| edterm_c |
|
Table of contents
Procedure
edterm_c ( Ellipsoid terminator )
void edterm_c ( ConstSpiceChar * trmtyp,
ConstSpiceChar * source,
ConstSpiceChar * target,
SpiceDouble et,
ConstSpiceChar * fixref,
ConstSpiceChar * abcorr,
ConstSpiceChar * obsrvr,
SpiceInt npts,
SpiceDouble * trgepc,
SpiceDouble obspos [3],
SpiceDouble trmpts [ ][3] )
AbstractCompute a set of points on the umbral or penumbral terminator of a specified target body, where the target shape is modeled as an ellipsoid. Required_ReadingFRAMES PCK SPK TIME KeywordsBODY GEOMETRY MATH Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- trmtyp I Terminator type. source I Light source. target I Target body. et I Observation epoch. fixref I Body-fixed frame associated with target. abcorr I Aberration correction. obsrvr I Observer. npts I Number of points in terminator set. trgepc O Epoch associated with target center. obspos O Position of observer in body-fixed frame. trmpts O Terminator point set. Detailed_Input
trmtyp is a string indicating the type of terminator to
compute: umbral or penumbral. The umbral terminator is
the boundary of the portion of the ellipsoid surface in
total shadow. The penumbral terminator is the boundary
of the portion of the surface that is completely
illuminated. Note that in astronomy references, the
unqualified word "terminator" refers to the umbral
terminator. Here, the unqualified word refers to either
type of terminator.
Possible values of `trmtyp' are
"UMBRAL"
"PENUMBRAL"
Case and leading or trailing blanks in `trmtyp' are
not significant.
source is the name of the body acting as a light source.
`source' is case-insensitive, and leading and trailing
blanks in `target' are not significant. Optionally, you
may supply a string containing the integer ID code for
the object. For example both "SUN" and "10" are
legitimate strings that indicate the Sun is the light
source.
This routine assumes that a kernel variable representing
the light source's radii is present in the kernel pool.
Normally the kernel variable would be defined by loading
a PCK file.
The shape of the light source is always modeled as a
sphere, regardless of whether radii defining a triaxial
ellipsoidal shape model are available in the kernel
pool. The maximum radius of the body is used as the
radius of the sphere.
target is the name of the target body. `target' is
case-insensitive, and leading and trailing blanks in
`target' are not significant. Optionally, you may supply
a string containing the integer ID code for the object.
For example both "MOON" and "301" are legitimate strings
that indicate the moon is the target body.
This routine assumes that a kernel variable representing
the target's radii is present in the kernel pool.
Normally the kernel variable would be defined by loading
a PCK file.
et is the epoch of participation of the observer, expressed
as ephemeris seconds past J2000 TDB: `et' is the epoch
at which the observer's position is computed.
When aberration corrections are not used, `et' is also
the epoch at which the position and orientation of the
target body and position of the light source are
computed.
When aberration corrections are used, `et' is the epoch
at which the observer's position relative to the solar
system barycenter is computed; in this case the position
and orientation of the target body are computed at
et-lt, where lt is the one-way light time between the
target body's center and the observer. See the
description of `abcorr' below for details.
fixref is the name of the reference frame relative to which the
output terminator points are expressed. This must be a
body-centered, body-fixed frame associated with the
target. The frame's axes must be compatible with the
triaxial ellipsoidal shape model associated with the
target body (normally provide via a PCK): this routine
assumes that the first, second, and third axis lengths
correspond, respectively, to the x, y, and z-axes of the
frame designated by `fixref'.
`fixref' may refer to a built-in frame (documented in
the Frames Required Reading) or a frame defined by a
loaded frame kernel (FK).
The orientation of the frame designated by `fixref' is
evaluated at epoch of participation of the target body.
See the descriptions of `et' and `abcorr' for details.
abcorr indicates the aberration correction to be applied
when computing the observer-target position, the
orientation of the target body, and the target-
source position vector. `abcorr' may be any of
the following.
"NONE" Apply no correction. Compute the
terminator points using the position
of the light source and target, and
the orientation of the target, at `et'.
Let `lt' represent the one-way light time between the
observer and the target body's center. The following
values of `abcorr' apply to the "reception" case in
which photons depart from the target body's center 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 location of the terminator
points at the approximate time they
emitted photons arriving at the
observer at `et' (the difference between
light time to the target center and
light time to the terminator points
is ignored).
The light time correction uses an
iterative solution of the light time
equation. The solution invoked by the
"LT" option uses one iteration.
