Remote Sensing Hands-On Lesson, using CASSINI (FORTRAN) |
Table of ContentsRemote Sensing Hands-On Lesson, using CASSINI (FORTRAN) Overview Note About HTML Links References Tutorials Required Readings The Permuted Index API Documentation Kernels Used SPICE Modules Used Time Conversion (convtm) Task Statement Learning Goals Approach Solution Solution Meta-Kernel Solution Source Code Solution Sample Output Extra Credit Task statements and questions Solutions and answers Obtaining Target States and Positions (getsta) Task Statement Learning Goals Approach Solution Solution Meta-Kernel Solution Source Code Solution Sample Output Extra Credit Task statements and questions Solutions and answers Spacecraft Orientation and Reference Frames (xform) Task Statement Learning Goals Approach Solution Solution Meta-Kernel Solution Source Code Solution Sample Output Extra Credit Task statements and questions Solutions and answers Computing Sub-s/c and Sub-solar Points on an Ellipsoid and a DSK (subpts) Task Statement Learning Goals Approach Solution Solution Meta-Kernel Solution Source Code Solution Sample Output Extra Credit Task statements and questions Solutions and answers Intersecting Vectors with an Ellipsoid and a DSK (fovint) Task Statement Learning Goals Approach Solution Solution Meta-Kernel Solution Source Code Solution Sample Output Extra Credit Remote Sensing Hands-On Lesson, using CASSINI (FORTRAN)
Overview
Note About HTML Links
In order for the links to be resolved, if not done already by installing the lessons package under the Toolkit's ``doc/html'' directory, create a subdirectory called ``lessons'' under the ``doc/html'' directory of the ``toolkit/'' tree and copy this document to that subdirectory before loading it into a Web browser. References
Of these documents, the ``Tutorials'' contains the highest level descriptions with the least number of details while the ``Required Reading'' documents contain much more detailed specifications. The most complete specifications are provided in the ``API Documentation''. In some cases the lesson explanations also refer to the information provided in the meta-data area of the kernels used in the lesson examples. It is especially true in case of the FK and IK files, which often contain comprehensive descriptions of the frames, instrument FOVs, etc. Since both the FK and IK are text kernels, the information provided in them can be viewed using any text editor, while the meta information provided in binary kernels---SPKs and CKs---can be viewed using ``commnt'' or ``spacit'' utility programs located in ``toolkit/exe'' of Toolkit installation tree. Tutorials
Name Lesson steps/routines it describes ---------------- ----------------------------------------------- Time Time Conversion SCLK and LSK Time Conversion SPK Obtaining Ephemeris Data Frames Reference Frames Using Frames Reference Frames PCK Planetary Constants Data CK Spacecraft Orientation Data DSK Detailed Target Shape (Topography) DataThese tutorials are available from the NAIF server at JPL:
https://naif.jpl.nasa.gov/naif/tutorials.html Required Readings
Name Lesson steps/routines that it describes --------------- ----------------------------------------- ck.req Obtaining spacecraft orientation data dsk.req Obtaining detailed body shape data frames.req Using reference frames naif_ids.req Determining body ID codes pck.req Obtaining planetary constants data sclk.req SCLK time conversion spk.req Obtaining ephemeris Data time.req Time conversion The Permuted Index
This text document provides a simple mechanism by which users can discover which SPICE routines perform functions of interest, as well as the names of the source files that contain these routines. It is particularly useful for FORTRAN programmers because some of the routines are entry points; the names of these routines do not translate directly into the name of the respective source files that contain them. API Documentation
For example the path of the source code of the STR2ET routine is
toolkit/src/spicelib/str2et.forSince some of the FORTRAN routines are entry points they may be part of a source file that has different name. The ``Permuted Index'' document mentioned above can be used to locate the name of their source file. Kernels Used
# FILE NAME TYPE DESCRIPTION -- ------------------------- ---- ----------------------------------- 1 naif0008.tls LSK Generic LSK 2 cas00084.tsc SCLK Cassini SCLK 3 981005_PLTEPH-DE405S.bsp SPK Solar System Ephemeris 4 020514_SE_SAT105.bsp SPK Saturnian Satellite Ephemeris 5 030201AP_SK_SM546_T45.bsp SPK Cassini Spacecraft SPK 6 cas_v37.tf FK Cassini FK 7 04135_04171pc_psiv2.bc CK Cassini Spacecraft CK 8 cpck05Mar2004.tpc PCK Cassini Project PCK 9 phoebe_64q.bds DSK Phoebe DSK 10 cas_iss_v09.ti IK ISS Instrument KernelThese SPICE kernels are included in the lesson package. In addition to these kernels, the extra credit exercises require the following kernels:
# FILE NAME TYPE DESCRIPTION -- --------------- ---- --------------------------------------------- 11 jup310_2004.bsp SPK Generic Jovian Satellite EphemerisThese SPICE kernels are available from the NAIF server at JPL:
https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/satellites/ SPICE Modules Used
CHAPTER EXERCISE ROUTINES FUNCTIONS KERNELS ------- --------- --------- --------- ---------- 1 convtm FURNSH 1,2 PROMPT STR2ET ETCAL TIMOUT SCE2S extra (*) UNLOAD UNITIM 1,2 SCT2E ET2UTC SCS2E 2 getsta FURNSH VNORM 1,3-5 PROMPT STR2ET SPKEZR SPKPOS CONVRT extra (*) KCLEAR 1,3-5,11 UNLOAD 3 xform FURNSH VSEP 1-8 PROMPT STR2ET SPKEZR SXFORM MXVG SPKPOS PXFORM MXV CONVRT extra (*) KCLEAR 1-8 UNLOAD 4 subpts FURNSH VNORM 1,3-5,8,9 PROMPT STR2ET SUBPNT SUBSLR extra (*) KCLEAR DPR 1,3-5,8 RECLAT BODVRD RECPGR 5 fovint FURNSH DPR 1-10 PROMPT STR2ET GETFVN MOVED BODN2C BYEBYE SINCPT RECLAT ILLUMF ET2LST (*) Additional APIs and kernels used in Extra Credit tasks.Refer to the headers of the various routines listed above, as detailed interface specifications are provided with the source code. Time Conversion (convtm)Task Statement
