTC) : 2003 JUL 04 19:00:00.000
R (kilometers) : 73822235.3312 -27127919.1784 -18741306.2848
Light time (secs) : 269.6898816
between observer
and target
At epoch (UTC) : 2003 JUL 05 22:46:40.000
R (kilometers) : 73140185.4372 -26390524.9551 -18446763.0157
Light time (secs) : 266.5640396
between observer
and target
At epoch (UTC) : 2003 JUL 07 02:33:20.000
R (kilometers) : 72456239.6858 -25681031.1854 -18163339.1239
Light time (secs) : 263.4803536
between observer
and target
At epoch (UTC) : 2003 JUL 08 06:20:00.000
R (kilometers) : 71771127.0353 -24999259.6270 -17890946.6135
Light time (secs) : 260.4395237
between observer
and target
At epoch (UTC) : 2003 JUL 09 10:06:40.000
R (kilometers) : 71085543.8563 -24345021.3427 -17629490.6857
Light time (secs) : 257.4422004
between observer
and target
A sister version of this routine exists named cspice_spkpos that returns
the structure field data as separate arguments.
Alternatively, if needed, the user can extract the field data from
vectorized `ptarg' structures into separate arrays.
Extract the N `pos' field data to a 6XN array `position':
position = reshape( [ptarg(:).pos], 3, [] )
Extract the N `lt' field data to a 1XN array `lighttime':
lighttime = reshape( [ptarg(:).lt], 1, [] )
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 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 position 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 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
==============
mice_spkpos 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', mice_spkpos 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, mice_spkpos 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.
1) If name of target or observer cannot be translated to its NAIF
ID code, the error SPICE(IDCODENOTFOUND) is signaled by a
routine in the call tree of this routine.
2) If the reference frame `ref' is not a recognized reference
frame, the error SPICE(UNKNOWNFRAME) is signaled by a routine
in the call tree of this routine.
3) If the loaded kernels provide insufficient data to compute the
requested position vector, an error is signaled by a routine
in the call tree of this routine.
4) If an error occurs while reading an SPK or other kernel file,
the error is signaled by a routine in the call tree
of this routine.
5) If any of the input arguments, `targ', `et', `ref', `abcorr'
or `obs', is undefined, an error is signaled by the Matlab
error handling system.
6) If any of the input arguments, `targ', `et', `ref', `abcorr'
or `obs', is not of the expected type, or it does not have the
expected dimensions and size, an error is signaled by the Mice
interface.
This routine computes positions using SPK files that have been loaded
into the SPICE system, normally via the kernel loading interface routine
cspice_furnsh. See the routine cspice_furnsh and the SPK and KERNEL
Required Reading for further information on loading (and unloading)
kernels.
If the output position `pos' is to be expressed relative to a
non-inertial frame, or if any of the ephemeris data used to
compute `pos' 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 position. Normally these additional kernels are PCK
files or frame kernels. Any such kernels must already be loaded
at the time this routine is called.
None.
MICE.REQ
SPK.REQ
NAIF_IDS.REQ
FRAMES.REQ
TIME.REQ
None.
N.J. Bachman (JPL)
J. Diaz del Rio (ODC Space)
B.V. Semenov (JPL)
E.D. Wright (JPL)
-Mice Version 1.1.0, 02-NOV-2021 (EDW) (JDR)
Edited the header comply with NAIF standard. Added
example's problem statement and meta-kernel.
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections.
Updated -Particulars to reflect latest status of sister
API cspice_spkpos.
Eliminated use of "lasterror" in rethrow.
Removed reference to the function's corresponding CSPICE header from
-Required_Reading section.
-Mice Version 1.0.3, 03-DEC-2014 (NJB) (BVS) (EDW)
Corrections made to author identifier for 1.0.2, 07-NOV-2013
to indicate institution.
Discussion of light time corrections was updated. Assertions
that converged light time corrections are unlikely to be
useful were removed.
-Mice Version 1.0.2, 07-NOV-2013 (EDW)
-I/O descriptions edits to conform to Mice documentation format.
Added aberration algorithm explanation to -Particulars section.
-Mice Version 1.0.1, 22-DEC-2008 (EDW)
Header edits performed to improve argument descriptions.
These descriptions should now closely match the descriptions
in the corresponding CSPICE routine.
-Mice Version 1.0.0, 22-NOV-2005 (EDW)
using names get target position relative to an observer
position relative to observer corrected for aberrations
read ephemeris data
read trajectory data
|