| azlcpo_c |
|
Table of contents
Procedure
azlcpo_c ( AZ/EL, constant position observer state )
void azlcpo_c ( ConstSpiceChar * method,
ConstSpiceChar * target,
SpiceDouble et,
ConstSpiceChar * abcorr,
SpiceBoolean azccw,
SpiceBoolean elplsz,
ConstSpiceDouble obspos [3],
ConstSpiceChar * obsctr,
ConstSpiceChar * obsref,
SpiceDouble azlsta [6],
SpiceDouble * lt )
AbstractReturn the azimuth/elevation coordinates of a specified target relative to an "observer," where the observer has constant position in a specified reference frame. The observer's position is provided by the calling program rather than by loaded SPK files. Required_ReadingFRAMES PCK SPK TIME KeywordsCOORDINATES EPHEMERIS Brief_I/O
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
method I Method to obtain the surface normal vector.
target I Name of target ephemeris object.
et I Observation epoch.
abcorr I Aberration correction.
azccw I Flag indicating how azimuth is measured.
elplsz I Flag indicating how elevation is measured.
obspos I Observer position relative to center of motion.
obsctr I Center of motion of observer.
obsref I Body-fixed, body-centered frame of observer's
center.
azlsta O State of target with respect to observer,
in azimuth/elevation coordinates.
lt O One way light time between target and
observer.
Detailed_Input
method is a short string providing parameters defining the
computation method to be used to obtain the surface
normal vector that defines the local zenith. Parameters
include, but are not limited to, the shape model used to
represent the body's surface of observer's center of
motion.
The only choice currently supported is
"ELLIPSOID" The intercept computation uses
a triaxial ellipsoid to model
the body's surface of the
observer's center of motion.
The ellipsoid's radii must be
available in the kernel pool.
Neither case nor white space are significant in
`method'. For example, the string " eLLipsoid " is
valid.
In a later Toolkit release, this argument will be
used to invoke a wider range of surface
representations. For example, it will be possible to
represent the target body's surface using a digital
shape model.
target is the name of a target body. Optionally, you may supply
the ID code of the object as an integer string. For
example, both "EARTH" and "399" are legitimate strings
to supply to indicate the target is Earth.
Case and leading and trailing blanks are not significant
in the string `target'.
et is the ephemeris time at which the state of the
target relative to the observer is to be computed. `et'
is expressed as seconds past J2000 TDB. `et' refers to
time at the observer's location.
abcorr is a short string that indicates the aberration
corrections to be applied to the observer-target state
to account for one-way light time and stellar
aberration.
`abcorr' may be any of the following:
"NONE" Apply no correction. Return the
geometric state of the target
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. 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.
"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
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 and stellar
aberration corrections.
Neither special nor general relativistic effects are
accounted for in the aberration corrections applied
by this routine.
Case and leading and trailing blanks are not
significant in the string `abcorr'.
azccw is a flag indicating how the azimuth is measured.
If `azccw' is SPICETRUE, the azimuth increases in the
counterclockwise direction; otherwise it increases
in the clockwise direction.
elplsz is a flag indicating how the elevation is measured.
If `elplsz' is SPICETRUE, the elevation increases from
the XY plane toward +Z; otherwise toward -Z.
obspos is the fixed (constant) geometric position of an
observer relative to its center of motion `obsctr',
expressed in the reference frame `obsref'.
`obspos' does not need to be located on the surface of
the object centered at `obsctr'.
Units are always km.
obsctr is the name of the center of motion of `obspos'. The
ephemeris of `obsctr' is provided by loaded SPK files.
Optionally, you may supply the integer ID code for the
object as an integer string. For example both "MOON" and
"301" are legitimate strings that indicate the moon is
the center of motion.
Case and leading and trailing blanks are not significant
in the string `obsctr'.
obsref is the name of the body-fixed, body-centered reference
frame associated with the observer's center of motion,
relative to which the input position `obspos' is
expressed. The observer has constant position relative
to its center of motion in this reference frame.
Case and leading and trailing blanks are not significant
in the string `obsref'.
Detailed_Output
azlsta is a state vector representing the position and
velocity of the target relative to the specified
observer, corrected for the specified aberrations
and expressed in azimuth/elevation coordinates. The
first three components of `azlsta' represent the range,
azimuth and elevation of the target's position; the
last three components form the corresponding velocity
vector:
azlsta = ( r, az, el, dr/dt, daz/dt, del/dt )
The position component of `azlsta' 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.
The velocity component of `azlsta' is the derivative with
respect to time of the position component of `azlsta'.
Azimuth, elevation and its derivatives are measured with
respect to the axes of the local topocentric reference
frame. See the -Particulars section for the definition
of this reference frame.
The azimuth is the angle between the projection onto the
local topocentric principal (X-Y) plane of the vector
from the observer's position to the target and the
principal axis of the reference frame. The azimuth is
zero on the +X axis.