The target position as seen by the
observer, the position of the light
source as seen from the target at
et-lt, and the rotation of the target
body, are corrected for light time.
'LT+S' Correct for one-way light time and
stellar aberration using a Newtonian
formulation. This option modifies the
positions obtained with the "LT" option
to account for the observer's velocity
relative to the solar system
barycenter. This correction also
applies to the position of the light
source relative to the target. The
result is the apparent terminator 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. The
position and rotation of the target
body and the position of the light
source relative to the target are
corrected for light time.
'CN+S' Converged Newtonian light time
and stellar aberration corrections.
obsrvr is the name of the observing body. This is typically
a spacecraft, the Earth, or a surface point on the
Earth. `obsrvr' is case-insensitive, and leading and
trailing blanks in `obsrvr' are not significant.
Optionally, you may supply a string containing the
integer ID code for the object. For example both
"EARTH" and "399" are legitimate strings that indicate
the Earth is the observer.
npts is the number of terminator points to compute.
Detailed_Output
trgepc is the "target epoch." `trgepc' is defined as follows:
letting `lt' be the one-way light time between the
target center and observer, `trgepc' is either the
epoch et-lt or `et' depending on whether the requested
aberration correction is, respectively, for received
radiation or omitted. `lt' is computed using the
method indicated by `abcorr'.
`trgepc' is expressed as seconds past J2000 TDB.
obspos is the vector from the center of the target body at
epoch `trgepc' to the observer at epoch `et'. `obspos' is
expressed in the target body-fixed reference frame
`fixref', which is evaluated at `trgepc'.
`obspos' is returned to simplify various related
computations that would otherwise be cumbersome. For
example, the vector `xvec' from the observer to the
ith terminator point can be calculated via the call
vsub_c ( trmpts[i], obspos, xvec );
To transform the vector `obspos' from a reference frame
`fixref' at time `trgepc' to a time-dependent reference
frame `ref' at time `et', the routine pxfrm2_c should be
called. Let `xform' be the 3x3 matrix representing the
rotation from the reference frame `fixref' at time
`trgepc' to the reference frame `ref' at time `et'. Then
`obspos' can be transformed to the result `refvec' as
follows:
pxfrm2_c ( fixref, ref, trgepc, et, xform );
mxv_c ( xform, obspos, refvec );
trmpts is an array of points on the umbral or penumbral
terminator of the ellipsoid, as specified by the
input argument `trmtyp'. The ith point is contained in
the array elements
trmpts[i][j], j = 0, 1, 2
Each terminator point is the point of tangency of a
plane that is also tangent to the light source. These
associated points of tangency on the light source have
uniform distribution in longitude when expressed in a
cylindrical coordinate system whose Z-axis is the target
center to source center vector. The magnitude of the
separation in longitude between the tangency points on
the light source is
2*pi / npts
If the target is spherical, the terminator points
also are uniformly distributed in longitude in the
cylindrical system described above. If the target is
non-spherical, the longitude distribution of the
points generally is not uniform.
The terminator points are expressed in the body-fixed
reference frame designated by `fixref'. Units are km.
ParametersNone. Exceptions
1) If the input frame name `fixref' cannot be mapped
to a frame ID code, the error SPICE(NOTRANSLATION) is
signaled by a routine in the call tree of this routine.
2) If the target name `target' cannot be mapped
to a body ID code, the error SPICE(NOTRANSLATION) is
signaled by a routine in the call tree of this routine.
3) If the frame designated by `fixref' is not centered
on the target, the error SPICE(INVALIDFIXREF) is
signaled by a routine in the call tree of this routine.
4) If the terminator type is not recognized, an error
is signaled by a routine in the call tree of
this routine.
5) If the terminator point count `npts' is not at least 1, an error
is signaled by a routine in the call tree of this routine.
6) If the light source has non-positive radius, an error
is signaled by a routine in the call tree of
this routine.
7) If the light source intersects the smallest sphere centered at
the origin and containing the ellipsoid, an error is signaled
by a routine in the call tree of this routine.
8) If radii for the target body or light source are not
available in the kernel pool, an error is signaled by
a routine in the call tree of this routine.
9) If radii are available but either body does not have three
radii, an error is signaled by a routine in the call tree of
this routine.
10) If any of the radii is less-than or equal to zero, an error is
signaled by a routine in the call tree of this routine.
11) If any SPK look-up fails, an error is signaled by
a routine in the call tree of this routine.
12) If any of the `trmtyp', `source', `target', `fixref', `abcorr'
or `obsrvr' input string pointers is null, the error
SPICE(NULLPOINTER) is signaled.