Learning Goals
Approach
When completing the ``calendar format'' step above, consider using one of two possible methods: ETCAL or TIMOUT. SolutionSolution Meta-Kernel
KPL/MK This is the meta-kernel used in the solution of the ``Time Conversion'' task in the Remote Sensing Hands On Lesson. The names and contents of the kernels referenced by this meta-kernel are as follows: File name Contents -------------------------- ----------------------------- naif0008.tls Generic LSK cas00084.tsc Cassini SCLK \begindata KERNELS_TO_LOAD = ( 'kernels/lsk/naif0008.tls', 'kernels/sclk/cas00084.tsc' ) \begintext Solution Source Code
PROGRAM CONVTM IMPLICIT NONE C C Local Parameters C C The name of the meta-kernel that lists the kernels C to load into the program. C CHARACTER*(*) METAKR PARAMETER ( METAKR = 'convtm.tm' ) C C The spacecraft clock ID code for CASSINI. C INTEGER SCLKID PARAMETER ( SCLKID = -82 ) C C The length of various string variables. C INTEGER STRLEN PARAMETER ( STRLEN = 50 ) C C Local Variables C CHARACTER*(STRLEN) CALET CHARACTER*(STRLEN) SCLKST CHARACTER*(STRLEN) UTCTIM DOUBLE PRECISION ET C C Load the kernels this program requires. C Both the spacecraft clock kernel and a C leapseconds kernel should be listed C in the meta-kernel. C CALL FURNSH ( METAKR ) C C Prompt the user for the input time string. C CALL PROMPT ( 'Input UTC Time: ', UTCTIM ) WRITE (*,*) 'Converting UTC Time: ', UTCTIM C C Convert UTCTIM to ET. C CALL STR2ET ( UTCTIM, ET ) WRITE (*,'(A,F16.3)') ' ET Seconds Past J2000: ', ET C C Now convert ET to a formal calendar time C string. This can be accomplished in two C ways. C CALL ETCAL ( ET, CALET ) WRITE (*,*) ' Calendar ET (ETCAL): ', CALET C C Or use TIMOUT for finer control over the C output format. The picture below was built C by examining the header of TIMOUT. C CALL TIMOUT ( ET, 'YYYY-MON-DDTHR:MN:SC ::TDB', CALET ) WRITE (*,*) ' Calendar ET (TIMOUT): ', CALET C C Convert ET to spacecraft clock time. C CALL SCE2S ( SCLKID, ET, SCLKST ) WRITE (*,*) ' Spacecraft Clock Time: ', SCLKST END Solution Sample Output
Input UTC Time: 2004 jun 11 19:32:00 Converting UTC Time: 2004 jun 11 19:32:00 ET Seconds Past J2000: 140254384.185 Calendar ET (ETCAL): 2004 JUN 11 19:33:04.184 Calendar ET (TIMOUT): 2004-JUN-11T19:33:04 Spacecraft Clock Time: 1/1465674964.105 Extra Credit
These ``extra credit'' tasks are provided as task statements, and unlike the regular tasks, no approach or solution source code is provided. In the next section, you will find the numeric solutions (when applicable) and answers to the questions asked in these tasks. Task statements and questions
Solutions and answers
Julian Date TDB: 2453168.3146318
===================================================================== =========== Toolkit version: N0067 SPICE(NOLEAPSECONDS) -- The variable that points to the leapseconds (DELTET/DELTA_AT) could n ot be located in the kernel pool. It is likely that the leapseconds kernel has not been loaded. A traceback follows. The name of the highest level module is first. STR2ET --> TTRANS Oh, by the way: The SPICELIB error handling actions are USER-TAILORA BLE. You can choose whether the Toolkit aborts or continues when errors occur, which error messages to output, and where to send the output. Please read the ERROR "Required Reading" file, or see the routines ERRACT, ERRDEV, and ERRP RT. ===================================================================== ===========
===================================================================== =========== Toolkit version: N0067 SPICE(KERNELVARNOTFOUND) -- The Variable Was not Found in the Kernel Pool. Kernel variable SCLK_DATA_TYPE_82 was not found in the kernel pool. A traceback follows. The name of the highest level module is first. SCE2S --> SCE2T --> SCTYPE --> SCTY01 Oh, by the way: The SPICELIB error handling actions are USER-TAILORA BLE. You can choose whether the Toolkit aborts or continues when errors occur, which error messages to output, and where to send the output. Please read the ERROR "Required Reading" file, or see the routines ERRACT, ERRDEV, and ERRP RT. ===================================================================== ===========
Earliest UTC convertible to SCLK: 1980-01-01T00:00:00.000
Spacecraft Clock Time: 1/1465674964.105 UTC time from spacecraft clock: 2004-06-11T19:31:59.999 Obtaining Target States and Positions (getsta)Task Statement
Learning Goals
Approach
When deciding which SPK files to load, the Toolkit utility ``brief'' may be of some use. ``brief'' is located in the ``toolkit/exe'' directory for FORTRAN toolkits. Consult its user's guide available in ``toolkit/doc/brief.ug'' for details. SolutionSolution Meta-Kernel
KPL/MK This is the meta-kernel used in the solution of the ``Obtaining Target States and Positions'' task in the Remote Sensing Hands On Lesson. The names and contents of the kernels referenced by this meta-kernel are as follows: File name Contents -------------------------- ----------------------------- naif0008.tls Generic LSK 981005_PLTEPH-DE405S.bsp Solar System Ephemeris 020514_SE_SAT105.bsp Saturnian Satellite Ephemeris 030201AP_SK_SM546_T45.bsp Cassini Spacecraft SPK \begindata KERNELS_TO_LOAD = ( 'kernels/lsk/naif0008.tls', 'kernels/spk/981005_PLTEPH-DE405S.bsp', 'kernels/spk/020514_SE_SAT105.bsp', 'kernels/spk/030201AP_SK_SM546_T45.bsp' ) \begintext Solution Source Code
