| termpt |
|
Table of contents
Procedure
TERMPT ( Terminator points on an extended object )
SUBROUTINE TERMPT ( METHOD, ILUSRC, TARGET, ET, FIXREF,
. ABCORR, CORLOC, OBSRVR, REFVEC, ROLSTP,
. NCUTS, SCHSTP, SOLTOL, MAXN, NPTS,
. POINTS, EPOCHS, TRMVCS )
Abstract
Find terminator points on a target body. The caller specifies
half-planes, bounded by the illumination source center-target
center vector, in which to search for terminator points.
The terminator can be either umbral or penumbral. The umbral
terminator is the boundary of the region on the target surface
where no light from the source is visible. The penumbral
terminator is the boundary of the region on the target surface
where none of the light from the source is blocked by the target
itself.
The surface of the target body may be represented either by a
triaxial ellipsoid or by topographic data.
Required_Reading
CK
DSK
FRAMES
NAIF_IDS
PCK
SPK
TIME
Keywords
DSK
GEOMETRY
SHADOW
TERMINATOR
Declarations
IMPLICIT NONE
INCLUDE 'dsk.inc'
INCLUDE 'frmtyp.inc'
INCLUDE 'gf.inc'
INCLUDE 'zzabcorr.inc'
INCLUDE 'zzctr.inc'
INCLUDE 'zzdsk.inc'
CHARACTER*(*) METHOD
CHARACTER*(*) ILUSRC
CHARACTER*(*) TARGET
DOUBLE PRECISION ET
CHARACTER*(*) FIXREF
CHARACTER*(*) ABCORR
CHARACTER*(*) CORLOC
CHARACTER*(*) OBSRVR
DOUBLE PRECISION REFVEC ( 3 )
DOUBLE PRECISION ROLSTP
INTEGER NCUTS
DOUBLE PRECISION SCHSTP
DOUBLE PRECISION SOLTOL
INTEGER MAXN
INTEGER NPTS ( * )
DOUBLE PRECISION POINTS ( 3, * )
DOUBLE PRECISION EPOCHS ( * )
DOUBLE PRECISION TRMVCS ( 3, * )
Brief_I/O
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
METHOD I Computation method.
ILUSRC I Illumination source.
TARGET I Name of target body.
ET I Epoch in ephemeris seconds past J2000 TDB.
FIXREF I Body-fixed, body-centered target body frame.
ABCORR I Aberration correction.
CORLOC I Aberration correction locus.
OBSRVR I Name of observing body.
REFVEC I Reference vector for cutting half-planes.
ROLSTP I Roll angular step for cutting half-planes.
NCUTS I Number of cutting half-planes.
SCHSTP I Angular step size for searching.
SOLTOL I Solution convergence tolerance.
MAXN I Maximum number of entries in output arrays.
NPTS O Counts of terminator points corresponding to cuts.
POINTS O Terminator points.
EPOCHS O Times associated with terminator points.
TRMVCS O Terminator vectors emanating from the observer.
Detailed_Input
METHOD is a short string providing parameters defining
the computation method to be used. In the syntax
descriptions below, items delimited by angle brackets
"<>" are to be replaced by actual values. Items
delimited by brackets "[]" are optional.
METHOD may be assigned the following values:
'<shadow>/<curve type>/<shape specification>'
An example of such a string is
'UMBRAL/TANGENT/DSK/UNPRIORITIZED'
In the METHOD string
<shadow> may be either of the strings
'UMBRAL' indicates the terminator is the
boundary of the portion of the surface
that receives no light from the
illumination source. The shape of the
source is modeled as a sphere. See the
$Particulars section below for details.
'PENUMBRAL' indicates the terminator is the
boundary of the portion of the surface
that receives all possible light from
the illumination source. The shape of
the source is modeled as a sphere.
The penumbral terminator bounds the
portion of the surface that is not
subject to self-occultation of light
from the illumination source. Given
that the light source is modeled as a
sphere, from any target surface point
nearer to the source than the
penumbral terminator, the source
appears to be a lit disc. See the
$Particulars section below for details.
<curve type> may be either of the strings
'TANGENT' for topographic (DSK) target models
indicates that a terminator point is
defined as the point of tangency, on
the surface represented by the
specified data, of a line also tangent
to the illumination source.
For ellipsoidal target models, a
terminator point is a point of
tangency of a plane that is also
tangent to the illumination source.
See the $Particulars section below for
details.
Terminator points are generated within
a specified set of "cutting"
half-planes that have as an edge the
line containing the illumination
source center-target center vector.
Multiple terminator points may be
found within a given half-plane, if
the target body shape allows for this.
This is the highest-accuracy method
supported by this subroutine. It
generally executes much more slowly
than the GUIDED method described
below.
'GUIDED' indicates that terminator points are
"guided" so as to lie on rays
emanating from the target body's
center and passing through the
terminator on the target body's
reference ellipsoid. The terminator
points are constrained to lie on the
target body's surface. As with the
'TANGENT' method (see above), cutting
half-planes are used to generate
terminator points.
The GUIDED method produces a unique
terminator point for each cutting
half-plane. If multiple terminator
point candidates lie in a given
cutting half-plane, the outermost one
is chosen.
This method may be used only with the
CENTER aberration correction locus
(see the description of CORLOC below).
Terminator points generated by this
method are approximations; they are
generally not true ray-surface tangent
points. However, these approximations
can be generated much more quickly
than tangent points.
<shape specification> may be either of the strings
'DSK/UNPRIORITIZED[/SURFACES = <surface list>]'
The DSK option indicates that terminator point
computation is to use topographic data provided
by DSK files (abbreviated as "DSK data" below)
to model the surface of the target body.
The surface list specification is optional. The
syntax of the list is
<surface 1> [, <surface 2>...]
If present, it indicates that data only for the
listed surfaces are to be used; however, data
need not be available for all surfaces in the
list. If the list is absent, loaded DSK data
for any surface associated with the target body
are used.
The surface list may contain surface names or
surface ID codes. Names containing blanks must
be delimited by double quotes, for example
SURFACES = "Mars MEGDR 128 PIXEL/DEG"
If multiple surfaces are specified, their names
or IDs must be separated by commas.
See the $Particulars section below for details
concerning use of DSK data.
'ELLIPSOID'
The ELLIPSOID shape option generates terminator
points on the target body's reference
ellipsoid. When the ELLIPSOID shape is
selected, The TANGENT curve option may be used
with any aberration correction locus, while the
GUIDED option may be used only with the CENTER
locus (see the description of CORLOC below).
