Table of contents
CSPICE_STLABX corrects the position of a target for the stellar
aberration effect on radiation transmitted from a specified observer to
the target.
Given:
pobj the cartesian position vector of an object with respect to
the observer, possibly corrected for light time.
[3,1] = size(pobj); double = class(pobj)
Units are km.
vobs the cartesian velocity vector of the observer with respect to
the Solar System barycenter.
[3,1] = size(vobs); double = class(vobs)
Units are km/s.
the call:
[corpos] = cspice_stlabx( pobj, vobs )
returns:
corpos the position of the object relative to the observer,
corrected for the stellar aberration effect on radiation
directed toward the target.
[3,1] = size(corpos); double = class(corpos)
This correction is the inverse of the usual stellar
aberration correction: the corrected vector indicates the
direction in which radiation must be emitted from the
observer, as seen in an inertial reference frame having
velocity equal to that of the observer, in order to reach the
position indicated by the input vector `pobj'.
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) Compute the apparent position of the Moon relative to the
Earth, corrected for one way light-time and stellar aberration
effect on radiation transmitted from the Earth to the Moon,
given the geometric state of the Earth relative to the Solar
System Barycenter, and the difference between the stelar
aberration corrected and uncorrected position vectors, taking
several steps.
First, compute the light-time corrected state of the Moon body
as seen by the Earth, using its geometric state. Then apply
the correction for stellar aberration to the light-time
corrected state of the target body, both for the transmission
case.
The code in this example could be replaced by a single call
to cspice_spkpos:
[pos, lt] = cspice_spkpos( 'MOON', et, ...
'J2000', 'XLT+S', ...
'EARTH' );
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: stlabx_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
naif0009.tls Leapseconds
\begindata
KERNELS_TO_LOAD = ( 'de418.bsp',
'naif0009.tls' )
\begintext
End of meta-kernel
Example code begins here.
function stlabx_ex1()
%
% Assign an observer, Earth, target, Moon, time of interest
% and reference frame for returned vectors.
%
idobs = 399;
idtarg = 301;
utcstr = 'July 4 2004';
reffrm = 'J2000';
%
% Load the needed kernels.
%
cspice_furnsh( 'stlabx_ex1.tm' );
%
% Convert the time string to ephemeris time.
%
[et] = cspice_str2et( utcstr );
%
% Get the state of the observer with respect to the solar
% system barycenter.
%
[sobs] = cspice_spkssb( idobs, et, reffrm );
%
% Get the light-time corrected position `pos' of the target
% body `idtarg' as seen by the observer. Normally we would
% call cspice_spkpos to obtain this vector, but we already have
% the state of the observer relative to the solar system
% barycenter, so we can avoid looking up that state twice
% by calling cspice_spkapo.
%
[pos, lt] = cspice_spkapo( idtarg, et, reffrm, sobs, 'XLT' );
%
% Output the uncorrected vector.
%
fprintf( 'Uncorrected position vector\n' )
fprintf( ' %18.6f %18.6f %18.6f\n', pos(1), pos(2), pos(3) )
%
% Apply the correction for stellar aberration to the
% light-time corrected position of the target body.
%
[pcorr] = cspice_stlabx( pos, sobs(4:6) );
%
% Output the corrected position vector and the apparent
% difference from the uncorrected vector.
%
fprintf( '\n' )
fprintf( 'Corrected position vector\n' )
fprintf( ' %18.6f %18.6f %18.6f\n', ...
pcorr(1), pcorr(2), pcorr(3) )
%
% Apparente difference.
%
appdif = pos - pcorr;
fprintf( '\n' )
fprintf( 'Apparent difference\n' )
fprintf( ' %18.6f %18.6f %18.6f\n', ...
appdif(1), appdif(2), appdif(3) )
%
% 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/Octave5.x/64-bit
platform, the output was:
Uncorrected position vector
201809.933536 -260878.049826 -147716.077987
Corrected position vector
201782.730972 -260894.375627 -147724.405897
Apparent difference
27.202563 16.325802 8.327911
In order to transmit radiation from an observer to a specified
target, the emission direction must be corrected for one way
light time and for the motion of the observer relative to the
solar system barycenter. The correction for the observer's
motion when transmitting to a target is the inverse of the
usual stellar aberration correction applied to the light-time
corrected position of the target as seen by the observer.
Below is the description of the stellar aberration correction
used in the Mice routine cspice_stelab (with the notation changed
slightly):
Let `r' be the 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.
This routine applies the inverse correction, so here the rotation
about `h' is by -phi radians.
1) If the velocity of the observer is greater than or equal to
the speed of light, an error is signaled by a routine in the
call tree of this routine. The outputs are undefined.
2) If any of the input arguments, `pobj' or `vobs', is undefined,
an error is signaled by the Matlab error handling system.
3) If any of the input arguments, `pobj' or `vobs', is not of the
expected type, or it does not have the expected dimensions and
size, an error is signaled by the Mice interface.
None.
None.
MICE.REQ
[1] W. Owen, "The Treatment of Aberration in Optical Navigation",
JPL IOM #314.8-524, 8 February 1985.
J. Diaz del Rio (ODC Space)
-Mice Version 1.0.0, 09-AUG-2021 (JDR)
stellar aberration for transmission case
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