PROGRAM GETSTA IMPLICIT NONE C C SPICELIB Functions C DOUBLE PRECISION VNORM C C Local Parameters C C C The name of the meta-kernel that lists the kernels C to load into the program. C CHARACTER*(*) METAKR PARAMETER ( METAKR = 'getsta.tm' ) C C The length of various string variables. C INTEGER STRLEN PARAMETER ( STRLEN = 50 ) C C Local Variables C CHARACTER*(STRLEN) UTCTIM DOUBLE PRECISION DIST DOUBLE PRECISION ET DOUBLE PRECISION LTIME DOUBLE PRECISION POS ( 3 ) DOUBLE PRECISION STATE ( 6 ) C C Load the kernels that this program requires. We C will need a leapseconds kernel to convert input C UTC time strings into ET. We also will need the C necessary SPK files with coverage for the bodies C in which we are interested. C CALL FURNSH ( METAKR ) C C Prompt the user for the input time string. C CALL PROMPT ( 'Input UTC Time: ', UTCTIM ) WRITE (*,*) 'Converting UTC Time: ', UTCTIM C C Convert UTCTIM to ET. C CALL STR2ET ( UTCTIM, ET ) WRITE (*,'(A,F16.3)') ' ET seconds past J2000: ', ET C C Compute the apparent state of Phoebe as seen from C CASSINI in the J2000 frame. All of the ephemeris C readers return states in units of kilometers and C kilometers per second. C CALL SPKEZR ( 'PHOEBE', ET, 'J2000', 'LT+S', . 'CASSINI', STATE, LTIME ) WRITE (*,*) ' Apparent state of Phoebe as seen from ' .// 'CASSINI in the J2000' WRITE (*,*) ' frame (km, km/s):' WRITE (*,'(A,F16.3)') ' X = ', STATE(1) WRITE (*,'(A,F16.3)') ' Y = ', STATE(2) WRITE (*,'(A,F16.3)') ' Z = ', STATE(3) WRITE (*,'(A,F16.3)') ' VX = ', STATE(4) WRITE (*,'(A,F16.3)') ' VY = ', STATE(5) WRITE (*,'(A,F16.3)') ' VZ = ', STATE(6) C C Compute the apparent position of Earth as seen from C CASSINI in the J2000 frame. Note: We could have continued C using SPKEZR and simply ignored the velocity components. C CALL SPKPOS ( 'EARTH', ET, 'J2000', 'LT+S', . 'CASSINI', POS, LTIME ) WRITE (*,*) ' Apparent position of Earth as seen from ' .// 'CASSINI in the J2000' WRITE (*,*) ' frame (km):' WRITE (*,'(A,F16.3)') ' X = ', POS(1) WRITE (*,'(A,F16.3)') ' Y = ', POS(2) WRITE (*,'(A,F16.3)') ' Z = ', POS(3) C C We need only display LTIME, as it is precisely the light C time in which we are interested. C WRITE (*,*) ' One way light time between CASSINI and the ' .// 'apparent position' WRITE (*,'(A,F16.3)') ' of Earth (seconds): ', LTIME C C Compute the apparent position of the Sun as seen from C Phoebe in the J2000 frame. C CALL SPKPOS ( 'SUN', ET, 'J2000', 'LT+S', . 'PHOEBE', POS, LTIME ) WRITE (*,*) ' Apparent position of Sun as seen from ' .// 'Phoebe in the' WRITE (*,*) ' J2000 frame (km):' WRITE (*,'(A,F16.3)') ' X = ', POS(1) WRITE (*,'(A,F16.3)') ' Y = ', POS(2) WRITE (*,'(A,F16.3)') ' Z = ', POS(3) C C Now we need to compute the actual distance between the Sun C and Phoebe. The above SPKPOS call gives us the apparent C distance, so we need to adjust our aberration correction C appropriately. C CALL SPKPOS ( 'SUN', ET, 'J2000', 'NONE', . 'PHOEBE', POS, LTIME ) C C Compute the distance between the body centers in C kilometers. C DIST = VNORM(POS) C C Convert this value to AU using CONVRT. C CALL CONVRT ( DIST, 'KM', 'AU', DIST ) WRITE (*,*) ' Actual distance between Sun and Phoebe body ' .// 'centers: ' WRITE (*,'(A,F16.3)') ' (AU):', DIST END Solution Sample Output
Input UTC Time: 2004 jun 11 19:32:00 Converting UTC Time: 2004 jun 11 19:32:00 ET seconds past J2000: 140254384.185 Apparent state of Phoebe as seen from CASSINI in the J2000 frame (km, km/s): X = -119.921 Y = 2194.139 Z = -57.639 VX = -5.980 VY = -2.119 VZ = -0.295 Apparent position of Earth as seen from CASSINI in the J2000 frame (km): X = 353019393.123 Y = -1328180352.140 Z = -568134171.697 One way light time between CASSINI and the apparent position of Earth (seconds): 4960.427 Apparent position of Sun as seen from Phoebe in the J2000 frame (km): X = 376551465.272 Y = -1190495630.303 Z = -508438699.110 Actual distance between Sun and Phoebe body centers: (AU): 9.012 Extra Credit
These ``extra credit'' tasks are provided as task statements, and unlike the regular tasks, no approach or solution source code is provided. In the next section, you will find the numeric solutions (when applicable) and answers to the questions asked in these tasks. Task statements and questions
Solutions and answers
===================================================================== =========== Toolkit version: N0067 SPICE(SPKINSUFFDATA) -- Insufficient ephemeris data has been loaded to compute the state of - 82 (CASSINI) relative to 0 (SOLAR SYSTEM BARYCENTER) at the ephemeris ep och 2004 JUN 11 19:33:04.184. A traceback follows. The name of the highest level module is first. SPKEZR --> SPKEZ --> SPKACS --> SPKGEO Oh, by the way: The SPICELIB error handling actions are USER-TAILORA BLE. You can choose whether the Toolkit aborts or continues when errors occur, which error messages to output, and where to send the output. Please read the ERROR "Required Reading" file, or see the routines ERRACT, ERRDEV, and ERRP RT. ===================================================================== ===========
BRIEF -- Version 4.1.0, September 17, 2021 -- Toolkit Version N0067 Summary for: kernels/spk/981005_PLTEPH-DE405S.bsp Bodies: MERCURY BARYCENTER (1) w.r.t. SOLAR SYSTEM BARYCENTER (0) VENUS BARYCENTER (2) w.r.t. SOLAR SYSTEM BARYCENTER (0) EARTH BARYCENTER (3) w.r.t. SOLAR SYSTEM BARYCENTER (0) MARS BARYCENTER (4) w.r.t. SOLAR SYSTEM BARYCENTER (0) JUPITER BARYCENTER (5) w.r.t. SOLAR SYSTEM BARYCENTER (0) SATURN BARYCENTER (6) w.r.t. SOLAR SYSTEM BARYCENTER (0) URANUS BARYCENTER (7) w.r.t. SOLAR SYSTEM BARYCENTER (0) NEPTUNE BARYCENTER (8) w.r.t. SOLAR SYSTEM BARYCENTER (0) PLUTO BARYCENTER (9) w.r.t. SOLAR SYSTEM BARYCENTER (0) SUN (10) w.r.t. SOLAR SYSTEM BARYCENTER (0) MERCURY (199) w.r.t. MERCURY BARYCENTER (1) VENUS (299) w.r.t. VENUS BARYCENTER (2) MOON (301) w.r.t. EARTH BARYCENTER (3) EARTH (399) w.r.t. EARTH BARYCENTER (3) MARS (499) w.r.t. MARS BARYCENTER (4) Start of Interval (UTC) End of Interval (UTC) ----------------------------- ------------------------- ---- 2004-JUN-11 05:00:00.000 2004-JUN-12 