Remote Sensing Hands-On Lesson, using MPO (MATLAB) |
Table of ContentsRemote Sensing Hands-On Lesson, using MPO (MATLAB) Overview Note About HTML Links References Tutorials Required Readings The Permuted Index Mice API Documentation Kernels Used Mice 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 MPO (MATLAB)
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 ``mice/'' 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 ``mice/exe'' of Toolkit installation tree. Tutorials
Name Lesson steps/functions 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/functions 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 mice.req The Mice API The Permuted Index
This text document provides a simple mechanism by which users can discover which Mice functions perform functions of interest, as well as the names of the source files that contain these functions.
Mice API Documentation
For example, the document
mice/doc/html/mice/cspice_str2et.htmldescribes the cspice_str2et routine. Kernels Used
1. Generic LSK: naif0012.tls 2. BepiColombo MPO SCLK: bc_mpo_step_20230117.tsc 3. Solar System Ephemeris SPK, subsetted to cover only the time range of interest: de432s.bsp 4. BepiColombo MPO Spacecraft Trajectory SPK, subsetted to cover only the time range of interest: bc_mpo_mlt_50037_20260314_20280529_v05.bsp 5. BepiColombo MPO FK: bc_mpo_v32.tf 6. BepiColombo MPO Spacecraft CK, subsetted to cover only the time range of interest: bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc 7. Generic PCK: pck00011.tpc 8. Low-resolution Mercury DSK: mercury_lowres.bds 9. SIMBIO-SYS IK: bc_mpo_simbio-sys_v08.tiThese 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 -- --------------- ---- --------------------------------------------- 10 jup365_2027.bsp SPK Generic Jovian Satellite Ephemeris SPKThese SPICE kernels are available from the NAIF server at JPL, in the ``satellites/a_old_versions'' subdurectory:
https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/ Mice Modules Used
CHAPTER EXERCISE FUNCTIONS NON-VOID KERNELS ------- --------- ------------- ------------- ---------- 1 convtm cspice_furnsh cspice_str2et 1,2 cspice_unload cspice_etcal cspice_timout cspice_sce2s extra (*) cspice_unitim 1,2 cspice_sct2e cspice_et2utc cspice_scs2e 2 getsta cspice_furnsh cspice_str2et 1,3,4 cspice_kclear cspice_spkezr cspice_spkpos cspice_convrt extra (*) cspice_unload cspice_vnorm 1,4,10 3 xform cspice_furnsh cspice_str2et 1-7 cspice_kclear cspice_spkezr cspice_sxform cspice_spkpos cspice_pxform cspice_convrt cspice_vsep extra (*) cspice_unload 1-7 4 subpts cspice_furnsh cspice_str2et 1,3-4,7,8 cspice_kclear cspice_subpnt cspice_subslr extra (*) cspice_reclat 1,3-4,7,10 cspice_dpr cspice_bodvrd cspice_recpgr 5 fovint cspice_furnsh cspice_str2et 1-9 cspice_unload cspice_getfvn cspice_bodn2c cspice_sincpt cspice_reclat cspice_dpr cspice_illumf cspice_et2lst (*) Additional APIs and kernels used in Extra Credit tasks.Refer to the Mice HTML API documentation pages located under ``mice/doc/html/mice'' for detailed interface specifications of these functions. Time Conversion (convtm)Task Statement
Learning Goals
Approach
When completing the ``calendar format'' step above, consider using one of two possible methods: cspice_etcal or cspice_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: 1. Generic LSK: naif0012.tls 2. BepiColombo MPO SCLK: bc_mpo_step_20230117.tsc \begindata KERNELS_TO_LOAD = ( 'kernels/lsk/naif0012.tls', 'kernels/sclk/bc_mpo_step_20230117.tsc' ) \begintext Solution Source Code