When the locus is set to 'CENTER', the
'TANGENT' and 'GUIDED' curve options produce
the same results.
Neither case nor white space are significant in
METHOD, except within double-quoted strings. For
example, the string ' eLLipsoid/tAnGenT ' is valid.
Within double-quoted strings, blank characters are
significant, but multiple consecutive blanks are
considered equivalent to a single blank. Case is
not significant. So
"Mars MEGDR 128 PIXEL/DEG"
is equivalent to
" mars megdr 128 pixel/deg "
but not to
"MARS MEGDR128PIXEL/DEG"
ILUSRC is the name of the illumination source. This source
may be any ephemeris object. Case, blanks, and
numeric values are treated in the same way as for the
input TARGET.
The shape of the illumination source is considered
to be spherical. The radius of the sphere is the
largest radius of the source's reference ellipsoid.
TARGET is the name of the target body. The target body is
an extended ephemeris object.
The string 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.
When the target body's surface is represented by a
tri-axial ellipsoid, this routine assumes that a
kernel variable representing the ellipsoid'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 TDB seconds past J2000 TDB: ET is
the epoch at which the observer's state is computed.
When aberration corrections are not used, ET is also
the epoch at which the position and orientation of
the target body are computed.
When aberration corrections are used, the position
and orientation of the target body are computed at
ET-LT, where LT is the one-way light time between the
aberration correction locus and the observer. The
locus is specified by the input argument CORLOC.
See the descriptions of ABCORR and CORLOC below for
details.
FIXREF is the name of a body-fixed reference frame centered
on the target body. FIXREF may be any such 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). The
string FIXREF is case-insensitive, and leading and
trailing blanks in FIXREF are not significant.
The output terminator points in the array POINTS and
the output observer-terminator vectors in the array
TRMVCS are expressed relative to this reference
frame.
ABCORR indicates the aberration corrections to be applied
when computing the target's position and orientation.
Corrections are applied at the location specified by
the aberration correction locus argument CORLOC,
which is described below.
For remote sensing applications, where apparent
terminator points seen by the observer are desired,
normally either of the corrections
'LT+S'
'CN+S'
should be used. These and the other supported options
are described below. ABCORR may be any of the
following:
'NONE' Apply no correction. Return the
geometric terminator points on the
target body.
Let LT represent the one-way light time between the
observer and the aberration correction locus. The
following values of ABCORR apply to the "reception"
case in which photons depart from the locus 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 locus 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.
Both the target position as seen by the
observer, and rotation of the target
body, are corrected for light time. The
position of the illumination source as
seen from the target is corrected as
well.
'LT+S' Correct for one-way light time and
stellar aberration using a Newtonian
formulation. This option modifies the
locus obtained with the 'LT' option to
account for the observer's velocity
relative to the solar system
barycenter. These corrections yield
points on the apparent terminator.
'CN' Converged Newtonian light time
correction. In solving the light time
equation, the 'CN' correction iterates
until the solution converges. Both the
position and rotation of the target
body are corrected for light time. The
position of the illumination source as
seen from the target is corrected as
well.
'CN+S' Converged Newtonian light time and
stellar aberration corrections. This
option produces a solution that is at
least as accurate at that obtainable
with the 'LT+S' option. Whether the
'CN+S' solution is substantially more
accurate depends on the geometry of the
participating objects and on the
accuracy of the input data. In all
cases this routine will execute more
slowly when a converged solution is
computed.
CORLOC is a string specifying the aberration correction
locus: the point or set of points for which
aberration corrections are performed. CORLOC may be
assigned the values:
'CENTER'
Light time and stellar aberration corrections
are applied to the vector from the observer to
the center of the target body. The one way
light time from the target center to the
observer is used to determine the epoch at
which the target body orientation is computed.
This choice is appropriate for small target
objects for which the light time from the
surface to the observer varies little across
the entire target. It may also be appropriate
for large, nearly ellipsoidal targets when the
observer is very far from the target.
Computation speed for this option is faster
than for the ELLIPSOID TERMINATOR option.
'ELLIPSOID TERMINATOR'
Light time and stellar aberration corrections
are applied to individual terminator points on
the reference ellipsoid. For a terminator
point on the surface described by topographic
data, lying in a specified cutting half-plane,
the unique reference ellipsoid terminator
point in the same half-plane is used as the
locus of the aberration corrections.
This choice is appropriate for large target
objects for which the light time from the
terminator to the observer is significantly
different from the light time from the target
center to the observer.
Because aberration corrections are repeated
for individual terminator points,
computational speed for this option is
relatively slow.
OBSRVR is the name of the observing body. The observing body
is an ephemeris object: it typically is 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 'MOON' and '301' are
legitimate strings that indicate the Moon is the
observer.
REFVEC,
ROLSTP,
NCUTS are, respectively, a reference vector, a roll step
angle, and a count of cutting half-planes.
REFVEC defines the first of a sequence of cutting
half-planes in which terminator points are to be
found. Each cutting half-plane has as its edge the
line containing the illumination source center-target
center vector; the first half-plane contains REFVEC.
REFVEC is expressed in the body-fixed reference frame
designated by FIXREF.
ROLSTP is an angular step by which to roll the
cutting half-planes about the target-illumination
source vector, which we'll call the "axis." The Ith
half-plane is rotated from REFVEC about the axis in
the counter-clockwise direction by (I-1)*ROLSTP.
Units are radians. ROLSTP should be set to
2*pi/NCUTS
to generate an approximately uniform distribution of
points along the terminator.
NCUTS is the number of cutting half-planes used to
find terminator points; the angular positions of
consecutive half-planes increase in the positive
(counterclockwise) sense about the axis and are
distributed roughly equally about that vector: each
half-plane has angular separation of approximately
ROLSTP radians
from each of its neighbors. When the aberration
correction locus is set to 'CENTER', the angular
separation is the value above, up to round-off.
When the locus is 'TANGENT', the separations are
less uniform due to differences in the aberration
corrections used for the respective terminator points.
