Deprecated: This routine has been superseded by the CSPICE routine
cspice_termpt. This routine is supported for purposes of backward
compatibility only.
CSPICE_TERM_PL02 computes a set of points on the umbral or penumbral
terminator of a specified target body, where the target body's surface
is represented by a triangular plate model contained in a type 2 DSK
segment.
Given:
handle the DAS file handle of a DSK file open for read
access. This kernel must contain a type 2 segment
that provides a plate model representing the entire
surface of the target body.
[1,1] = size(handle); int32 = class(handle)
dladsc the DLA descriptor of a DSK segment representing
the surface of a target body.
[SPICE_DLA_DSCSIZ,1] = size(dladsc)
int32 = class(dladsc)
trmtyp a string indicating the type of terminator to
compute: umbral or penumbral. The umbral terminator is
the boundary of the portion of the target 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.
[1,c1] = size(trmtyp); char = class(trmtyp)
or
[1,1] = size(trmtyp); cell = class(trmtyp)
To compute the terminator points, this routine first
computes a set of points on the terminator of the
indicated type on the surface of a reference ellipsoid
for the target body. Each such point defines the
direction of a ray emanating from the target center and
associated with a terminator point on the actual surface
defined by the plate model. The outermost surface
intercept of each such ray is a considered to be a
terminator point of the surface defined by the plate
model.
Possible values of `trmtyp' are
'UMBRAL'
'PENUMBRAL'
Case and leading or trailing blanks in `trmtyp' are
not significant.
source 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.
[1,c2] = size(source); char = class(source)
or
[1,1] = size(source); cell = class(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 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.
[1,c3] = size(target); char = class(target)
or
[1,1] = size(target); cell = class(target)
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 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.
[1,1] = size(et); double = class(et)
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 or et+lt, where `lt' is the one-way
light time between the target body's center and the
observer, and the sign applied to `lt' depends on the
selected correction. See the description of `abcorr'
below for details.
fixfrm the name of the reference frame relative to which
the output terminator points are expressed. This must
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 `fixfrm'.
[1,c4] = size(fixfrm); char = class(fixfrm)
or
[1,1] = size(fixfrm); cell = class(fixfrm)
`fixfrm' 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 `fixfrm' 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.
[1,c5] = size(abcorr); char = class(abcorr)
or
[1,1] = size(abcorr); cell = class(abcorr)
`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 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.
[1,c6] = size(obsrvr); char = class(obsrvr)
or
[1,1] = size(obsrvr); cell = class(obsrvr)
npoints the number of terminator points to compute.
the call:
[trgepc, obspos, termpts, plateids] = ...
cspice_term_pl02( handle, dladsc, ...
trmtyp, source, target, ...
et, fixref, abcorr, ...
obsrvr, npoints )
returns:
trgepc 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'.
[1,1] = size(trgepc); double = class(trgepc)
`trgepc' is expressed as seconds past J2000 TDB.
obspos 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
`fixfrm', which is evaluated at `trgepc'.
[3,1] = size(obspos); double = class(obspos)
`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
expression
xvec = termpts(:,i) - obspos
The components of `obspos' are given in units of km.
termpts an array of points on the umbral or penumbral
terminator of the target, as specified by the input
argument `trmtyp'.
[3,npoints] = size(termpts); double = class(termpts)
The ith point is contained in the array elements
termpts(:,i)
As described above, each terminator point lies on a ray
emanating from the center of the target and passing
through a terminator point on the target's reference
ellipsoid. Each terminator point *on the reference
ellipsoid* 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 `obspos'.
The magnitude of the separation in longitude between the
tangency points on the light source is
2*Pi / npoints
If the reference ellipsoid for the target is spherical,
the terminator points also are uniformly distributed in
longitude in the cylindrical system described above. If
the reference ellipsoid of 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 `fixfrm'. Units are km.
plateids an array of integer ID codes of the plates on which
the terminator points are located. The ith plate ID
corresponds to the ith terminator point. These ID codes can
be use to look up data associated with the plate, such
as the plate's vertices or outward normal vector.
[1,npoints] = size(plateIDs); int32 = class(plateIDs)
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.
Compute sets of umbral and penumbral terminator points on Phobos
as seen from Mars. Perform a consistency check using the solar
incidence angle at each point, where the solar incidence angle
is computed using both a reference ellipsoid and the actual
plate model surface and surface normal. 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 Sun, the solar incidence angle
at an umbral or penumbral terminator point should be,
respectively, greater than or less than 90 degrees by
approximately the angular radius of the Sun as seen from each
terminator point.
In the following example program, the file
phobos_3_3.dsk
is a DSK file containing a type 2 segment that provides a plate model
representation of the surface of Phobos. The file
mar097.bsp
is a binary SPK file containing data for Phobos, the Earth, and the
Sun for a time interval bracketing the date
2006 NOV 3 00:00:00 UTC.
pck00010.tpc is a planetary constants kernel file containing radii
and rotation model constants. naif0010.tls is a leapseconds kernel.