% % Remote sensing lesson: Time conversion % function convtm() % % Local parameters % METAKR = 'convtm.tm'; SCLKID = -121; % % Load the kernels this program requires. % Both the spacecraft clock kernel and a % leapseconds kernel should be listed in % the meta-kernel. % cspice_furnsh ( METAKR ); % % Prompt the user for the input time string. % utctim = input ( 'Input UTC Time: ', 's' ); fprintf ( 'Converting UTC Time: %s\n', utctim ) % % Convert utctim to et. % et = cspice_str2et ( utctim ); fprintf ( ' ET Seconds Past J2000: %16.3f\n', et ) % % Now convert ET to a formal calendar time % string. This can be accomplished in two % ways. % calet = cspice_etcal ( et ); fprintf ( ' Calendar ET (cspice_etcal): %s\n', calet ) % % Or use cspice_timout for finer control over the % output format. The picture below was built % by examining the header of cspice_timout. % calet = cspice_timout ( et, 'YYYY-MON-DDTHR:MN:SC ::TDB' ); fprintf ( ' Calendar ET (cspice_timout): %s\n', calet ) % % Convert ET to spacecraft clock time. % sclkst = cspice_sce2s ( SCLKID, et ); fprintf ( ' Spacecraft Clock Time: %s\n', sclkst ) % % Unload kernels we loaded at the start of the function. % cspice_unload ( METAKR ); % % End of function convtm % Solution Sample Output
Input UTC Time: 2027 JAN 05 02:04:36 Converting UTC Time: 2027 JAN 05 02:04:36 ET Seconds Past J2000: 852386745.184 Calendar ET (cspice_etcal): 2027 JAN 05 02:05:45.184 Calendar ET (cspice_timout): 2027-JAN-05T02:05:45 Spacecraft Clock Time: 1/0863834674:28127 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: 2461410.5873285
Error using mice SPICE(NOLEAPSECONDS): [str2et_c->STR2ET->TTRANS] The variable that points to the leapseconds (DELTET/DELTA_AT) could not be located in the kernel pool. It is likely that the leapseconds kernel has not been loaded. (CSPICE_N0067) Error in cspice_str2et (line 710) [et] = mice('str2et_c', timstr); Error in convtm (line 32) et = cspice_str2et ( utctim );
Error using mice SPICE(KERNELVARNOTFOUND): [sce2s_c->SCE2S->SCE2T->SCTYPE->SCTY01] Kernel variable SCLK_DATA_TYPE_121 was not found in the kernel pool. (CSPICE_N0067) Error in cspice_sce2s (line 303) [sclkch] = mice('sce2s_c',sc, et); Error in convtm (line 61) sclkst = cspice_sce2s ( SCLKID, et );
Earliest UTC convertible to SCLK: 1999-08-22T00:00:05.204
Spacecraft Clock Time: 1/0863834674:28127 UTC time from spacecraft clock: 2027-01-05T02:04:36.000 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 ``mice/exe'' directory for MATLAB toolkits. Consult its user's guide available in ``mice/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: 1. Generic LSK: naif0012.tls 2. Solar System Ephemeris SPK, subsetted to cover only the time range of interest: de432s.bsp 3. BepiColombo MPO Spacecraft Trajectory SPK, subsetted to cover only the time range of interest: bc_mpo_mlt_50037_20260314_20280529_v05.bsp \begindata KERNELS_TO_LOAD = ( 'kernels/lsk/naif0012.tls', 'kernels/spk/de432s.bsp', 'kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp', ) \begintext Solution Source Code
% % Remote sensing lesson: State vector lookup % function getsta() % % Local parameters % METAKR = 'getsta.tm'; % % Load the kernels that this program requires. We % will need a leapseconds kernel to convert input % UTC time strings into ET. We also will need % SPK files with coverage for the bodies % in which we are interested. % cspice_furnsh ( METAKR ); % % Prompt the user for the input time string. % utctim = input ( 'Input UTC Time: ', 's' ); fprintf ( 'Converting UTC Time: %s\n', utctim ) % % Convert utctim to ET. % et = cspice_str2et ( utctim ); fprintf ( ' ET seconds past J2000: %16.3f\n', et ) % % Compute the apparent state of Mercury as seen from % BepiColombo MPO in the J2000 frame. All of the ephemeris % readers return states in units of kilometers and % kilometers per second. % [state, ltime] = cspice_spkezr ( 'MERCURY', et, ... 