edterm_c |

Table of contents## Procedureedterm_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_Inputtrmtyp 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_Outputtrgepc 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. ## Exceptions1) 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. ## FilesAppropriate 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. ## ParticularsThis 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. ## ExamplesThe 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++ ) { ## 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