SCHSTP,
SOLTOL are used only for DSK-based surfaces. These inputs
are, respectively, the search angular step size and
solution convergence tolerance used to find tangent
rays and associated terminator points within each
cutting half plane. These values are used when the
METHOD argument includes the TANGENT option. In this
case, terminator points are found by a two-step
search process:
1) Bracketing: starting with a direction having
sufficiently small angular separation from the
axis, rays emanating from the surface of the
illumination source are generated within the
half-plane at successively greater angular
separations from the axis, where the increment
of angular separation is SCHSTP. The rays are
tested for intersection with the target
surface. When a transition from
non-intersection to intersection is found, the
angular separation of a tangent ray has been
bracketed.
2) Root finding: each time a tangent ray is
bracketed, a search is done to find the angular
separation from the starting direction at which
a tangent ray exists. The search terminates
when successive rays are separated by no more
than SOLTOL. When the search converges, the
last ray-surface intersection point found in
the convergence process is considered to be a
terminator point.
SCHSTP and SOLTOL have units of radians.
Target bodies with simple surfaces---for example,
convex shapes---will have a single terminator point
within each cutting half-plane. For such surfaces,
SCHSTP can be set large enough so that only one
bracketing step is taken. A value greater than pi,
for example 4.D0, is recommended.
Target bodies with complex surfaces can have
multiple terminator points within a given cutting
half-plane. To find all terminator points, SCHSTP
must be set to a value smaller than the angular
separation of any two terminator points in any
cutting half-plane, where the vertex of the angle is
near a point on the surface of the illumination
source. SCHSTP must not be too small, or the search
will be excessively slow.
For both kinds of surfaces, SOLTOL must be chosen so
that the results will have the desired precision.
Note that the choice of SOLTOL required to meet a
specified bound on terminator point height errors
depends on the illumination source-target distance.
MAXN is the maximum number of terminator points that can
be stored in the output array POINTS.
Detailed_Output
NPTS is an array of counts of terminator points within
the specified set of cutting half-planes. The Ith
element of NPTS is the terminator point count in the
Ith half-plane. NPTS should be declared with length
at least NCUTS.
POINTS is an array containing the terminator points found
by this routine. Terminator points are ordered by
the indices of the half-planes in which they're
found. The terminator points in a given half-plane
are ordered by decreasing angular separation from
the illumination source-target direction; the
outermost terminator point in a given half-plane is
the first of that set.
The terminator points for the half-plane containing
REFVEC occupy array elements
POINTS(1,1) through POINTS(3,NPTS(1))
Terminator points for the second half plane occupy
elements
POINTS(1, NPTS(1)+1 ) through
POINTS(3, NPTS(1)+NPTS(2) )
and so on.
POINTS should be declared with dimensions
( 3, MAXN )
Terminator points are expressed in the reference
frame designated by FIXREF. For each terminator
point, the orientation of the frame is evaluated at
the epoch corresponding to the terminator point; the
epoch is provided in the output array EPOCHS
(described below).
Units of the terminator points are km.
EPOCHS is an array of epochs associated with the terminator
points, accounting for light time if aberration
corrections are used. EPOCHS contains one element
for each terminator point. EPOCHS should be declared
with length
MAXN
The element
EPOCHS(I)
is associated with the terminator point
POINTS(J,I), J = 1 to 3
If CORLOC is set to 'CENTER', all values of EPOCHS
will be the epoch associated with the target body
center. That is, if aberration corrections are used,
and if LT is the one-way light time from the target
center to the observer, the elements of EPOCHS will
all be set to
ET - LT
If CORLOC is set to 'ELLIPSOID TERMINATOR', all
values of EPOCHS for the terminator points in a
given half plane will be those for the reference
ellipsoid terminator point in that half plane. That
is, if aberration corrections are used, and if LT(I)
is the one-way light time to the observer from the
reference ellipsoid terminator point in the Ith half
plane, the elements of EPOCHS for that half plane
will all be set to
ET - LT(I)
TRMVCS is an array of vectors connecting the observer to
the terminator points. The terminator vectors are
expressed in the frame designated by FIXREF. For the
Ith vector, the orientation of the frame is
evaluated at the Ith epoch provided in the output
array EPOCHS (described above).
TRMVCS should be declared with dimensions
( 3, MAXN )
The elements
TRMVCS(J,I), J = 1 to 3
are associated with the terminator point
POINTS(J,I), J = 1 to 3
Units of the terminator vectors are km.
Parameters
None.
Exceptions
1) If the specified aberration correction is unrecognized, an
error is signaled by a routine in the call tree of this
routine.
2) If transmission corrections are commanded, the error
SPICE(INVALIDOPTION) is signaled.
3) If either the target or observer input strings cannot be
converted to an integer ID code, the error
SPICE(IDCODENOTFOUND) is signaled.
4) If OBSRVR and TARGET map to the same NAIF integer ID code,
the error SPICE(BODIESNOTDISTINCT) is signaled.
5) If the input target body-fixed frame FIXREF is not
recognized, the error SPICE(NOFRAME) is signaled. 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.
6) If the input frame FIXREF is not centered at the target body,
the error SPICE(INVALIDFRAME) is signaled.
7) If the input argument METHOD is not recognized, the error
SPICE(INVALIDMETHOD) is signaled by either this routine or a
routine in the call tree of this routine.
8) If METHOD contains an invalid terminator type, the error
SPICE(INVALIDTERMTYPE) is signaled.
9) If the target and observer have distinct identities but are
at the same location, the error SPICE(NOSEPARATION) is
signaled.
10) If insufficient ephemeris data have been loaded prior to
calling TERMPT, an error is signaled by a routine in
the call tree of this routine. When light time correction is
used, sufficient ephemeris data must be available to
propagate the states of both observer and target to the solar
system barycenter.
11) If the computation method requires an ellipsoidal target shape
and triaxial radii of the target body have not been loaded
into the kernel pool prior to calling TERMPT, an error is
signaled by a routine in the call tree of this routine.
When the target shape is modeled by topographic data, radii
of the reference triaxial ellipsoid are still required if
the aberration correction locus is ELLIPSOID TERMINATOR or if
the terminator point generation method is GUIDED.
12) If the target body's shape is modeled as an ellipsoid, and if
any of the radii of the target body are non-positive, an error
is signaled by a routine in the call tree of this routine. The
target must be an extended body.
13) If PCK data specifying the target body-fixed frame orientation
have not been loaded prior to calling TERMPT, an error is
signaled by a routine in the call tree of this routine.
14) If METHOD specifies that the target surface is represented by
DSK data, and no DSK files are loaded for the specified
target, an error is signaled by a routine in the call tree
of this routine.
15) If the array bound MAXN is less than 1, the error
SPICE(INVALIDSIZE) is signaled.