'J2000', 'LT+S', 'MPO' ); fprintf ( [ ' Apparent state of Mercury as seen ', ... 'from BepiColombo MPO in the\n' , ... ' J2000 frame (km, km/s):\n'] ) fprintf ( ' X = %16.3f\n', state(1) ) fprintf ( ' Y = %16.3f\n', state(2) ) fprintf ( ' Z = %16.3f\n', state(3) ) fprintf ( ' VX = %16.3f\n', state(4) ) fprintf ( ' VY = %16.3f\n', state(5) ) fprintf ( ' VZ = %16.3f\n', state(6) ) % % Compute the apparent position of Earth as seen from % BepiColombo MPO in the J2000 frame. Note: We could have % continued using cspice_spkezr and simply ignored the % velocity components. % [pos, ltime] = cspice_spkpos ( 'EARTH', et, ... 'J2000', 'LT+S', 'MPO' ); fprintf ( [ ' Apparent position of Earth as seen ', ... 'from BepiColombo MPO in the\n', ... ' J2000 frame (km):\n' ] ) fprintf ( ' X = %16.3f\n', pos(1) ) fprintf ( ' Y = %16.3f\n', pos(2) ) fprintf ( ' Z = %16.3f\n', pos(3) ) % % Display the light time from target to observer. % fprintf ( [ ' One way light time between BepiColombo ', ... 'MPO and the apparent\n', ... ' position of Earth (seconds): ' ... '%16.3f\n' ], ltime ) % % Compute the apparent position of the Sun as seen % from Mercury in the J2000 frame. % [pos, ltime] = cspice_spkpos ( 'SUN', et, ... 'J2000', 'LT+S', 'MERCURY' ); fprintf ( [ ' Apparent position of Sun as seen ', ... 'from Mercury in the \n', ... ' J2000 frame (km):\n' ] ) fprintf ( ' X = %16.3f\n', pos(1) ) fprintf ( ' Y = %16.3f\n', pos(2) ) fprintf ( ' Z = %16.3f\n', pos(3) ) % % Now we need to compute the actual distance between % the Sun and Mercury. The above SPKPOS call gives us % the apparent distance, so we need to adjust our % aberration correction appropriately. % [pos, ltime] = cspice_spkpos ( 'SUN', et, ... 'J2000', 'NONE', 'MERCURY' ); % % Compute the distance between the body centers in % kilometers. % dist = norm ( pos ); % % Convert this value to AU using cspice_convrt. % dist_au = cspice_convrt ( dist, 'KM', 'AU' ); fprintf ( [ ' Actual distance between Sun and Mercury ' ... 'body centers:\n' ] ) fprintf ( ' (AU): %16.3f\n', dist_au ) % % Unload all kernels. % cspice_kclear; % % End of function getsta % Solution Sample Output
Input UTC Time: 2027 JAN 05 02:04:36 Converting UTC Time: 2027 JAN 05 02:04:36 ET seconds past J2000: 852386745.184 Apparent state of Mercury as seen from BepiColombo MPO in the J2000 frame (km, km/s): X = -683.207 Y = -1438.946 Z = -2427.819 VX = 0.036 VY = 2.360 VZ = -1.783 Apparent position of Earth as seen from BepiColombo MPO in the J2000 frame (km): X = -59257854.691 Y = 185201786.218 Z = 88178321.179 One way light time between BepiColombo MPO and the apparent position of Earth (seconds): 712.193 Apparent position of Sun as seen from Mercury in the J2000 frame (km): X = -23429947.239 Y = 54297427.572 Z = 31434173.468 Actual distance between Sun and Mercury body centers: (AU): 0.448 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
Error using mice SPICE(SPKINSUFFDATA): [spkezr_c->SPKEZR->SPKEZ->SPKACS->SPKGEO] Insufficient ephemeris data has been loaded to compute the state of -121 (BEPICOLOMBO MPO) relative to 0 (SOLAR SYSTEM BARYCENTER) at the ephemeris epoch 2027 JAN 05 02:05:45.184. (CSPICE_N0067) Error in cspice_spkezr (line 660) [starg_s] = mice('spkezr_s',targ,et,ref,abcorr,obs); Error in getsta (line 42) [state, ltime] = cspice_spkezr ( 'MERCURY', et, ...