13) If any of the `trmtyp', `source', `target', `fixref', `abcorr'
or `obsrvr' input strings has zero length, the error
SPICE(EMPTYSTRING) is signaled.
14) If any of the `obspos' or `trmpts' output array pointers is
null, the error SPICE(NULLPOINTER) is signaled.
Files
Appropriate SPK, PCK, and frame kernels must be loaded by the
calling program before this routine is called.
The following data are required:
- SPK data: ephemeris data for the target, observer, and light
source must be loaded. If aberration corrections are used, the
states of all three objects 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 via furnsh_c.
- PCK data: triaxial radii for the target body and the light
source must be loaded into the kernel pool. Typically this is
done by loading a text PCK file via furnsh_c.
- Further PCK data: rotation data for the target body must be
loaded. These may be provided in a text or binary PCK file.
- Frame data: if a frame definition is required to convert the
observer and target states to the target body-fixed frame
designated by `fixref', that definition must be available in
the kernel pool. Typically the definitions of frames not
already built-in to SPICE are supplied by loading a frame
kernel.
In all cases, kernel data are normally loaded once per program
run, NOT every time this routine is called.
Particulars
This routine models the boundaries of shadow regions on an
ellipsoidal target body "illuminated" by a spherical light
source. Light rays are assumed to travel along straight lines;
refraction is not modeled.
Points on the target body's surface are classified according to
their illumination as follows:
- A target surface point X for which no vector from X to any
point in the light source intersects the target, except at
X, is considered to be "completely illuminated."
- A target surface point X for which each vector from X to a
point in the light source intersects the target at points
other than X is considered to be "in total shadow."
- All other target points are considered to be in partial
shadow.
In this routine, we use the term "umbral terminator" to denote
the curve usually called the "terminator": this curve is the
boundary of the portion of the target body's surface that lies in
total shadow. We use the term "penumbral terminator" to denote
the boundary of the completely illuminated portion of the
surface.
In general, the terminator on an ellipsoid is a more complicated
curve than the limb (which is always an ellipse). Aside from
various special cases, the terminator does not lie in a plane.
However, the condition for a point X on the ellipsoid to lie on
the terminator is simple: a plane tangent to the ellipsoid at X
must also be tangent to the light source. If this tangent plane
does not intersect the vector from the center of the ellipsoid to
the center of the light source, then X lies on the umbral
terminator; otherwise X lies on the penumbral terminator.
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) Compute sets of umbral and penumbral terminator points on the
Moon. Perform a consistency check using the solar incidence
angle at each point. We expect to see a solar incidence angle of
approximately 90 degrees. Since the solar incidence angle is
measured between the local outward normal and the direction to
the center of the Sun, the solar incidence angle at an umbral
terminator point should exceed 90 degrees by approximately the
angular radius of the Sun, while the angle at a penumbral
terminator points should be less than 90 degrees by that amount.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: edterm_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 edterm_ex1
./
#include <stdio.h>
#include <math.h>
#include "SpiceUsr.h"
int main()
{
/.
Local constants
./
#define META "edterm_ex1.tm"
#define NPTS 3
/.
Local variables
./
SpiceBoolean first = SPICETRUE;
SpiceChar * abcorr;
SpiceChar * fixref;
SpiceChar * obsrvr;
SpiceChar * source;
SpiceChar * target;
SpiceChar * trmtyps [2] = { "UMBRAL",
"PENUMBRAL" };
SpiceChar * utc;
SpiceDouble angrad;
SpiceDouble emissn;
SpiceDouble et;
SpiceDouble lat;
SpiceDouble lon;
SpiceDouble lt;
SpiceDouble obspos [3];
SpiceDouble phase;
SpiceDouble radius;
SpiceDouble s [2] = { -1.0, 1.0};
SpiceDouble solar;
SpiceDouble srcpos [3];
SpiceDouble srcrad [3];
SpiceDouble srfvec [3];
SpiceDouble trgepc;
SpiceDouble trmpts [NPTS][3];
SpiceInt i;
SpiceInt n;
SpiceInt trmidx;
/.
Load meta-kernel.
./
furnsh_c ( META );
/.
Set observation time.
./
utc = "2007 FEB 3 00:00:00.000";
str2et_c ( utc, &et );
/.
Set participating objects, frame, and aberration
corrections.
./
obsrvr = "EARTH";
target = "MOON";
source = "SUN";
fixref = "IAU_MOON";
abcorr = "LT+S";
/.