16) If the number of cutting half-planes specified by NCUTS
is negative or greater than MAXN, the error
SPICE(INVALIDCOUNT) is signaled.
17) If the aberration correction locus is not recognized, the
error SPICE(INVALIDLOCUS) is signaled.
18) If the GUIDED terminator type is used with the
ELLIPSOID TERMINATOR aberration correction locus, the
error SPICE(BADTERMLOCUSMIX) is signaled.
19) If the reference vector REFVEC is the zero vector, the
error SPICE(ZEROVECTOR) is signaled.
20) If the reference vector REFVEC and the observer target
vector are linearly dependent, the error
SPICE(DEGENERATECASE) is signaled.
21) If the terminator points cannot all be stored in the output
POINTS array, the error SPICE(OUTOFROOM) is signaled.
22) If NCUTS is greater than 1, the roll step ROLSTP must be
positive. Otherwise, the error SPICE(INVALIDROLLSTEP) 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 target, observer, and
illumination source must be loaded. If aberration
corrections are used, the states of target and observer
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.
- Target body orientation data: these may be provided in a text
or binary PCK file. In some cases, target body orientation
may be provided by one more more CK files. In either case,
data are made available by loading the files via FURNSH.
- Shape data for the target body:
PCK data:
If the target body shape is modeled as an ellipsoid,
triaxial radii for the target body must be loaded into
the kernel pool. Typically this is done by loading a
text PCK file via FURNSH.
Triaxial radii are also needed if the target shape is
modeled by DSK data but one or both of the GUIDED
terminator definition method or the ELLIPSOID
TERMINATOR aberration correction locus are selected.
DSK data:
If the target shape is modeled by DSK data, DSK files
containing topographic data for the target body must be
loaded. If a surface list is specified, data for at
least one of the listed surfaces must be loaded.
- Shape data for the illumination source:
PCK data:
Triaxial radii for the illumination source must be
loaded into the kernel pool. Typically this is done by
loading a text PCK file via FURNSH.
The following data may be required:
- Frame data: if a frame definition is required to convert the
observer and target states to the body-fixed frame of the
target, that definition must be available in the kernel
pool. Typically the definition is supplied by loading a
frame kernel via FURNSH.
- Surface name-ID associations: if surface names are specified
in `method', the association of these names with their
corresponding surface ID codes must be established by
assignments of the kernel variables
NAIF_SURFACE_NAME
NAIF_SURFACE_CODE
NAIF_SURFACE_BODY
Normally these associations are made by loading a text
kernel containing the necessary assignments. An example
of such a set of assignments is
NAIF_SURFACE_NAME += 'Mars MEGDR 128 PIXEL/DEG'
NAIF_SURFACE_CODE += 1
NAIF_SURFACE_BODY += 499
- SCLK data: if the target body's orientation is provided by
CK files, an associated SCLK kernel must be loaded.
In all cases, kernel data are normally loaded once per program
run, NOT every time this routine is called.
Particulars
Terminator definition
=====================
The definitions of terminators used by this routine vary
depending on the target surface model.
In all cases, the surface of the illumination source is
modeled as a sphere.
Ellipsoidal target surface model
--------------------------------
The umbral terminator is the boundary of the set of target
surface points at which the illumination source is completely
below the local tangent plane: the entire illumination source is
below the horizon as seen from any surface point on the far side,
relative to the source, of the umbral terminator. At an umbral
terminator point, the target surface tangent plane containing
that point is tangent to the surface of the light source as well,
and the outward normal vectors at the two points of tangency are
parallel.
The penumbral terminator is the boundary of the set of target
surface points at which the illumination source is completely
above the local tangent plane: the entire illumination source is
above the horizon as seen from any surface point on the near
side, relative to the source, of the penumbral terminator. At a
penumbral terminator point, the target surface tangent plane
containing that point is tangent to the surface of the light
source as well, and the outward normal vectors at the two points
of tangency are anti-parallel.
Topographic target surface model (DSK case)
-------------------------------------------
The concept of a plane tangent to both a topographic target
surface and an illumination source is problematic. If the target
tangent point is required to lie in a given cutting half-plane
bounded by the line containing the target-source vector, the
desired plane may not exist. In general, planes tangent to both
the illumination source and the target will rest upon the high
points of the target surface.
For topographic target surface models, this routine uses a
modified terminator definition: terminator points are target
surface points at which a line is tangent to both the target and
the illumination source. The line is constrained to lie in the
plane containing the specified cutting half-plane. The concepts
of umbral and penumbral terminators still apply. For umbral
terminator points, the common tangent line does not cross the
target-source line; for penumbral points, it does.
Note that for ellipsoids, the terminator definitions based on
tangent lines are not equivalent to the definitions based on
tangent planes. Typically, a plane tangent to the target
ellipsoid at a point found by the method described above will not
be tangent to the illumination source: it will be rotated about
the common tangent line and "cut into" the sphere representing
the light source. This implies that some of the source will be
visible at umbral terminator points and some will be blocked at
penumbral terminator points: both umbral and penumbral terminator
points found by this method will lie in a region bounded by the
true terminators.
The two definitions are equivalent for spherical targets.
Using DSK data
==============
DSK loading and unloading
-------------------------
DSK files providing data used by this routine are loaded by
calling FURNSH and can be unloaded by calling UNLOAD or
KCLEAR. See the documentation of FURNSH for limits on numbers
of loaded DSK files.
For run-time efficiency, it's desirable to avoid frequent
loading and unloading of DSK files. When there is a reason to
use multiple versions of data for a given target body---for
example, if topographic data at varying resolutions are to be
used---the surface list can be used to select DSK data to be
used for a given computation. It is not necessary to unload
the data that are not to be used. This recommendation presumes
that DSKs containing different versions of surface data for a
given body have different surface ID codes.
DSK data priority
-----------------
A DSK coverage overlap occurs when two segments in loaded DSK
files cover part or all of the same domain---for example, a
given longitude-latitude rectangle---and when the time
intervals of the segments overlap as well.
When DSK data selection is prioritized, in case of a coverage
overlap, if the two competing segments are in different DSK
files, the segment in the DSK file loaded last takes
precedence. If the two segments are in the same file, the
segment located closer to the end of the file takes
precedence.
When DSK data selection is unprioritized, data from competing
segments are combined. For example, if two competing segments
both represent a surface as sets of triangular plates, the
union of those sets of plates is considered to represent the
surface.