BRIEF -- Version 4.1.0, September 17, 2021 -- Toolkit Version N0067 Summary for: kernels/spk/de432s.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) Start of Interval (UTC) End of Interval (UTC) ----------------------------- ------------------------- ---- 2027-JAN-02 23:01:53.350 2027-JAN-08 00:59:37.932 Summary for: kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp Body: BEPICOLOMBO MPO (-121) w.r.t. MERCURY (199) Start of Interval (UTC) End of Interval (UTC) ----------------------------- --------------------------- -- 2027-JAN-02 23:01:53.350 2027-JAN-08 00:59:37.932 Bodies: -121000 w.r.t. BEPICOLOMBO MPO (-121) -121540 w.r.t. BEPICOLOMBO MPO (-121) -121600 w.r.t. BEPICOLOMBO MPO (-121) Start of Interval (UTC) End of Interval (UTC) ----------------------------- ------------------------- ---- 2027-JAN-02 23:01:53.350 2027-JAN-08 00:59:37.932
Additional kernels required for this task: 1. Generic Jovian Satellite Ephemeris SPK: jup365_2027.bsp available in the NAIF server at: https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/ satellites/a_old_versions
Actual position of Jupiter as seen from Mercury in the J2000 frame (km): X = -623644094.418 Y = 532767093.112 Z = 251130102.035
Actual (geometric) position of Sun as seen from Mercury in the J2000 frame (km): X = -23438490.402 Y = 54294213.485 Z = 31433347.025 Light-time corrected position of Sun as seen from Mercury in the J2000 frame (km): X = -23438492.550 Y = 54294212.272 Z = 31433346.550 Apparent position of Sun as seen from Mercury in the J2000 frame (km): X = -23430052.903 Y = 54297381.156 Z = 31434164.775 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: 1. Generic LSK: naif0012.tls 2. BepiColombo MPO SCLK: bc_mpo_step_20230117.tsc 3. Solar System Ephemeris SPK, subsetted to cover only the time range of interest: de432s.bsp 4. BepiColombo MPO Spacecraft Trajectory SPK, subsetted to cover only the time range of interest: bc_mpo_mlt_50037_20260314_20280529_v05.bsp 5. BepiColombo MPO FK: bc_mpo_v32.tf 6. BepiColombo MPO Spacecraft CK, subsetted to cover only the time range of interest: bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc 7. Generic PCK: pck00011.tpc \begindata KERNELS_TO_LOAD = ( 'kernels/lsk/naif0012.tls', 'kernels/sclk/bc_mpo_step_20230117.tsc', 'kernels/spk/de432s.bsp', 'kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp', 'kernels/fk/bc_mpo_v32.tf', 'kernels/ck/bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc', 'kernels/pck/pck00011.tpc' ) \begintext Solution Source Code
% % Remote sensing lesson: Spacecraft Orientation and Reference Frames % function xform() % % Local Parameters % METAKR = 'xform.tm'; % % Load the kernels that this program requires. We % will need: % % A leapseconds kernel % A spacecraft clock kernel for BepiColombo MPO % The necessary ephemerides % A planetary constants file (PCK) % A spacecraft orientation kernel for BepiColombo MPO (CK) % A frame kernel (TF) % cspice_furnsh ( METAKR ); % % Prompt the user for the input time string. % utctim = input ( 'Input UTC Time: ', 's' ); fprintf ( 'Converting UTC Time: %s\n', utctim ) % % Convert utctim to ET. % et = cspice_str2et ( utctim ); fprintf ( ' ET seconds past J2000: %16.3f\n', et ) % % Compute the apparent state of Mercury as seen from % BepiColombo MPO in the J2000 frame. All of the ephemeris % readers return states in units of kilometers and % kilometers per second. % [state, ltime] = cspice_spkezr ( 'MERCURY', et, ... 'J2000', 'LT+S', 'MPO' ); % % Now obtain the transformation from the inertial % J2000 frame to the non-inertial body-fixed IAU_MERCURY % frame. Since we want the apparent state in the % (body-fixed) IAU_MERCURY reference frame, we % need to correct the orientation of this frame for % one-way light time; hence we subtract ltime from et % in the call below. % sxfmat = cspice_sxform ( 'J2000', 'IAU_MERCURY', et-ltime ); % % Now rotate the apparent J2000 state into IAU_MERCURY % with the following matrix multiplication: % bfixst = sxfmat * state; % % Display the results. % fprintf ( [ ' Apparent state of Mercury as seen ', ... 