The elevation is the angle between the vector from the
observer's position to the target and the local
topocentric principal plane. The elevation is zero on
the plane.
Units are km for `r', radians for `az' and `el', km/sec for
dr/dt, and radians/sec for daz/dt and del/dt. The range
of `az' is [0, 2*pi] and the range of `el' is [-pi/2, pi/2].
The way azimuth and elevation are measured depend
respectively on the value of the logical flags `azccw' and
`elplsz'. See the description of these input arguments for
details.
lt is the one-way light time between the observer and
target in seconds. If the target state is corrected
for aberrations, then `lt' is the one-way light time
between the observer and the light time corrected
target location.
ParametersNone. Exceptions
1) If either the name of the center of motion or the target
cannot be translated to its NAIF ID code, an error is signaled
by a routine in the call tree of this routine.
2) If the reference frame `obsref' is not recognized, the error
SPICE(UNKNOWNFRAME) is signaled by a routine in the call tree
of this routine. A frame name may fail to be recognized
because a required frame specification kernel has not been
loaded; another cause is a misspelling of the frame name.
3) If the reference frame `obsref' is not centered at the
observer's center of motion `obsctr', the error
SPICE(INVALIDFRAME) is signaled by a routine in the call tree
of this routine.
4) If the radii of the center of motion body are not available
from the kernel pool, an error is signaled by a routine in
the call tree of this routine.
5) If the size of the `obsctr' body radii kernel variable is not
three, an error is signaled by a routine in the call tree of
this routine.
6) If any of the three `obsctr' body radii is less-than or equal to
zero, an error is signaled by a routine in the call tree of
this routine.
7) If the ratio of the longest to the shortest
radii is large enough so that arithmetic expressions
involving its squared value may overflow, an error is
signaled by a routine in the call tree of this routine.
8) If the radii of the center of motion body and the axes of
`obspos' have radically different magnitudes so that arithmetic
overflow may occur during the computation of the nearest
point of the observer on the center of motion's reference
ellipsoid, an error is signaled by a routine in the call tree
of this routine. Note that even if there is no overflow, if
the ratios of the radii lengths, or the ratio of the
magnitude of `obspos' and the shortest radius vary by many
orders of magnitude, the results may have poor precision.
9) If the computation `method' is not recognized, the error
SPICE(INVALIDMETHOD) is signaled by a routine in the call tree
of this routine.
10) If the loaded kernels provide insufficient data to compute
the requested state vector, an error is signaled by a routine
in the call tree of this routine.
11) 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.
12) If the aberration correction `abcorr' is not recognized, an
error is signaled by a routine in the call tree of this
routine.
13) If `target' is on the Z-axis ( x = 0 and y = 0 ) of the local
topocentric frame centered at `obspos', an error is signaled by
a routine in the call tree of this routine. See item 2 in the
-Restrictions section for further details.
14) If any of the `method', `target', `abcorr', `obsctr' or
`obsref' input string pointers is null, the error
SPICE(NULLPOINTER) is signaled.
15) If any of the `method', `target', `abcorr', `obsctr' or
`obsref' input strings has zero length, the error
SPICE(EMPTYSTRING) is signaled.
Files
Appropriate kernels must be loaded by the calling program before
this routine is called.
The following data are required:
- SPK data: ephemeris data for the observer center and target
must be loaded. If aberration corrections are used, the
states of the observer center and target relative to the
solar system barycenter must be calculable from the
available ephemeris data. Typically ephemeris data are made
available by loading one or more SPK files using furnsh_c.
- Shape and orientation data: if the computation method is
specified as "Ellipsoid," triaxial radii for the center body
must be loaded into the kernel pool. Typically this is done by
loading a text PCK file via furnsh_c. Additionally, rotation
data for the body-fixed, body-centered frame associated with
the observer's center of motion must be loaded. These may be
provided in a text or binary PCK file. In some cases these
data may be provided by a CK file.
The following data may be required:
- Frame data: if a frame definition not built into SPICE is
required, for example to convert the observer-target state
to the body-fixed body-centered frame, that definition
must be available in the kernel pool. Typically frame
definitions are supplied by loading a frame kernel using
furnsh_c.
- Additional kernels: if a CK frame is used in this routine's
state computation, then at least one CK and corresponding SCLK
kernel is required. If dynamic frames are used, additional
SPK, PCK, CK, or SCLK kernels may be required.
In all cases, kernel data are normally loaded once per program
run, NOT every time this routine is called.
Particulars
This routine computes azimuth/elevation coordinates of a target
as seen from an observer whose trajectory is not provided by SPK
files.
Observers supported by this routine must have constant position
with respect to a specified center of motion, expressed in a
caller-specified reference frame. The state of the center of
motion relative to the target must be computable using
loaded SPK data.