Look up the radii of the sun.
./
bodvrd_c ( source, "RADII", 3, &n, srcrad );
/.
Compute terminator points.
./
for ( trmidx = 0; trmidx < 2; trmidx++ )
{
edterm_c ( trmtyps[trmidx], source, target,
et, fixref, abcorr,
obsrvr, NPTS, &trgepc,
obspos, trmpts );
/.
Validate terminator points.
Look up the target-sun vector at the light-time
corrected target epoch.
./
if ( first )
{
spkpos_c ( source, trgepc, fixref,
abcorr, target, srcpos, < );
first = SPICEFALSE;
}
printf ( "\n"
" Terminator type: %s\n", trmtyps[trmidx] );
for ( i = 0; i < NPTS; i++ )
{
/.
Convert the ith terminator point to latitudinal
coordinates. Display the point.
./
reclat_c ( trmpts[i], &radius, &lon, &lat );
printf ( "\n"
" Terminator point %d:\n"
" Radius (km): %18.9f\n"
" Planetocentric longitude (deg): %18.9f\n"
" Planetocentric latitude (deg): %18.9f\n",
(int)i,
radius,
lon * dpr_c(),
lat * dpr_c() );
/.
Find the illumination angles at the
ith terminator point.
./
ilumin_c ( "Ellipsoid", target, et, fixref,
abcorr, obsrvr, trmpts[i], &trgepc,
srfvec, &phase, &solar, &emissn );
printf ( " Solar incidence angle (deg): %18.9f\n",
solar * dpr_c() );
/.
Find the angular radius of the Sun as seen from
the terminator point.
./
angrad = asin ( srcrad[0]
/ vdist_c ( srcpos, trmpts[i] ) );
/.
Display the solar incidence angle after
adjusting the angular radius of the Sun
as seen from the terminator point.The
result should be approximately 90 degrees.
./
printf ( " Solar incidence angle adjusted for\n"
" sun's angular radius (deg): %18.9f\n",
( solar + ( s[trmidx]*angrad ) ) * dpr_c() );
}
}
return ( 0 );
}
When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:
Terminator type: UMBRAL
Terminator point 0:
Radius (km): 1737.400000000
Planetocentric longitude (deg): -95.084552819
Planetocentric latitude (deg): 0.004052763
Solar incidence angle (deg): 90.269765815
Solar incidence angle adjusted for
sun's angular radius (deg): 90.000000125
Terminator point 1:
Radius (km): 1737.400000000
Planetocentric longitude (deg): 84.228091534
Planetocentric latitude (deg): 59.995755519
Solar incidence angle (deg): 90.269765709
Solar incidence angle adjusted for
sun's angular radius (deg): 90.000000019
Terminator point 2:
Radius (km): 1737.400000000
Planetocentric longitude (deg): 87.216417974
Planetocentric latitude (deg): -59.979550515
Solar incidence angle (deg): 90.269765733
Solar incidence angle adjusted for
sun's angular radius (deg): 90.000000043
Terminator type: PENUMBRAL
Terminator point 0:
Radius (km): 1737.400000000
Planetocentric longitude (deg): 84.914100511
Planetocentric latitude (deg): -0.004073047
Solar incidence angle (deg): 89.730234402
Solar incidence angle adjusted for
sun's angular radius (deg): 90.000000122
Terminator point 1:
Radius (km): 1737.400000000
Planetocentric longitude (deg): -95.769215814
Planetocentric latitude (deg): -59.995785101
Solar incidence angle (deg): 89.730234301
Solar incidence angle adjusted for
sun's angular radius (deg): 90.000000021
Terminator point 2:
Radius (km): 1737.400000000
Planetocentric longitude (deg): -92.780892017
Planetocentric latitude (deg): 59.979498997
Solar incidence angle (deg): 89.730234325
Solar incidence angle adjusted for
sun's angular radius (deg): 90.000000044
Restrictions1) This routine models light paths as straight lines. Literature_ReferencesNone. Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) E.D. Wright (JPL) Version
-CSPICE Version 1.0.2, 01-NOV-2021 (JDR)
Edited the header to comply with NAIF standard.
-CSPICE Version 1.0.1, 12-JUL-2016 (EDW)
Edit to example program to use "%d" with explicit casts
to int for printing SpiceInts with printf.
-CSPICE Version 1.0.0, 13-JUN-2012 (NJB) (EDW)
Index_Entriesfind terminator on ellipsoid find umbral terminator on ellipsoid find penumbral terminator on ellipsoid |
Fri Dec 31 18:41:05 2021