'from BepiColombo MPO in the\n', ... ' IAU_MERCURY body-fixed frame (km, km/s):\n' ] ) fprintf ( ' X = %19.6f\n', bfixst(1) ) fprintf ( ' Y = %19.6f\n', bfixst(2) ) fprintf ( ' Z = %19.6f\n', bfixst(3) ) fprintf ( ' VX = %19.6f\n', bfixst(4) ) fprintf ( ' VY = %19.6f\n', bfixst(5) ) fprintf ( ' VZ = %19.6f\n', bfixst(6) ) % % It is worth pointing out, all of the above could % have been done with a single use of cspice_spkezr: % % [state, ltime] = cspice_spkezr ( 'MERCURY', et, ... 'IAU_MERCURY', 'LT+S', ... 'MPO' ); % % Display the results. % fprintf ( [ ' Apparent state of Mercury as seen ', ... 'from BepiColombo MPO in the\n', ... ' IAU_MERCURY body-fixed frame ', ... '(km, km/s) obtained using\n', ... ' cspice_spkezr directly:\n' ] ) fprintf ( ' X = %19.6f\n', state(1) ) fprintf ( ' Y = %19.6f\n', state(2) ) fprintf ( ' Z = %19.6f\n', state(3) ) fprintf ( ' VX = %19.6f\n', state(4) ) fprintf ( ' VY = %19.6f\n', state(5) ) fprintf ( ' VZ = %19.6f\n', state(6) ) % % Note that the velocity found by using cspice_spkezr % to compute the state in the IAU_MERCURY frame differs % at the few mm/second level from that found previously % by calling cspice_spkezr and then cspice_sxform. % Computing velocity via a single call to cspice_spkezr % as we've done immediately above is slightly more % accurate than the previous method because the latter % accounts for the effect of the rate of change of light % time on the apparent angular velocity of the target's % body-fixed reference frame. % % Now we are to compute the angular separation between % the apparent position of Mercury as seen from the orbiter % and the nominal instrument view direction. First, % compute the apparent position of Mercury as seen from % BepiColombo MPO in the J2000 frame. % [pos, ltime] = cspice_spkpos ( 'MERCURY', et, ... 'J2000', 'LT+S', 'MPO' ); % % Now compute the location of the nominal instrument view % direction. From reading the frame kernel we know that % the instrument view direction is nominally the +Z axis % of the MPO_SPACECRAFT frame defined there. % bsight = [ 0.D0; 0.D0; 1.D0 ]; % % Now compute the rotation matrix from MPO_SPACECRAFT into % J2000. % pform = cspice_pxform ( 'MPO_SPACECRAFT', 'J2000', et ); % % And multiply the result to obtain the nominal instrument % view direction in the J2000 reference frame. % bsight = pform * bsight; % % Lastly compute the angular separation. % sep = cspice_convrt ( cspice_vsep(bsight, pos), ... 'RADIANS', 'DEGREES' ); fprintf ( [ ' Angular separation between the ', ... 'apparent position of Mercury and\n', ... ' the BepiColombo MPO nominal instrument ' ... 'view direction\n' ... ' (degrees):\n' ... ' %16.3f\n' ], ... sep ) % % Or alternatively we can work in the spacecraft % frame directly. % [pos, ltime] = cspice_spkpos ( 'MERCURY', et, 'MPO_SPACECRAFT', ... 'LT+S', 'MPO' ); % % The nominal instrument view direction is the +Z-axis % in the MPO_SPACECRAFT frame. % bsight = [ 0.D0; 0.D0; 1.D0 ]; % % Lastly compute the angular separation. % sep = cspice_convrt ( cspice_vsep(bsight, pos), ... 'RADIANS', 'DEGREES' ); fprintf ( [ ' Angular separation between the ', ... 'apparent position of Mercury and\n' ... ' the BepiColombo MPO nominal instrument ' ... 'view direction computed\n' ... ' using vectors in the ' ... 'MPO_SPACECRAFT frame (degrees):\n' ... ' %16.3f\n' ], ... sep ) % % Unload all kernels. % cspice_kclear; % % End of function xform % Solution Sample Output