Currently only unprioritized data selection is supported.
Because prioritized data selection may be the default behavior
in a later version of the routine, the UNPRIORITIZED keyword is
required in the METHOD argument.
Syntax of the METHOD input argument
-----------------------------------
The keywords and surface list in the METHOD argument
are called "clauses." The clauses may appear in any
order, for example
UMBRAL/TANGENT/DSK/UNPRIORITIZED/<surface list>
DSK/UMBRAL/TANGENT/<surface list>/UNPRIORITIZED
UNPRIORITIZED/<surface list>/DSK/TANGENT/UMBRAL
The simplest form of the METHOD argument specifying use of
DSK data is one that lacks a surface list, for example:
'PENUMBRAL/TANGENT/DSK/UNPRIORITIZED'
'UMBRAL/GUIDED/DSK/UNPRIORITIZED'
For applications in which all loaded DSK data for the target
body are for a single surface, and there are no competing
segments, the above strings suffice. This is expected to be
the usual case.
When, for the specified target body, there are loaded DSK
files providing data for multiple surfaces for that body, the
surfaces to be used by this routine for a given call must be
specified in a surface list, unless data from all of the
surfaces are to be used together.
The surface list consists of the string
SURFACES =
followed by a comma-separated list of one or more surface
identifiers. The identifiers may be names or integer codes in
string format. For example, suppose we have the surface
names and corresponding ID codes shown below:
Surface Name ID code
------------ -------
'Mars MEGDR 128 PIXEL/DEG' 1
'Mars MEGDR 64 PIXEL/DEG' 2
'Mars_MRO_HIRISE' 3
If data for all of the above surfaces are loaded, then
data for surface 1 can be specified by either
'SURFACES = 1'
or
'SURFACES = "Mars MEGDR 128 PIXEL/DEG"'
Double quotes are used to delimit the surface name because
it contains blank characters.
To use data for surfaces 2 and 3 together, any
of the following surface lists could be used:
'SURFACES = 2, 3'
'SURFACES = "Mars MEGDR 64 PIXEL/DEG", 3'
'SURFACES = 2, Mars_MRO_HIRISE'
'SURFACES = "Mars MEGDR 64 PIXEL/DEG", Mars_MRO_HIRISE'
An example of a METHOD argument that could be constructed
using one of the surface lists above is
'UMBRAL/TANGENT/DSK/UNPRIORITIZED/
SURFACES= "Mars MEGDR 64 PIXEL/DEG",3'
Examples
The numerical results shown for these examples 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 apparent terminator points on Phobos as seen from Mars.
Use the "umbral" shadow definition.
Due to Phobos' irregular shape, the TANGENT terminator point
definition will be used. It suffices to compute light time and
stellar aberration corrections for the center of Phobos, so
the CENTER aberration correction locus will be used. Use
converged Newtonian light time and stellar aberration
corrections in order to model the apparent position and
orientation of Phobos.
For comparison, compute terminator points using both ellipsoid
and topographic shape models.
Use the target body-fixed +Z axis as the reference direction
for generating cutting half-planes. This choice enables the
user to see whether the first terminator point is near the
target's north pole.
For each option, use just three cutting half-planes in order
to keep the volume of output manageable. In most applications,
the number of cuts and the number of resulting terminator
points would be much greater.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File: termpt_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
pck00010.tpc Planet orientation and
radii
naif0011.tls Leapseconds
phobos512.bds DSK based on
Gaskell ICQ Q=512
Phobos plate model
\begindata
KERNELS_TO_LOAD = ( 'de430.bsp',
'mar097.bsp',
'pck00010.tpc',
'naif0011.tls',
'phobos512.bds' )
\begintext
Example code begins here.
C
C Find terminator points on Phobos as seen from Mars.
C
C Compute terminator points using the tangent
C definition, using the "umbral" shadow type.
C The sun is the illumination source. Perform
C aberration corrections for the target center.
C Use both ellipsoid and DSK shape models.
C
PROGRAM TERMPT_EX1
IMPLICIT NONE
C
C SPICELIB functions
C
DOUBLE PRECISION DPR
DOUBLE PRECISION PI
DOUBLE PRECISION VNORM
C
C Local parameters
C
CHARACTER*(*) META
PARAMETER ( META = 'termpt_ex1.tm' )
CHARACTER*(*) FM1
PARAMETER ( FM1 = '(A,F21.9)' )
CHARACTER*(*) FM2
PARAMETER ( FM2 = '(1X,3F20.9)' )
CHARACTER*(*) FM3
PARAMETER ( FM3 = '(A,I2)' )
INTEGER BDNMLN
PARAMETER ( BDNMLN = 36 )
INTEGER FRNMLN
PARAMETER ( FRNMLN = 32 )
INTEGER CORLEN
PARAMETER ( CORLEN = 20 )
INTEGER MTHLEN
PARAMETER ( MTHLEN = 50 )
INTEGER NMETH
PARAMETER ( NMETH = 2 )
INTEGER MAXN
PARAMETER ( MAXN = 10000 )
C
C Local variables
C
CHARACTER*(CORLEN) ABCORR
CHARACTER*(CORLEN) CORLOC
CHARACTER*(FRNMLN) FIXREF
CHARACTER*(BDNMLN) ILUSRC
CHARACTER*(MTHLEN) METHOD ( NMETH )
CHARACTER*(BDNMLN) OBSRVR
CHARACTER*(BDNMLN) TARGET
DOUBLE PRECISION DELROL
DOUBLE PRECISION DIST
DOUBLE PRECISION ET
DOUBLE PRECISION LT
DOUBLE PRECISION POINTS ( 3, MAXN )
DOUBLE PRECISION POS ( 3 )
DOUBLE PRECISION ROLL
DOUBLE PRECISION SCHSTP
DOUBLE PRECISION SOLTOL
DOUBLE PRECISION TRMVCS ( 3, MAXN )
DOUBLE PRECISION TRGEPS ( MAXN )
DOUBLE PRECISION Z ( 3 )
INTEGER I
INTEGER J
INTEGER K
INTEGER M
INTEGER NCUTS
INTEGER NPTS ( MAXN )
INTEGER START
C
C Initial values
C
DATA METHOD /
. 'UMBRAL/TANGENT/ELLIPSOID',
. 'UMBRAL/TANGENT/DSK/UNPRIORITIZED'
. /
DATA Z / 0.D0, 0.D0, 1.D0 /
C
C Load kernel files via the meta-kernel.