This routine is suitable for computing the azimuth/elevation
coordinates and its derivatives of target ephemeris
objects, as seen from landmarks on the surface of an extended
object, in cases where no SPK data are available for those
landmarks.
The azimuth/elevation coordinates are defined with respect to
the observer's local topocentric reference frame. This frame is
generally defined as follows:
- the +Z axis is aligned with the surface normal outward
vector at the observer's location;
- the +X axis is aligned with the component of the +Z axis
of the body-fixed reference frame orthogonal to the
outward normal vector, i.e. the +X axis points towards
the body's North pole;
- the +Y axis completes the right-handed system.
For observers located on the +Z axis of the body-fixed frame
designated by `obsref', the following definition of the local
topocentric reference frame is used by this routine:
- the +Z axis is aligned with the surface normal outward
vector at the observer's location;
- the +X axis aligned with the +X axis of the body-fixed
reference frame;
- the +Y axis completes the right-handed system.
In both cases, the origin of the local topocentric frame is
the observer's location.
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) Find the azimuth/elevation state of Venus as seen from the
DSS-14 station at a given epoch first using the position of
the station given as a vector in the ITRF93 frame and then
using the data provided in the kernel pool for the DSS-14
station.
Task description
================
In this example, we will obtain the apparent state of Venus as
seen from DSS-14 station in the DSS-14 topocentric reference
frame. For this computation, we'll use the DSS-14 station's
location given as a vector in the ITRF93 frame.
Then we will compute same apparent state using spkpos_c to
obtain a Cartesian state vector, after which we will transform
the vector coordinates to azimuth, elevation and range and
their derivatives using recazl_c and dazldr_c.
In order to introduce the usage of the logical flags `azccw'
and `elplsz', we will request the azimuth to be measured
clockwise and the elevation positive towards the +Z
axis of the DSS-14_TOPO reference frame.
Results from the two computations will not agree exactly
because of time-dependent differences in the orientation,
relative to the ITRF93 frame, of the topocentric frame centered
at DSS-14. This orientation varies with time due to movement of
the station, which is affected by tectonic plate motion. The
computation using azlcpo_c evaluates the orientation of this
frame using the station location at the observation epoch,
while the spkpos_c computation uses the orientation provided by
the station frame kernel. The latter is fixed and is derived
from the station location at an epoch specified in the
documentation of that kernel.
Kernels
=======
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: azlcpo_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
naif0011.tls Leapseconds
pck00010.tpc Planetary constants
earth_720101_070426.bpc Earth historical
binary PCK
earthstns_itrf93_050714.bsp DSN station SPK
earth_topo_050714.tf DSN station FK
\begindata
KERNELS_TO_LOAD = ( 'de430.bsp',
'naif0011.tls',
'pck00010.tpc',
'earth_720101_070426.bpc',
'earthstns_itrf93_050714.bsp',
'earth_topo_050714.tf' )
\begintext
End of meta-kernel.
Example code begins here.
/.
Program azlcpo_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"
int main( )
{
/.
Local parameters
./
#define META "azlcpo_ex1.tm"
/.
Local variables
./
SpiceChar * abcorr;
SpiceChar * obs;
SpiceChar * obsctr;
SpiceChar * obsref;
SpiceChar * obstim;
SpiceChar * method;
SpiceChar * ref;
SpiceChar * target;
SpiceDouble az;
SpiceDouble azlsta [6];
SpiceDouble azlvel [3];
SpiceDouble el;
SpiceDouble et;
SpiceDouble jacobi [3][3];
SpiceDouble lt;
SpiceDouble state [6];
SpiceDouble obspos [3];
SpiceDouble r;
SpiceBoolean azccw;
SpiceBoolean elplsz;
/.
Load SPICE kernels.
./
furnsh_c ( META );
/.
Convert the observation time to seconds past J2000 TDB.
./
obstim = "2003 Jan 01 00:00:00 TDB";
str2et_c ( obstim, &et );
/.
Set the method, target, center of motion of the observer,
frame of observer position, and aberration corrections.
./
method = "ELLIPSOID";
target = "VENUS";
obsctr = "EARTH";
obsref = "ITRF93";
abcorr = "CN+S";
/.
Set the position of DSS-14 relative to the earth's
center at the observation epoch, expressed in the
ITRF93 reference frame. Values come from the
earth station SPK specified in the meta-kernel.
The actual station velocity is non-zero due
to tectonic plate motion; we ignore the motion
in this example.
./
obspos[0] = -2353.621419700;
obspos[1] = -4641.341471700;
obspos[2] = 3677.052317800;
/.