12:00:00.000 Summary for: kernels/spk/020514_SE_SAT105.bsp Bodies: MIMAS (601) w.r.t. SATURN BARYCENTER (6) ENCELADUS (602) w.r.t. SATURN BARYCENTER (6) TETHYS (603) w.r.t. SATURN BARYCENTER (6) DIONE (604) w.r.t. SATURN BARYCENTER (6) RHEA (605) w.r.t. SATURN BARYCENTER (6) TITAN (606) w.r.t. SATURN BARYCENTER (6) HYPERION (607) w.r.t. SATURN BARYCENTER (6) IAPETUS (608) w.r.t. SATURN BARYCENTER (6) PHOEBE (609) w.r.t. SATURN BARYCENTER (6) SATURN (699) w.r.t. SATURN BARYCENTER (6) Start of Interval (UTC) End of Interval (UTC) ----------------------------- ------------------------- ---- 2004-JUN-11 05:00:00.000 2004-JUN-12 12:00:00.000 Summary for: kernels/spk/030201AP_SK_SM546_T45.bsp Body: CASSINI (-82) w.r.t. SATURN BARYCENTER (6) Start of Interval (UTC) End of Interval (UTC) ----------------------------- --------------------------- -- 2004-JUN-11 05:00:00.000 2004-JUN-12 12:00:00.000
Additional kernels required for this task: File name Contents ----------------------- ---------------------------------- jup310_2004.bsp Generic Jovian Satellite Ephemeris available in the NAIF server at: https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/satellites/
Actual position of Jupiter as seen from Saturn in the J2000 frame (km): X = -436016583.291 Y = -1094176737.323 Z = -446585337.431
Actual (geometric) position of Sun as seen from Saturn in the J2000 frame (km): X = 367770592.367 Y = -1197330367.359 Z = -510369088.677 Light-time corrected position of Sun as seen from Saturn in the J2000 frame (km): X = 367770572.921 Y = -1197330417.733 Z = -510369109.509 Apparent position of Sun as seen from Saturn in the J2000 frame (km): X = 367726456.168 Y = -1197342627.879 Z = -510372252.747 Spacecraft Orientation and Reference Frames (xform)Task Statement
Learning Goals
Approach
You may find it useful to consult the permuted index, the headers of various source modules, and the following toolkit documentation:
SolutionSolution Meta-Kernel
KPL/MK This is the meta-kernel used in the solution of the ``Spacecraft Orientation and Reference Frames'' task in the Remote Sensing Hands On Lesson. The names and contents of the kernels referenced by this meta-kernel are as follows: File name Contents -------------------------- ----------------------------- naif0008.tls Generic LSK cas00084.tsc Cassini SCLK 981005_PLTEPH-DE405S.bsp Solar System Ephemeris 020514_SE_SAT105.bsp Saturnian Satellite Ephemeris 030201AP_SK_SM546_T45.bsp Cassini Spacecraft SPK cas_v37.tf Cassini FK 04135_04171pc_psiv2.bc Cassini Spacecraft CK cpck05Mar2004.tpc Cassini Project PCK \begindata KERNELS_TO_LOAD = ( 'kernels/lsk/naif0008.tls', 'kernels/sclk/cas00084.tsc', 'kernels/spk/981005_PLTEPH-DE405S.bsp', 'kernels/spk/020514_SE_SAT105.bsp', 'kernels/spk/030201AP_SK_SM546_T45.bsp', 'kernels/fk/cas_v37.tf', 'kernels/ck/04135_04171pc_psiv2.bc', 'kernels/pck/cpck05Mar2004.tpc' ) \begintext Solution Source Code
PROGRAM XFORM IMPLICIT NONE C C SPICELIB Functions C DOUBLE PRECISION VSEP C C Local Parameters C C C The name of the meta-kernel that lists the kernels C to load into the program. C CHARACTER*(*) METAKR PARAMETER ( METAKR = 'xform.tm' ) C C The length of various string variables. C INTEGER STRLEN PARAMETER ( STRLEN = 50 ) C C Local Variables C CHARACTER*(STRLEN) UTCTIM DOUBLE PRECISION ET DOUBLE PRECISION LTIME DOUBLE PRECISION STATE ( 6 ) DOUBLE PRECISION BFIXST ( 6 ) DOUBLE PRECISION POS ( 3 ) DOUBLE PRECISION SXFMAT ( 6, 6 ) DOUBLE PRECISION PFORM ( 3, 3 ) DOUBLE PRECISION BSIGHT ( 3 ) DOUBLE PRECISION SEP C C Load the kernels that this program requires. We C will need: C C A leapseconds kernel C A spacecraft clock kernel for CASSINI C The necessary ephemerides C A planetary constants file (PCK) C A spacecraft orientation kernel for CASSINI (CK) C A frame kernel (TF) C CALL FURNSH ( METAKR ) C C Prompt the user for the input time string. C CALL PROMPT ( 'Input UTC Time: ', UTCTIM ) WRITE (*,*) 'Converting UTC Time: ', UTCTIM C C Convert UTCTIM to ET. C CALL STR2ET ( UTCTIM, ET ) WRITE (*,'(A,F16.3)') ' ET seconds past J2000: ', ET C C Compute the apparent state of Phoebe as seen from CASSINI C in the J2000 reference frame. C CALL SPKEZR ( 'PHOEBE', ET, 'J2000', 'LT+S', . 'CASSINI', STATE, LTIME ) C C Now obtain the transformation from the inertial C J2000 frame to the non-inertial, body-fixed IAU_PHOEBE C frame. Since we'll use this transformation to produce C the apparent state in the IAU_PHOEBE reference frame, C we need to correct the orientation of this frame for C one-way light time; hence we subtract LTIME from ET C in the call below. C CALL SXFORM ( 'J2000', 'IAU_PHOEBE', ET-LTIME, SXFMAT ) C C Now transform the apparent J2000 state into IAU_PHOEBE C with the following matrix multiplication: C CALL MXVG ( SXFMAT, STATE, 6, 6, BFIXST ) C C Display the results. C WRITE (*,*) ' Apparent state of Phoebe as seen from ' .// 'CASSINI in the IAU_PHOEBE' WRITE (*,*) ' body-fixed frame (km, km/s):' WRITE (*,'(A,F19.6)') ' X = ', BFIXST(1) WRITE (*,'(A,F19.6)') ' Y = ', BFIXST(2) WRITE (*,'(A,F19.6)') ' Z = ', BFIXST(3) WRITE (*,'(A,F19.6)') ' VX = ', BFIXST(4) WRITE (*,'(A,F19.6)') ' VY = ', BFIXST(5) WRITE (*,'(A,F19.6)') ' VZ = ', BFIXST(6) C C It is worth pointing out, all of the above could have C been done with a single call to SPKEZR: C CALL SPKEZR ( 'PHOEBE', ET, 'IAU_PHOEBE', 'LT+S', . 'CASSINI', STATE, LTIME ) C C Display the results. C WRITE (*,*) ' Apparent state of Phoebe as seen from CASSINI ' .// 'in the IAU_PHOEBE' WRITE (*,*) ' body-fixed frame (km, km/s) ' .