All of the kernels other than the DSK file should be loaded via
a meta-kernel. An example of the contents of such a kernel is:
KPL/MK
\begindata
KERNELS_TO_LOAD = ( 'naif0010.tls'
'pck00010.tpc'
'mar097.bsp' )
\begintext
function term_pl02_t
%
% Constants
%
NPOINTS = 3;
NTYPES = 2;
TIMLEN = 40;
ILUM_METHOD = 'ELLIPSOID';
TOL = 1.d-12;
UTCSTR = '2007 FEB 9 00:00:00 UTC';
%
% Initial values
%
target = 'Phobos';
fixfrm = 'IAU_PHOBOS';
abcorr = 'CN+S';
fixfrm = 'IAU_PHOBOS';
obsrvr = 'Mars';
trmtypes = { 'Umbral', 'Penumbral' };
utcstr = '2007 FEB 9 00:00:00 UTC';
%
% Prompt for the name of a meta-kernel specifying
% all of the other kernels we need. Load the
% metakernel.
%
meta = input( 'Enter meta-kernel name > ','s');
cspice_furnsh( meta )
%
% Prompt for the name of a DSK file.
%
dsk = input( 'Enter DSK name > ','s');
%
% Open the DSK file for read access.
% We use the DAS-level interface for
% this function.
%
handle = cspice_dasopr( dsk );
%
% Begin a forward search through the
% kernel, treating the file as a DLA.
% In this example, it's a very short
% search.
%
[dladsc, found] = cspice_dlabfs( handle );
if ~found
%
% We arrive here only if the kernel
% contains no segments. This is
% unexpected, but we're prepared for it.
%
fprintf( 'No segments found in DSK file %s\n', dsk )
return
end
%
% If we made it this far, `dladsc' is the
% DLA descriptor of the first segment.
%
% Now compute sub-points using both computation
% methods. We'll vary the aberration corrections
% and the epochs.
%
et = cspice_str2et( UTCSTR );
timstr = cspice_timout( et, ...
'YYYY-MON-DD HR:MN:SC.### ::TDB(TDB)' );
fprintf( '\n\n' )
fprintf( ' Observer: %s\n', obsrvr )
fprintf( ' Target: %s\n', target )
fprintf( ' Observation epoch: %s\n', timstr )
fprintf( ' Aberration correction: %s\n', abcorr )
fprintf( ' Body-fixed frame: %s\n', fixfrm )
%
% Look up the radii of the Sun. We'll use these as
% part of a computation to check the solar incidence
% angles at the terminator points.
%
sunRadii = cspice_bodvrd( 'SUN', 'RADII', 3 );
%
% Now compute grids of terminator points using both
% terminator types.
%
for typidx = 1:NTYPES
%
% Select the terminator type.
%
trmtyp = trmtypes( typidx );
fprintf( '\n Terminator type: %s\n', char(trmtyp) )
%
% Compute the terminator point set.
%
[trgepc, obpos, termpts, plateids] = ...
cspice_term_pl02( handle, dladsc, ...
trmtyp, 'Sun', target, ...
et, fixfrm, abcorr, ...
obsrvr, NPOINTS );
%
% Display the terminator points.
%
for i = 1:NPOINTS
[radius, lon, lat] = cspice_reclat( termpts(:,i) );
fprintf( '\n Terminator point: %d\n', i )
fprintf( ' Radius (km): %f\n', ...
radius )
fprintf( ' Planetocentric longitude (deg): %f\n', ...
lon * cspice_dpr() )
fprintf( ' Planetocentric latitude (deg): %f\n', ...
lat * cspice_dpr() )
fprintf( ' Plate ID: %d\n', ...
plateids(i) )
%
% Compute the angular radius of the Sun as seen from
% the current terminator point. Subtracting (adding)
% this value from (to) the solar incidence angle for
% umbral (penumbral) terminator points should yield a
% value close to 90 degrees. This provides a sanity
% check on the locations of the terminator points.
%
% First find the position of the Sun relative to the
% target's center at the light time corrected epoch
% trgepc.
%
[sunPos, ltime] = cspice_spkpos( 'Sun', trgepc, fixfrm, ...
abcorr, target );
sunVec = sunPos - termpts(:,i);
sunAngRad = asin( sunRadii(1) / cspice_vnorm(sunVec) );
%
% Compute the delta by which we adjust the solar
% incidence angles.
%
if ( typidx == 1 )
%
% Umbral
%
delta = -sunAngRad;
else
%
% Penumbral
%
delta = sunAngRad;
end
%
% Compute the illumination angles using an ellipsoidal
% representation of the target's surface. The role of
% this representation is to provide an outward surface
% normal.