C
CALL FURNSH ( META )
C
C Set target, observer, and target body-fixed,
C body-centered reference frame.
C
ILUSRC = 'SUN'
OBSRVR = 'MARS'
TARGET = 'PHOBOS'
FIXREF = 'IAU_PHOBOS'
C
C Set aberration correction and correction locus.
C
ABCORR = 'CN+S'
CORLOC = 'CENTER'
C
C Convert the UTC request time string seconds past
C J2000, TDB.
C
CALL STR2ET ( '2008 AUG 11 00:00:00', ET )
C
C Compute a set of terminator points using light
C time and stellar aberration corrections. Use
C both ellipsoid and DSK shape models. Use an
C angular step size corresponding to a height of
C about 100 meters to ensure we don't miss the
C terminator. Set the convergence tolerance to limit
C the height convergence error to about 1 meter.
C Compute 3 terminator points for each computation
C method.
C
C Get the approximate light source-target distance
C at ET. We'll ignore the observer-target light
C time for this approximation.
C
CALL SPKPOS ( ILUSRC, ET, 'J2000', ABCORR,
. TARGET, POS, LT )
DIST = VNORM(POS)
SCHSTP = 1.D-1 / DIST
SOLTOL = 1.D-3 / DIST
NCUTS = 3
WRITE (*,*) ' '
WRITE (*,*) 'Light source: '//ILUSRC
WRITE (*,*) 'Observer: '//OBSRVR
WRITE (*,*) 'Target: '//TARGET
WRITE (*,*) 'Frame: '//FIXREF
WRITE (*,*) ' '
WRITE (*,*) 'Number of cuts: ', NCUTS
WRITE (*,*) ' '
DELROL = 2*PI() / NCUTS
DO I = 1, NMETH
CALL TERMPT ( METHOD(I), ILUSRC, TARGET, ET,
. FIXREF, ABCORR, CORLOC, OBSRVR,
. Z, DELROL, NCUTS, SCHSTP,
. SOLTOL, MAXN, NPTS, POINTS,
. TRGEPS, TRMVCS )
C
C Write the results.
C
WRITE(*,*) ' '
WRITE(*,*) 'Computation method = ', METHOD(I)
WRITE(*,*) 'Locus = ', CORLOC
WRITE(*,*) ' '
START = 0
DO J = 1, NCUTS
ROLL = (J-1) * DELROL
WRITE(*,*) ' '
WRITE(*,FM1) ' Roll angle (deg) = ', ROLL * DPR()
WRITE(*,FM1) ' Target epoch = ', TRGEPS(J)
WRITE(*,FM3) ' Number of terminator points '
. // 'at this roll angle: ',
. NPTS(J)
WRITE (*,*) ' Terminator points:'
DO K = 1, NPTS(J)
WRITE (*,FM2) ( POINTS(M,K+START), M = 1, 3 )
END DO
START = START + NPTS(J)
END DO
WRITE (*,*) ' '
END DO
END
When this program was executed on a Mac/Intel/gfortran/64-bit
platform, the output was:
Light source: SUN
Observer: MARS
Target: PHOBOS
Frame: IAU_PHOBOS
Number of cuts: 3
Computation method = UMBRAL/TANGENT/ELLIPSOID
Locus = CENTER
Roll angle (deg) = 0.000000000
Target epoch = 271684865.152078211
Number of terminator points at this roll angle: 1
Terminator points:
2.040498332 5.012722925 8.047281838
Roll angle (deg) = 120.000000000
Target epoch = 271684865.152078211
Number of terminator points at this roll angle: 1
Terminator points:
-11.058054707 0.167672089 -4.782740292
Roll angle (deg) = 240.000000000
Target epoch = 271684865.152078211
Number of terminator points at this roll angle: 1
Terminator points:
8.195238564 -6.093889437 -5.122310498
Computation method = UMBRAL/TANGENT/DSK/UNPRIORITIZED
Locus = CENTER
Roll angle (deg) = 0.000000000
Target epoch = 271684865.152078211
Number of terminator points at this roll angle: 1
Terminator points:
1.626396028 3.995432180 8.853689595
Roll angle (deg) = 120.000000000
Target epoch = 271684865.152078211
Number of terminator points at this roll angle: 1
Terminator points:
-11.186660113 -0.142367244 -4.646136750
Roll angle (deg) = 240.000000000
Target epoch = 271684865.152078211
Number of terminator points at this roll angle: 1
Terminator points:
9.338447202 -6.091352186 -5.960849442
2) Find apparent terminator points on Mars as seen from the
earth.
Use both the "umbral" and "penumbral" shadow definitions. Use
only ellipsoid shape models for easier comparison. Find
distances between corresponding terminator points on the
umbral and penumbral terminators.
Use the ELLIPSOID TERMINATOR aberration correction locus
in order to perform separate aberration corrections for
each terminator point. Because of the large size of Mars,
corrections for the target center are less accurate.
For each option, use just three cutting half-planes, in order
to keep the volume of output manageable. In most applications,
the number of cuts and the number of resulting terminator
points would be much greater.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File: termpt_ex2.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
pck00010.tpc Planet orientation and
radii
naif0011.tls Leapseconds
megr90n000cb_plate.bds Plate model based on
MEGDR DEM, resolution
4 pixels/degree.
\begindata
KERNELS_TO_LOAD = ( 'de430.bsp',
'mar097.bsp',
'pck00010.tpc',
'naif0011.tls',
'megr90n000cb_plate.bds' )
\begintext
Example code begins here.
C
C Find terminator points on Mars as seen from the
C earth.
C
C Use only ellipsoid shape models. Use the
C ELLIPSOID TERMINATOR aberration correction
C locus.
C
C Use both UMBRAL and PENUMBRAL shadow definitions.
C Compute the distances between corresponding
C umbral and penumbral terminator points.
C
C Check terminator points by computing solar
C incidence angles at each point.