// 'obtained using SPKEZR directly:' WRITE (*,'(A,F19.6)') ' X = ', STATE(1) WRITE (*,'(A,F19.6)') ' Y = ', STATE(2) WRITE (*,'(A,F19.6)') ' Z = ', STATE(3) WRITE (*,'(A,F19.6)') ' VX = ', STATE(4) WRITE (*,'(A,F19.6)') ' VY = ', STATE(5) WRITE (*,'(A,F19.6)') ' VZ = ', STATE(6) C C Note that the velocity found by using SPKEZR C to compute the state in the IAU_PHOEBE frame differs C at the few mm/second level from that found previously C by calling SPKEZR and then SXFORM. Computing velocity C via a single call to SPKEZR as we've done immediately C above is slightly more accurate because it accounts for C the effect of the rate of change of light time on the C apparent angular velocity of the target's body-fixed C reference frame. C C Now we are to compute the angular separation between C the apparent position of the Earth as seen from the C orbiter and the nominal boresight of the high gain C antenna. First, compute the apparent position of C the Earth as seen from CASSINI in the J2000 frame. C CALL SPKPOS ( 'EARTH', ET, 'J2000', 'LT+S', . 'CASSINI', POS, LTIME ) C C Now compute the location of the antenna boresight C at this same epoch. From reading the frame kernel C we know that the antenna boresight is nominally the C +Z axis of the CASSINI_HGA frame defined there. C BSIGHT(1) = 0.0D0 BSIGHT(2) = 0.0D0 BSIGHT(3) = 1.0D0 C C Now compute the rotation matrix from CASSINI_HGA into C J2000. C CALL PXFORM ( 'CASSINI_HGA', 'J2000', ET, PFORM ) C C And multiply the result to obtain the nominal antenna C boresight in the J2000 reference frame. C CALL MXV ( PFORM, BSIGHT, BSIGHT ) C C Lastly compute the angular separation. C CALL CONVRT ( VSEP(BSIGHT, POS), 'RADIANS', . 'DEGREES', SEP ) WRITE (*,*) ' Angular separation between the ' .// 'apparent position of' WRITE (*,*) ' Earth and the CASSINI high ' .// 'gain antenna boresight (degrees): ' WRITE (*,'(A,F19.3)') ' ', SEP C C Or, alternately we can work in the antenna C frame directly. C CALL SPKPOS ( 'EARTH', ET, 'CASSINI_HGA', 'LT+S', . 'CASSINI', POS, LTIME ) C C The antenna boresight is the Z-axis in the C CASSINI_HGA frame. C BSIGHT(1) = 0.0D0 BSIGHT(2) = 0.0D0 BSIGHT(3) = 1.0D0 C C Lastly compute the angular separation. C CALL CONVRT ( VSEP(BSIGHT, POS), 'RADIANS', . 'DEGREES', SEP ) WRITE (*,*) ' Angular separation between the ' .// 'apparent position of' WRITE (*,*) ' Earth and the CASSINI high gain ' .// 'antenna boresight computed ' WRITE (*,*) ' using vectors in the CASSINI_HGA ' .// 'frame (degrees): ' WRITE (*,'(A,F19.3)') ' ', SEP END Solution Sample Output
Input UTC Time: 2004 jun 11 19:32:00 Converting UTC Time: 2004 jun 11 19:32:00 ET seconds past J2000: 140254384.185 Apparent state of Phoebe as seen from CASSINI in the IAU_PHOEBE body-fixed frame (km, km/s): X = -1982.639762 Y = -934.530471 Z = -166.562595 VX = 3.970833 VY = -3.812498 VZ = -2.371663 Apparent state of Phoebe as seen from CASSINI in the IAU_PHOEBE body-fixed frame (km, km/s) obtained using SPKEZR directly: X = -1982.639762 Y = -934.530471 Z = -166.562595 VX = 3.970832 VY = -3.812496 VZ = -2.371663 Angular separation between the apparent position of Earth and the CASSINI high gain antenna boresight (degrees): 71.924 Angular separation between the apparent position of Earth and the CASSINI high gain antenna boresight computed using vectors in the CASSINI_HGA frame (degrees): 71.924 Extra Credit
These ``extra credit'' tasks are provided as task statements, and unlike the regular tasks, no approach or solution source code is provided. In the next section, you will find the numeric solutions (when applicable) and answers to the questions asked in these tasks. Task statements and questions
Solutions and answers
===================================================================== =========== Toolkit version: N0067 SPICE(NOFRAMECONNECT) -- At epoch 1.4025036418463E+08 TDB (2004 JUN 11 18:26:04.184 TDB), ther e is insufficient information available to transform from reference frame -82101 (CASSINI_HGA) to reference frame 1 (J2000). Frame CASSINI_HGA could b e transformed to frame -82000 (CASSINI_SC_COORD). The latter is a CK fr ame; a CK file containing data for instrument or structure -82000 at the epoch shown above, as well as a corresponding SCLK kernel, must be loaded in orde r to use this frame. Failure to find required CK data could be due to one or m ore CK files not having been loaded, or to the epoch shown above lying withi n a coverage gap or beyond the coverage bounds of the loaded CK files. It is also possible that no loaded CK file has required angular velocity data fo r the input epoch, even if a loaded CK does have attitude data for that epo ch. You can use CKBRIEF with the -dump option to display coverage intervals o f a CK file. A traceback follows. The name of the highest level module is first. PXFORM --> REFCHG Oh, by the way: The SPICELIB error handling actions are USER-TAILORA BLE. You can choose whether the Toolkit aborts or continues when errors occur, which error messages to output, and where to send the output. Please read the ERROR "Required Reading" file, or see the routines ERRACT, ERRDEV, and ERRP RT. ===================================================================== ===========
CKBRIEF -- Version 6.1.0, June 27, 2014 -- Toolkit Version N0067 Summary for: kernels/ck/04135_04171pc_psiv2.bc Segment No.: 1 Object: -82000 Interval Begin UTC Interval End UTC AV ------------------------ ------------------------ --- 2004-JUN-11 05:00:00.000 2004-JUN-11 09:25:02.019 Y 2004-JUN-11 09:26:14.019 2004-JUN-11 18:24:37.152 Y 2004-JUN-11 18:26:13.152 2004-JUN-12 05:53:26.012 Y 2004-JUN-12 05:54:56.012 2004-JUN-12 10:32:08.016 Y 2004-JUN-12 10:33:26.016 2004-JUN-12 11:59:59.998 Y
CKBRIEF -- Version 6.1.0, June 27, 2014 -- Toolkit Version N0067 Summary for: kernels/ck/04135_04171pc_psiv2.bc Object: -82000 Interval Begin UTC Interval End UTC AV ------------------------ ------------------------ --- 2004-JUN-11 05:00:00.000 2004-JUN-12 11:59:59.998 Y
Angular separation between the apparent position of the Sun and the nominal boresight of the CASSINI high gain antenna (degrees): 73.130 HGA illumination: CASSINI high gain antenna IS illuminated.