We want the azimuth/elevation coordinates to be measured
with the azimuth increasing clockwise and the
elevation positive towards +Z axis of the local
topocentric reference frame
./
azccw = SPICEFALSE;
elplsz = SPICETRUE;
azlcpo_c ( method, target, et, abcorr, azccw, elplsz,
obspos, obsctr, obsref, azlsta, < );
/.
In order to check the results obtained using azlcpo_c
we are going to compute the same azimuth/elevation state
using the position of DSS-14 and its local topocentric
reference frame "DSS-14_TOPO" from the kernel pool.
./
obs = "DSS-14";
ref = "DSS-14_TOPO";
/.
Compute the observer-target state.
./
spkezr_c ( target, et, ref, abcorr, obs, state, < );
/.
Convert the position to azimuth/elevation coordinates.
./
recazl_c ( state, azccw, elplsz, &r, &az, &el );
/.
Convert velocity to azimuth/elevation coordinates.
./
dazldr_c ( state[0], state[1], state[2], azccw, elplsz, jacobi );
mxv_c ( jacobi, state+3, azlvel );
printf( "\n" );
printf( "AZ/EL coordinates (from azlcpo_c):\n" );
printf( "\n" );
printf( " Range (km) = %19.8f\n", azlsta[0] );
printf( " Azimuth (deg) = %19.8f\n",
azlsta[1] * dpr_c() );
printf( " Elevation (deg) = %19.8f\n",
azlsta[2] * dpr_c() );
printf( "\n" );
printf( "AZ/EL coordinates (using kernels):\n" );
printf( "\n" );
printf( " Range (km) = %19.8f\n", r );
printf( " Azimuth (deg) = %19.8f\n", az * dpr_c() );
printf( " Elevation (deg) = %19.8f\n", el * dpr_c() );
printf( "\n" );
printf( "AZ/EL velocity (from azlcpo_c):\n" );
printf( "\n" );
printf( " d Range/dt (km/s) = %19.8f\n", azlsta[3] );
printf( " d Azimuth/dt (deg/s) = %19.8f\n",
azlsta[4] * dpr_c() );
printf( " d Elevation/dt (deg/s) = %19.8f\n",
azlsta[5] * dpr_c() );
printf( "\n" );
printf( "AZ/EL velocity (using kernels):\n" );
printf( "\n" );
printf( " d Range/dt (km/s) = %19.8f\n", azlvel[0] );
printf( " d Azimuth/dt (deg/s) = %19.8f\n",
azlvel[1] * dpr_c() );
printf( " d Elevation/dt (deg/s) = %19.8f\n",
azlvel[2] * dpr_c() );
printf( "\n" );
return ( 0 );
}
When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:
AZ/EL coordinates (from azlcpo_c):
Range (km) = 89344802.82679011
Azimuth (deg) = 269.04481881
Elevation (deg) = -25.63088321
AZ/EL coordinates (using kernels):
Range (km) = 89344802.82679011
Azimuth (deg) = 269.04481846
Elevation (deg) = -25.63088278
AZ/EL velocity (from azlcpo_c):
d Range/dt (km/s) = 13.41734176
d Azimuth/dt (deg/s) = 0.00238599
d Elevation/dt (deg/s) = -0.00339644
AZ/EL velocity (using kernels):
d Range/dt (km/s) = 13.41734176
d Azimuth/dt (deg/s) = 0.00238599
d Elevation/dt (deg/s) = -0.00339644
Note the discrepancy in the AZ/EL coordinates found by the two
computation methods. Please refer to the task description for
an explanation.
Restrictions
1) This routine may not be suitable for work with stars or other
objects having large distances from the observer, due to loss
of precision in position vectors.
2) The Jacobian matrix of the transformation from rectangular to
azimuth/elevation coordinates has a singularity for points
located on the Z-axis ( x = 0 and y = 0 ) of the local
topocentric frame centered at `obspos'; therefore the
derivative of the azimuth/elevation coordinates cannot be
computed for those points.
A user who wishes to compute the azimuth/elevation
coordinates, without their derivatives, of `target' as seen
from `obspos' at the input time `et', for those cases when `target'
is located along the local topocentric Z-axis, could do so by
executing the following calls:
spkcpo_c ( target, et, obsref, "OBSERVER", abcorr,
obspos, obsctr, obsref, state, < );
range = vnorm_c ( state );
By definition, the azimuth is zero and the elevation is
either pi/2 if `elplsz' is SPICETRUE, or -pi/2 otherwise.
Literature_ReferencesNone. Author_and_InstitutionJ. Diaz del Rio (ODC Space) Version-CSPICE Version 1.0.0, 01-NOV-2021 (JDR) Index_EntriesAZ/EL_coordinates relative to constant_position_observer AZ/EL_coordinates w.r.t. constant_position surface_point AZ/EL_coordinates relative to surface_point extended_object AZ/EL_coordinates relative to landmark on extended_object |
Fri Dec 31 18:41:01 2021