C
C
PROGRAM TERMPT_EX2
IMPLICIT NONE
C
C SPICELIB functions
C
DOUBLE PRECISION DPR
DOUBLE PRECISION PI
DOUBLE PRECISION VDIST
DOUBLE PRECISION VNORM
C
C Local parameters
C
CHARACTER*(*) META
PARAMETER ( META = 'termpt_ex2.tm' )
CHARACTER*(*) FM1
PARAMETER ( FM1 = '(A,F21.9)' )
CHARACTER*(*) FM2
PARAMETER ( FM2 = '(A,I2)' )
INTEGER BDNMLN
PARAMETER ( BDNMLN = 36 )
INTEGER FRNMLN
PARAMETER ( FRNMLN = 32 )
INTEGER CORLEN
PARAMETER ( CORLEN = 20 )
INTEGER MTHLEN
PARAMETER ( MTHLEN = 50 )
INTEGER NMETH
PARAMETER ( NMETH = 2 )
INTEGER MAXN
PARAMETER ( MAXN = 100 )
C
C Local variables
C
CHARACTER*(CORLEN) ABCORR
CHARACTER*(CORLEN) CORLOC ( NMETH )
CHARACTER*(FRNMLN) FIXREF
CHARACTER*(MTHLEN) ILUMTH ( NMETH )
CHARACTER*(BDNMLN) ILUSRC
CHARACTER*(BDNMLN) OBSRVR
CHARACTER*(BDNMLN) TARGET
CHARACTER*(MTHLEN) METHOD ( NMETH )
DOUBLE PRECISION ADJANG
DOUBLE PRECISION ALT
DOUBLE PRECISION ANGSRC
DOUBLE PRECISION DELROL
DOUBLE PRECISION DIST
DOUBLE PRECISION EMISSN
DOUBLE PRECISION ET
DOUBLE PRECISION F
DOUBLE PRECISION ILUPOS ( 3 )
DOUBLE PRECISION LAT
DOUBLE PRECISION LON
DOUBLE PRECISION LT
DOUBLE PRECISION PHASE
DOUBLE PRECISION POINTS ( 3, MAXN )
DOUBLE PRECISION SVPNTS ( 3, MAXN )
DOUBLE PRECISION TPTILU ( 3 )
DOUBLE PRECISION RADII ( 3 )
DOUBLE PRECISION RE
DOUBLE PRECISION ROLL
DOUBLE PRECISION RP
DOUBLE PRECISION SCHSTP
DOUBLE PRECISION SOLAR
DOUBLE PRECISION SOLTOL
DOUBLE PRECISION SRCRAD ( 3 )
DOUBLE PRECISION SRFVEC ( 3 )
DOUBLE PRECISION TRMVCS ( 3, MAXN )
DOUBLE PRECISION TRGEPC
DOUBLE PRECISION TRGEPS ( MAXN )
DOUBLE PRECISION Z ( 3 )
INTEGER I
INTEGER J
INTEGER K
INTEGER M
INTEGER N
INTEGER NCUTS
INTEGER NPTS ( MAXN )
INTEGER START
C
C Initial values
C
DATA CORLOC /
. 'ELLIPSOID TERMINATOR',
. 'ELLIPSOID TERMINATOR'
. /
DATA ILUMTH /
. 'ELLIPSOID',
. 'ELLIPSOID'
. /
DATA METHOD /
. 'UMBRAL/ELLIPSOID/TANGENT',
. 'PENUMBRAL/ELLIPSOID/TANGENT'
. /
DATA Z / 0.D0, 0.D0, 1.D0 /
C
C Load kernel files via the meta-kernel.
C
CALL FURNSH ( META )
C
C Set target, observer, and target body-fixed,
C body-centered reference frame.
C
ILUSRC = 'SUN'
OBSRVR = 'EARTH'
TARGET = 'MARS'
FIXREF = 'IAU_MARS'
C
C Set the aberration correction. We'll set the
C correction locus below.
C
ABCORR = 'CN+S'
C
C Convert the UTC request time string seconds past
C J2000, TDB.
C
CALL STR2ET ( '2008 AUG 11 00:00:00', ET )
C
C Look up the target body's radii. We'll use these to
C convert Cartesian to planetographic coordinates. Use
C the radii to compute the flattening coefficient of
C the reference ellipsoid.
C
CALL BODVRD ( TARGET, 'RADII', 3, N, RADII )
C
C Compute the flattening coefficient for planetodetic
C coordinates
C
RE = RADII(1)
RP = RADII(3)
F = ( RE - RP ) / RE
C
C Get the radii of the illumination source as well.
C We'll use these radii to compute the angular radius
C of the source as seen from the terminator points.
C
CALL BODVRD ( ILUSRC, 'RADII', 3, N, SRCRAD )
C
C Compute a set of terminator points using light time and
C stellar aberration corrections. Use both ellipsoid
C and DSK shape models.
C
C Get the approximate light source-target distance
C at ET. We'll ignore the observer-target light
C time for this approximation.
C
CALL SPKPOS ( ILUSRC, ET, FIXREF, ABCORR,
. TARGET, ILUPOS, LT )
DIST = VNORM( ILUPOS )
C
C Set the angular step size so that a single step will
C be taken in the root bracketing process; that's all
C that is needed since we don't expect to have multiple
C terminator points in any cutting half-plane.
C
SCHSTP = 4.D0
C
C Set the convergence tolerance to minimize the
C height error. We can't achieve the precision
C suggested by the formula because the sun-Mars
C distance is about 2.4e8 km. Compute 3 terminator
C points for each computation method.
C
SOLTOL = 1.D-7/DIST
C
C Set the number of cutting half-planes and roll step.
C
NCUTS = 3
DELROL = 2*PI() / NCUTS
WRITE (*,*) ' '
WRITE (*,*) 'Light source: '//ILUSRC
WRITE (*,*) 'Observer: '//OBSRVR
WRITE (*,*) 'Target: '//TARGET
WRITE (*,*) 'Frame: '//FIXREF
WRITE (*,*) 'Aberration Correction: '//ABCORR
WRITE (*,*) ' '
WRITE (*,*) 'Number of cuts: ', NCUTS
DO I = 1, NMETH
CALL TERMPT ( METHOD(I), ILUSRC, TARGET, ET,
. FIXREF, ABCORR, CORLOC(I), OBSRVR,
. Z, DELROL, NCUTS, SCHSTP,
. SOLTOL, MAXN, NPTS, POINTS,
. TRGEPS, TRMVCS )
C
C Write the results.