Computing Sub-s/c and Sub-solar Points on an Ellipsoid and a DSK (subpts)Task Statement
near point/ellipsoiddefinition, and once using a DSK shape model and the
nadir/dsk/unprioritizeddefinition. The program displays the results. Use the program to compute these quantities at "2004 jun 11 19:32:00" UTC. Learning Goals
Approach
One point worth considering: how would the results change if the sub-solar and sub-observer points were computed using the
intercept/ellipsoidand
intercept/dsk/unprioritizeddefinitions? Which definition is appropriate? SolutionSolution Meta-Kernel
KPL/MK This is the meta-kernel used in the solution of the ``Computing Sub-spacecraft and Sub-solar Points'' task in the Remote Sensing Hands On Lesson. The names and contents of the kernels referenced by this meta-kernel are as follows: File name Contents -------------------------- ----------------------------- naif0008.tls Generic LSK 981005_PLTEPH-DE405S.bsp Solar System Ephemeris 020514_SE_SAT105.bsp Saturnian Satellite Ephemeris 030201AP_SK_SM546_T45.bsp Cassini Spacecraft SPK cpck05Mar2004.tpc Cassini Project PCK phoebe_64q.bds Phoebe DSK \begindata KERNELS_TO_LOAD = ( 'kernels/lsk/naif0008.tls', 'kernels/spk/981005_PLTEPH-DE405S.bsp', 'kernels/spk/020514_SE_SAT105.bsp', 'kernels/spk/030201AP_SK_SM546_T45.bsp', 'kernels/pck/cpck05Mar2004.tpc' 'kernels/dsk/phoebe_64q.bds' ) \begintext Solution Source Code
PROGRAM SUBPTS IMPLICIT NONE C C SPICELIB functions C DOUBLE PRECISION VNORM C C Local Parameters C C C The name of the meta-kernel that lists the kernels C to load into the program. C CHARACTER*(*) METAKR PARAMETER ( METAKR = 'subpts.tm' ) C C The length of various string variables. C INTEGER STRLEN PARAMETER ( STRLEN = 50 ) C C Local Variables C CHARACTER*(STRLEN) METHOD CHARACTER*(STRLEN) UTCTIM DOUBLE PRECISION ET DOUBLE PRECISION SPOINT ( 3 ) DOUBLE PRECISION SRFVEC ( 3 ) DOUBLE PRECISION TRGEPC INTEGER I C C Load the kernels that this program requires. We C will need: C C A leapseconds kernel C The necessary ephemerides C A planetary constants file (PCK) C A DSK file containing Phoebe shape data C CALL FURNSH ( METAKR ) C C Prompt the user for the input time string. C CALL PROMPT ( 'Input UTC Time: ', UTCTIM ) WRITE (*,*) 'Converting UTC Time: ', UTCTIM C C Convert UTCTIM to ET. C CALL STR2ET ( UTCTIM, ET ) WRITE (*,'(A,F16.3)') ' ET seconds past J2000: ', ET DO I = 1, 2 IF ( I .EQ. 1 ) THEN C C Use the "near point" sub-point definition C and an ellipsoidal model. C METHOD = 'NEAR POINT/Ellipsoid' ELSE C C Use the "nadir" sub-point definition and a C DSK model. C METHOD = 'NADIR/DSK/Unprioritized' END IF WRITE (*,*) ' ' WRITE (*,*) 'Sub-point/target shape model: '//METHOD WRITE (*,*) ' ' C C Compute the apparent sub-observer point of CASSINI C on Phoebe. C CALL SUBPNT ( METHOD, . 'PHOEBE', ET, 'IAU_PHOEBE', 'LT+S', . 'CASSINI', SPOINT, TRGEPC, SRFVEC ) WRITE (*,*) ' Apparent sub-observer point of CASSINI ' . // 'on Phoebe in the' WRITE (*,*) ' IAU_PHOEBE frame (km):' WRITE (*,'(A,F16.3)') ' X = ', SPOINT(1) WRITE (*,'(A,F16.3)') ' Y = ', SPOINT(2) WRITE (*,'(A,F16.3)') ' Z = ', SPOINT(3) WRITE (*,'(A,F16.3)') ' ALT = ', VNORM(SRFVEC) C C Compute the apparent sub-solar point on Phoebe as seen C from CASSINI. C CALL SUBSLR ( METHOD, . 'PHOEBE', ET, 'IAU_PHOEBE', 'LT+S', . 'CASSINI', SPOINT, TRGEPC, SRFVEC ) WRITE (*,*) ' Apparent sub-solar point on Phoebe as ' . // 'seen from CASSINI in' WRITE (*,*) ' the IAU_PHOEBE frame (km):' WRITE (*,'(A,F16.3)') ' X = ', SPOINT(1) WRITE (*,'(A,F16.3)') ' Y = ', SPOINT(2) WRITE (*,'(A,F16.3)') ' Z = ', SPOINT(3) END DO END Solution Sample Output
Input UTC Time: 2004 jun 11 19:32:00 Converting UTC Time: 2004 jun 11 19:32:00 ET seconds past J2000: 140254384.185 Sub-point/target shape model: NEAR POINT/Ellipsoid Apparent sub-observer point of CASSINI on Phoebe in the IAU_PHOEBE frame (km): X = 104.498 Y = 45.269 Z = 7.383 ALT = 2084.116 Apparent sub-solar point on Phoebe as seen from CASSINI in the IAU_PHOEBE frame (km): X = 78.681 Y = 76.879 Z = -21.885 Sub-point/target shape model: NADIR/DSK/Unprioritized Apparent sub-observer point of CASSINI on Phoebe in the IAU_PHOEBE frame (km): X = 95.373 Y = 40.948 Z = 6.610 ALT = 2094.242 Apparent sub-solar point on Phoebe as seen from CASSINI in the IAU_PHOEBE frame (km): X = 79.111 Y = 77.338 Z = -22.028 Extra Credit
These ``extra credit'' tasks are provided as task statements, and unlike the regular tasks, no approach or solution source code is provided. In the next section, you will find the numeric solutions (when applicable) and answers to the questions asked in these tasks. Task statements and questions
Solutions and answers
Apparent sub-solar point on Phoebe as seen from CASSINI in the IAU_PHOEBE frame using the 'Near Point: ellipsoid' method (km): X = 78.681 Y = 76.879 Z = -21.885 Apparent sub-solar point on Phoebe as seen from CASSINI in the IAU_PHOEBE frame using the 'Intercept: ellipsoid' method (km): X = 74.542 Y = 79.607 Z = -24.871
Geometric sub-spacecraft point of CASSINI on Phoebe in the IAU_PHOEBE frame using the 'Near Point: ellipsoid' method (km): X = 104.497 Y = 45.270 Z = 7.384
Planetocentric coordinates of the CASSINI sub-spacecraft point on Phoebe (degrees, km): LAT = 3.710 LON = 23.423 R = 114.121 Planetographic coordinates of the CASSINI sub-spacecraft point on Phoebe (degrees, km): LAT = 4.454 LON = 336.577 ALT = -0.831