%
[trgepc, srfvec, phase, solar, emissn] = ...
cspice_ilumin( ILUM_METHOD, target, et, ...
fixfrm, abcorr, obsrvr, ...
termpts(:,i) );
fprintf( ' Solar incidence angle derived using\n' )
fprintf( ' ' )
fprintf( ' - an ellipsoidal reference surface' )
fprintf( ' (deg): %f\n', solar * cspice_dpr() )
fprintf( ' ' )
fprintf( ' > adjusted for Solar angular ' )
fprintf( 'radius (deg): %f\n', (solar+delta) * cspice_dpr() )
%
% Compute the illumination angles at the terminator point
% using the actual plate model surface normal.
%
[phase, solar, emissn] = cspice_illum_pl02( ...
handle, dladsc, target, ...
et, abcorr, obsrvr, ...
termpts(:,i) );
fprintf( ' ' )
fprintf( ' - plate model''s surface and normal ' )
fprintf( 'vector (deg): %f\n', solar * cspice_dpr() )
end
end
%
% Close the DSK file. Unload all other kernels as well.
%
cspice_dascls( handle )
cspice_kclear
MATLAB outputs:
Observer: Mars
Target: Phobos
Observation epoch: 2007-FEB-09 00:01:05.184 (TDB)
Aberration correction: CN+S
Body-fixed frame: IAU_PHOBOS
Terminator type: Umbral
Terminator point: 1
Radius (km): 12.111257
Planetocentric longitude (deg): 34.584501
Planetocentric latitude (deg): -0.001298
Plate ID: 200400
Solar incidence angle derived using
- an ellipsoidal reference surface (deg): 90.182028
> adjusted for Solar angular radius (deg): 89.999999
- plate model's surface and normal vector (deg): 90.240660
Terminator point: 2
Radius (km): 9.774665
Planetocentric longitude (deg): -143.659941
Planetocentric latitude (deg): 43.397190
Plate ID: 156958
Solar incidence angle derived using
- an ellipsoidal reference surface (deg): 90.182028
> adjusted for Solar angular radius (deg): 90.000000
- plate model's surface and normal vector (deg): 87.138686
Terminator point: 3
Radius (km): 11.500619
Planetocentric longitude (deg): -146.128151
Planetocentric latitude (deg): -43.082379
Plate ID: 25552
Solar incidence angle derived using
- an ellipsoidal reference surface (deg): 90.182028
> adjusted for Solar angular radius (deg): 90.000000
- plate model's surface and normal vector (deg): 91.404206
Terminator type: Penumbral
Terminator point: 1
Radius (km): 12.859785
Planetocentric longitude (deg): -145.415505
Planetocentric latitude (deg): 0.001299
Plate ID: 86763
Solar incidence angle derived using
- an ellipsoidal reference surface (deg): 89.817971
> adjusted for Solar angular radius (deg): 90.000000
- plate model's surface and normal vector (deg): 89.055489
Terminator point: 2
Radius (km): 10.327413
Planetocentric longitude (deg): 36.340069
Planetocentric latitude (deg): -43.397192
Plate ID: 76977
Solar incidence angle derived using
- an ellipsoidal reference surface (deg): 89.817971
> adjusted for Solar angular radius (deg): 90.000000
- plate model's surface and normal vector (deg): 77.351956
Terminator point: 3
Radius (km): 10.086025
Planetocentric longitude (deg): 33.871859
Planetocentric latitude (deg): 43.082380
Plate ID: 282136
Solar incidence angle derived using
- an ellipsoidal reference surface (deg): 89.817971
> adjusted for Solar angular radius (deg): 90.000000
- plate model's surface and normal vector (deg): 88.997322
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.
Boundaries of illuminated regions on an arbitrary surface are often
complicated point sets: boundaries of shadows of mountains and
craters, if present, all contribute to the overall set. To make the
terminator computation tractable, we simplify the problem by using a
reference ellipsoid for guidance. We compute a set of terminator
points on the reference ellipsoid for the target body, then use
those points to define the latitudes and longitudes of terminator
points on the surface defined by the specified triangular shape
model. As such, the set of terminator points found by this routine
is just an approximation.
Below we discuss the computation of terminator points on the target
body's reference ellipsoid.
This routine assumes a spherical light source. Light rays are
assumed to travel along straight lines; refraction is not modeled.
Points on the reference ellipsoid at which the entire cap of
the light source is visible are considered to be completely
illuminated. Points on the ellipsoid at which some portion
(or all) of the cap of the light source are blocked are
considered to be in partial (or total) shadow.
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.
For important details concerning this module's function, please
refer to the CSPICE routine term_pl02.
MICE.REQ
ABCORR.REQ
DSK.REQ
PCK.REQ
SPK.REQ
TIME.REQ
-Mice Version 1.0.0, 25-JUL-2016, NJB, EDW (JPL)
find terminator on plate model
find terminator on triangular shape model
find terminator on dsk type_2 shape model
find umbral terminator on plate model
find umbral terminator on triangular shape model
find umbral terminator on dsk type_2 shape model
find penumbral terminator on plate model
find penumbral terminator on triangular shape model
find penumbral terminator on dsk type_2 shape model
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