C
WRITE(*,*) ' '
WRITE(*,*) 'Computation method = ', METHOD(I)
WRITE(*,*) 'Locus = ', CORLOC(I)
START = 0
DO J = 1, NCUTS
ROLL = (J-1) * DELROL
WRITE(*,*) ' '
WRITE(*,FM1) ' Roll angle (deg) = ', ROLL * DPR()
WRITE(*,FM1) ' Target epoch = ', TRGEPS(J)
WRITE(*,FM2) ' Number of terminator points at '
. // 'this roll angle: ',
. NPTS(J)
DO K = 1, NPTS(J)
WRITE (*,*) ' Terminator point planetodetic '
. // 'coordinates:'
CALL RECGEO ( POINTS(1,K+START), RE, F,
. LON, LAT, ALT )
WRITE (*,FM1) ' Longitude (deg): ',
. LON*DPR()
WRITE (*,FM1) ' Latitude (deg): ',
. LAT*DPR()
WRITE (*,FM1) ' Altitude (km): ',
. ALT
C
C Get illumination angles for this terminator
C point.
C
M = K+START
CALL ILLUMG ( ILUMTH, TARGET, ILUSRC, ET,
. FIXREF, ABCORR, OBSRVR,
. POINTS(1,M), TRGEPC, SRFVEC,
. PHASE, SOLAR, EMISSN )
WRITE (*,FM1) ' Incidence angle '
. // '(deg): ', SOLAR * DPR()
C
C Adjust the incidence angle for the angular
C radius of the illumination source. Use the
C epoch associated with the terminator point
C for this lookup.
C
CALL SPKPOS ( ILUSRC, TRGEPS(M), FIXREF,
. ABCORR, TARGET, TPTILU, LT )
DIST = VNORM( TPTILU )
ANGSRC = ASIN ( MAX( SRCRAD(1),
. SRCRAD(2),
. SRCRAD(3) ) / DIST )
IF ( I .EQ. 1 ) THEN
C
C For points on the umbral terminator,
C the ellipsoid outward normal is tilted
C away from the terminator-source center
C direction by the angular radius of the
C source. Subtract this radius from the
C illumination incidence angle to get the
C angle between the local normal and the
C direction to the corresponding tangent
C point on the source.
C
ADJANG = SOLAR - ANGSRC
ELSE
C
C For the penumbral case, the outward
C normal is tilted toward the illumination
C source by the angular radius of the
C source. Adjust the illumination
C incidence angle for this.
C
ADJANG = SOLAR + ANGSRC
END IF
WRITE (*,FM1) ' Adjusted angle '
. // '(deg): ', ADJANG * DPR()
IF ( I .EQ. 1 ) THEN
C
C Save terminator points for comparison.
C
CALL VEQU ( POINTS(1,M), SVPNTS(1,M) )
ELSE
C
C Compare terminator points with last
C saved values.
C
DIST = VDIST( POINTS(1,M), SVPNTS(1,M) )
WRITE (*,FM1)
. ' Distance offset (km): ', DIST
END IF
END DO
START = START + NPTS(J)
END DO
WRITE (*,*) ' '
END DO
END
When this program was executed on a Mac/Intel/gfortran/64-bit
platform, the output was:
Light source: SUN
Observer: EARTH
Target: MARS
Frame: IAU_MARS
Aberration Correction: CN+S
Number of cuts: 3
Computation method = UMBRAL/ELLIPSOID/TANGENT
Locus = ELLIPSOID TERMINATOR
Roll angle (deg) = 0.000000000
Target epoch = 271683700.369686902
Number of terminator points at this roll angle: 1
Terminator point planetodetic coordinates:
Longitude (deg): 4.189318082
Latitude (deg): 66.416132677
Altitude (km): 0.000000000
Incidence angle (deg): 90.163842885
Adjusted angle (deg): 89.999999980
Roll angle (deg) = 120.000000000
Target epoch = 271683700.372003794
Number of terminator points at this roll angle: 1
Terminator point planetodetic coordinates:
Longitude (deg): 107.074551917
Latitude (deg): -27.604435701
Altitude (km): 0.000000000
Incidence angle (deg): 90.163842793
Adjusted angle (deg): 89.999999888
Roll angle (deg) = 240.000000000
Target epoch = 271683700.364983618
Number of terminator points at this roll angle: 1
Terminator point planetodetic coordinates:
Longitude (deg): -98.695906077
Latitude (deg): -27.604435700
Altitude (km): -0.000000000
Incidence angle (deg): 90.163843001
Adjusted angle (deg): 90.000000096
Computation method = PENUMBRAL/ELLIPSOID/TANGENT
Locus = ELLIPSOID TERMINATOR
Roll angle (deg) = 0.000000000
Target epoch = 271683700.369747400
Number of terminator points at this roll angle: 1
Terminator point planetodetic coordinates:
Longitude (deg): 4.189317837
Latitude (deg): 66.743818467
Altitude (km): 0.000000000
Incidence angle (deg): 89.836157094
Adjusted angle (deg): 89.999999999
Distance offset (km): 19.483590936
Roll angle (deg) = 120.000000000
Target epoch = 271683700.372064054
Number of terminator points at this roll angle: 1
Terminator point planetodetic coordinates:
Longitude (deg): 107.404259674
Latitude (deg): -27.456458359
Altitude (km): -0.000000000
Incidence angle (deg): 89.836157182
Adjusted angle (deg): 90.000000087
Distance offset (km): 19.411414247
Roll angle (deg) = 240.000000000
Target epoch = 271683700.365043879
Number of terminator points at this roll angle: 1
Terminator point planetodetic coordinates:
Longitude (deg): -99.025614323
Latitude (deg): -27.456458357
Altitude (km): 0.000000000
Incidence angle (deg): 89.836156972
Adjusted angle (deg): 89.999999877
Distance offset (km): 19.411437239
Restrictions
None.
Literature_References
None.
Author_and_Institution
N.J. Bachman (JPL)
J. Diaz del Rio (ODC Space)
Version
SPICELIB Version 1.1.0, 12-SEP-2021 (NJB) (JDR)
Bug fix: PRVCOR is no longer set to blank before
ABCORR is parsed.
ZZVALCOR is now used instead of ZZPRSCOR. This provides
better error handling.
Edited the header to comply with NAIF standard.
Corrected the filename of code example #1's meta-kernel.
Removed unnecessary SAVE statement from code example #2.
SPICELIB Version 1.0.0, 04-APR-2017 (NJB)
11-MAR-2016 (NJB)
Changed ellipsoid algorithm to use ZZEDTMPT. Added ROLSTP
argument. Updated calls to ZZTANGNT to accommodate argument
list change. Added code examples. Updated $Detailed_Input. Made
various header corrections.
Original version 18-NOV-2015 (NJB)
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Fri Dec 31 18:37:02 2021