Intersecting Vectors with an Ellipsoid and a DSK (fovint)Task Statement
At each point of intersection compute the following:
Additionally compute the local solar time at the intercept of the camera boresight with the surface of Phoebe, using both ellipsoidal and DSK shape models. Use this program to compute values at the epoch:
Learning Goals
Approach
SolutionSolution Meta-Kernel
KPL/MK This is the meta-kernel used in the solution of the ``Intersecting Vectors with a Triaxial Ellipsoid'' task in the Remote Sensing Hands On Lesson. The names and contents of the kernels referenced by this meta-kernel are as follows: File name Contents -------------------------- ----------------------------- naif0008.tls Generic LSK cas00084.tsc Cassini SCLK 981005_PLTEPH-DE405S.bsp Solar System Ephemeris 020514_SE_SAT105.bsp Saturnian Satellite Ephemeris 030201AP_SK_SM546_T45.bsp Cassini Spacecraft SPK cas_v37.tf Cassini FK 04135_04171pc_psiv2.bc Cassini Spacecraft CK cpck05Mar2004.tpc Cassini Project PCK cas_iss_v09.ti ISS Instrument Kernel phoebe_64q.bds Phoebe DSK \begindata KERNELS_TO_LOAD = ( 'kernels/lsk/naif0008.tls', 'kernels/sclk/cas00084.tsc', 'kernels/spk/981005_PLTEPH-DE405S.bsp', 'kernels/spk/020514_SE_SAT105.bsp', 'kernels/spk/030201AP_SK_SM546_T45.bsp', 'kernels/fk/cas_v37.tf', 'kernels/ck/04135_04171pc_psiv2.bc', 'kernels/pck/cpck05Mar2004.tpc', 'kernels/ik/cas_iss_v09.ti' 'kernels/dsk/phoebe_64q.bds' ) \begintext Solution Source Code
PROGRAM FOVINT IMPLICIT NONE C C SPICELIB functions C DOUBLE PRECISION DPR C C Local Parameters C C The name of the meta-kernel that lists the kernels C to load into the program. C CHARACTER*(*) METAKR PARAMETER ( METAKR = 'fovint.tm' ) C C The length of various string variables. C INTEGER STRLEN PARAMETER ( STRLEN = 50 ) C C The maximum number of boundary corner vectors C we can retrieve. We've extended this array by 1 C element to make room for the boresight vector. C INTEGER BCVLEN PARAMETER ( BCVLEN = 5 ) C C Local Variables C CHARACTER*(STRLEN) AMPM CHARACTER*(STRLEN) INSFRM CHARACTER*(STRLEN) METHOD ( 2 ) CHARACTER*(STRLEN) SHAPE CHARACTER*(STRLEN) TIME CHARACTER*(STRLEN) UTCTIM CHARACTER*(STRLEN) VECNAM ( BCVLEN ) DOUBLE PRECISION BOUNDS ( 3, BCVLEN ) DOUBLE PRECISION BSIGHT ( 3 ) DOUBLE PRECISION EMISSN DOUBLE PRECISION ET DOUBLE PRECISION LAT DOUBLE PRECISION LON DOUBLE PRECISION PHASE DOUBLE PRECISION POINT ( 3 ) DOUBLE PRECISION RADIUS DOUBLE PRECISION SOLAR DOUBLE PRECISION SRFVEC ( 3 ) DOUBLE PRECISION TRGEPC INTEGER HR INTEGER I INTEGER J INTEGER MN INTEGER N INTEGER PHOEID INTEGER SC LOGICAL FOUND LOGICAL LIT LOGICAL VISIBL C C Load the kernels that this program requires. We C will need: C C A leapseconds kernel. C A SCLK kernel for CASSINI. C Any necessary ephemerides. C The CASSINI frame kernel. C A CASSINI C-kernel. C A PCK file with Phoebe constants. C The CASSINI ISS I-kernel. C A DSK file containing Phoebe shape data. C CALL FURNSH ( METAKR ) C C Prompt the user for the input time string. C CALL PROMPT ( 'Input UTC Time: ', UTCTIM ) WRITE (*,*) 'Converting UTC Time: ', UTCTIM C C Convert UTCTIM to ET. C CALL STR2ET ( UTCTIM, ET ) WRITE (*,'(A,F16.3)') ' ET seconds past J2000: ', ET C C Now we need to obtain the FOV configuration of the NAC C camera. C CALL GETFVN ( 'CASSINI_ISS_NAC', BCVLEN, SHAPE, INSFRM, . BSIGHT, N, BOUNDS ) C C Rather than treat BSIGHT as a separate vector, C copy it into the last slot of BOUNDS. C CALL MOVED ( BSIGHT, 3, BOUNDS(1,5) ) C C Define names for each of the vectors for display C purposes. C VECNAM (1) = 'Boundary Corner 1' VECNAM (2) = 'Boundary Corner 2' VECNAM (3) = 'Boundary Corner 3' VECNAM (4) = 'Boundary Corner 4' VECNAM (5) = 'Cassini NAC Boresight' C C Set values of "method" string that specify use of C ellipsoidal and DSK (topographic) shape models. C C In this case, we can use the same methods for calls to both C SINCPT and ILUMIN. Note that some SPICE routines require C different "method" inputs from those shown here. See the C API documentation of each routine for details. C METHOD(1) = 'Ellipsoid' METHOD(2) = 'DSK/Unprioritized' C C Get Phoebe ID. We'll use this ID code later, when we C compute local solar time. C CALL BODN2C ( 'PHOEBE', PHOEID, FOUND ) C C Stop the program if the code was not found. C IF ( .NOT. FOUND ) THEN WRITE (*,*) 'Unable to locate the ID code for PHOEBE' CALL BYEBYE ( 'FAILURE' ) END IF C C Now perform the same set of calculations for each C vector listed in the BOUNDS array. Use both C ellipsoidal and detailed (DSK) shape models. C DO I = 1, 5 WRITE (*,*) ' ' WRITE (*,*) 'Vector: ', VECNAM(I) WRITE (*,*) ' ' DO J = 1, 2 WRITE (*,*) ' Target shape model: '//METHOD(J) WRITE (*,*) ' ' C C Call SINCPT to determine coordinates of the C intersection of this vector with the surface C of Phoebe. C CALL SINCPT ( METHOD(J), 'PHOEBE', ET, . 'IAU_PHOEBE', 'LT+S', 'CASSINI', . INSFRM, BOUNDS(1,I), POINT, . TRGEPC, SRFVEC, FOUND ) C C Check the found flag. Display a message if the point C of intersection was not found, otherwise continue with C the calculations. C IF ( .NOT. FOUND ) THEN WRITE (*,*) 'No intersection point found at ' . // 'this epoch for this vector.' ELSE C C Now, we have discovered a point of intersection. C Start by displaying the position vector in the C IAU_PHOEBE frame of the intersection. C WRITE (*,*) ' Position vector of ' . // 'surface intercept in ' . // 'the IAU_PHOEBE frame (km):' WRITE (*,'(A,F16.3)') ' X = ', POINT(1) WRITE (*,'(A,F16.3)') ' Y = ', POINT(2) WRITE (*,'(A,F16.3)') ' Z = ', POINT(3) C C Display the planetocentric latitude and longitude C of the intercept. C CALL RECLAT ( POINT, RADIUS, LON, LAT ) WRITE (*,*) ' Planetocentric coordinates of the ' . // 'intercept (degrees):' WRITE (*,'(A,F16.3)') ' LAT = ', LAT * DPR() WRITE (*,'(A,F16.3)') ' LON = ', LON * DPR() C C Compute the illumination angles at this C point. C CALL ILLUMF ( METHOD(J), 'PHOEBE', 'SUN', . ET, 'IAU_PHOEBE', 'LT+S', . 'CASSINI', POINT, TRGEPC, . SRFVEC, PHASE, SOLAR, . EMISSN, VISIBL, LIT ) WRITE (*,'(A,F16.3)') ' Phase angle (degrees):' . // ' ', PHASE * DPR() WRITE (*,'(A,F16.3)') ' Solar incidence angle ' . // '(degrees): ', SOLAR * DPR() WRITE (*,'(A,F16.3)') ' Emission angle (degree' . // 's): ', EMISSN* DPR() WRITE (*,'(A,L2)' ) ' Observer visible: ', VISIBL WRITE (*,'(A,L2)' ) ' Sun visible: ', LIT IF ( I .EQ. 5 ) THEN C C Compute local time corresponding to the TDB C light time corrected epoch at the boresight C intercept. C CALL ET2LST ( TRGEPC, . PHOEID, . LON, . 'PLANETOCENTRIC', . HR, . MN, . SC, . TIME, . AMPM ) WRITE (*,*) ' ' WRITE (*,*) ' Local Solar Time at boresight ' . // 'intercept (24 Hour Clock): ' WRITE (*,*) ' ', TIME END IF END IF WRITE (*,*) ' ' END DO C C End of shape model loop. C END DO C C End of vector loop. C END Solution Sample Output
Input UTC Time: 2004 jun 11 19:32:00 Converting UTC Time: 2004 jun 11 19:32:00 ET seconds past J2000: 140254384.185 Vector: Boundary Corner 1 Target shape model: Ellipsoid Position vector of surface intercept in the IAU_PHOEBE frame (km): X = 91.026 Y = 67.190 Z = 2.030 Planetocentric coordinates of the intercept (degrees): LAT = 1.028 LON = 36.432 Phase angle (degrees): 28.110 Solar incidence angle (degrees): 16.121 Emission angle (degrees): 14.627 Observer visible: T Sun visible: T Target shape model: DSK/Unprioritized Position vector of surface intercept in the IAU_PHOEBE frame (km): X = 78.770 Y = 61.570 Z = 0.964 Planetocentric coordinates of the intercept (degrees): LAT = 0.552 LON = 38.013 Phase angle (degrees): 28.110 Solar incidence angle (degrees): 31.132 Emission angle (degrees): 16.539 Observer visible: T Sun visible: T Vector: Boundary Corner 2 Target shape model: Ellipsoid Position vector of surface intercept in the IAU_PHOEBE frame (km): X = 89.991 Y = 66.726 Z = 14.733 Planetocentric coordinates of the intercept (degrees): LAT = 7.492 LON = 36.556 Phase angle (degrees): 27.894 Solar incidence angle (degrees): 22.894 Emission angle (degrees): 14.988 Observer visible: T Sun visible: T Target shape model: DSK/Unprioritized Position vector of surface intercept in the IAU_PHOEBE frame (km): X = 76.586 Y = 60.579 Z = 13.657 Planetocentric coordinates of the intercept (degrees): LAT = 7.962 LON = 38.344 Phase angle (degrees): 27.894 Solar incidence angle (degrees): 32.013 Emission angle (degrees): 11.845 Observer visible: T Sun visible: T Vector: Boundary Corner 3 Target shape model: Ellipsoid Position vector of surface intercept in the IAU_PHOEBE frame (km): X = 80.963 Y = 76.643 Z = 14.427 Planetocentric coordinates of the intercept (degrees): LAT = 7.373 LON = 43.430 Phase angle (degrees): 28.171 Solar incidence angle (degrees): 21.315 Emission angle (degrees): 21.977 Observer visible: T Sun visible: T Target shape model: DSK/Unprioritized Position vector of surface intercept in the IAU_PHOEBE frame (km): X = 68.677 Y = 71.100 Z = 13.444 Planetocentric coordinates of the intercept (degrees): LAT = 7.745 LON = 45.993 Phase angle (degrees): 28.171 Solar incidence angle (degrees): 36.039 Emission angle (degrees): 14.474 Observer visible: T Sun visible: T Vector: Boundary Corner 4 Target shape model: Ellipsoid Position vector of surface intercept in the IAU_PHOEBE frame (km): X = 81.997 Y = 77.106 Z = 1.698 Planetocentric coordinates of the intercept (degrees): LAT = 0.865 LON = 43.239 Phase angle (degrees): 28.385 Solar incidence angle (degrees): 13.882 Emission angle (degrees): 21.763 Observer visible: T Sun visible: T Target shape model: DSK/Unprioritized Position vector of surface intercept in the IAU_PHOEBE frame (km): X = 73.186 Y = 73.131 Z = 0.934 Planetocentric coordinates of the intercept (degrees): LAT = 0.517 LON = 44.978 Phase angle (degrees): 28.385 Solar incidence angle (degrees): 41.268 Emission angle (degrees): 17.493 Observer visible: T Sun visible: T Vector: Cassini NAC Boresight Target shape model: Ellipsoid Position vector of surface intercept in the IAU_PHOEBE frame (km): X = 86.390 Y = 72.089 Z = 8.255 Planetocentric coordinates of the intercept (degrees): LAT = 4.196 LON = 39.844 Phase angle (degrees): 28.139 Solar incidence angle (degrees): 18.247 Emission angle (degrees): 17.858 Observer visible: T Sun visible: T Local Solar Time at boresight intercept (24 Hour Clock): 11:31:50 Target shape model: DSK/Unprioritized Position vector of surface intercept in the IAU_PHOEBE frame (km): X = 74.326 Y = 66.602 Z = 7.247 Planetocentric coordinates of the intercept (degrees): LAT = 4.153 LON = 41.863 Phase angle (degrees): 28.139 Solar incidence angle (degrees): 33.200 Emission angle (degrees): 9.230 Observer visible: T Sun visible: T Local Solar Time at boresight intercept (24 Hour Clock): 11:39:55 Extra Credit
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