Input UTC Time: 2027 JAN 05 02:04:36 Converting UTC Time: 2027 JAN 05 02:04:36 ET seconds past J2000: 852386745.184 Apparent state of Mercury as seen from BepiColombo MPO in the IAU_MERCURY body-fixed frame (km, km/s): X = -2354.697620 Y = -762.547549 Z = -1518.408470 VX = 1.208589 VY = 0.394259 VZ = -2.671125 Apparent state of Mercury as seen from BepiColombo MPO in the IAU_MERCURY body-fixed frame (km, km/s) obtained using cspice_spkezr directly: X = -2354.697620 Y = -762.547549 Z = -1518.408470 VX = 1.208589 VY = 0.394259 VZ = -2.671125 Angular separation between the apparent position of Mercury and the BepiColombo MPO nominal instrument view direction (degrees): 0.009 Angular separation between the apparent position of Mercury and the BepiColombo MPO nominal instrument view direction computed using vectors in the MPO_SPACECRAFT frame (degrees): 0.009 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
Error using mice SPICE(NOFRAMECONNECT): [pxform_c->PXFORM->REFCHG] At epoch 8.5252159418408E+08 TDB (2027 JAN 06 15:33:14.184 TDB), there is insufficient information available to transform from reference frame -121000 (MPO_SPACECRAFT) to reference frame 1 (J2000). MPO_SPACECRAFT is a CK frame; a CK file containing data for instrument or structure -121000 at the epoch shown above, as well as a corresponding SCLK kernel, must be loaded in order to use this frame. Failure to find required CK data could be due to one or more CK files not having been loaded, or to the epoch shown above lying within 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 for the input epoch, even if a loaded CK does have attitude data for that epoch. You can use CKBRIEF with the -dump option to display coverage intervals of a CK file. (CSPICE_N0067) Error in cspice_pxform (line 357) [rotate] = mice('pxform_c',from,to,et); Error in xform (line 137) pform = cspice_pxform ( 'MPO_SPACECRAFT', 'J2000', et );
CKBRIEF -- Version 6.1.0, June 27, 2014 -- Toolkit Version N0067 Summary for: kernels/ck/bc_mpo_sc_slt_50028_20260314_20280529_f201811 27_v03.bc Segment No.: 1 Object: -121000 Interval Begin UTC Interval End UTC AV ------------------------ ------------------------ --- 2027-JAN-02 23:01:53.350 2027-JAN-06 11:04:56.368 Y 2027-JAN-06 11:08:00.779 2027-JAN-06 15:30:56.685 Y 2027-JAN-06 15:33:04.016 2027-JAN-06 22:05:57.865 Y 2027-JAN-06 22:10:03.746 2027-JAN-08 00:59:37.932 Y
CKBRIEF -- Version 6.1.0, June 27, 2014 -- Toolkit Version N0067 Summary for: kernels/ck/bc_mpo_sc_slt_50028_20260314_20280529_f201811 27_v03.bc Object: -121000 Interval Begin UTC Interval End UTC AV ------------------------ ------------------------ --- 2027-JAN-02 23:01:53.350 2027-JAN-08 00:59:37.932 Y
Angular separation between the apparent position of the Sun and the BepiColombo MPO nominal instrument view direction (degrees): 135.393 Science Deck illumination: BepiColombo MPO Science Deck IS NOT 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 "2027 JAN 05 02:04:36" 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-s/c and Sub-solar Points on an Ellipsoid and a DSK'' task in the Remote Sensing Hands On Lesson. The names and contents of the kernels referenced by this meta-kernel are as follows: 1. Generic LSK: naif0012.tls 2. Solar System Ephemeris SPK, subsetted to cover only the time range of interest: de432s.bsp 3. BepiColombo MPO Spacecraft Trajectory SPK, subsetted to cover only the time range of interest: bc_mpo_mlt_50037_20260314_20280529_v05.bsp 4. Generic PCK: pck00011.tpc 5. Low-resolution Mercury DSK: mercury_lowres.bds \begindata KERNELS_TO_LOAD = ( 'kernels/lsk/naif0012.tls', 'kernels/spk/de432s.bsp', 'kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp', 'kernels/pck/pck00011.tpc' 'kernels/dsk/mercury_lowres.bds' ) \begintext Solution Source Code
% % Remote sensing lesson: Computing Sub-s/c and Sub-solar % Points on an Ellipsoid and a DSK % function subpts() % % Local parameters % METAKR = 'subpts.tm'; % % Load the kernels that this program requires. We % will need: % % A leapseconds kernel % The necessary ephemerides % A planetary constants file (PCK) % A DSK file containing Mercury shape data % cspice_furnsh ( METAKR ); % % Prompt the user for the input time string. % utctim = input ( 'Input UTC Time: ', 's' ); fprintf ( 'Converting UTC Time: %s\n', utctim ) % % Convert utctim to ET. % et = cspice_str2et ( utctim ); fprintf ( ' ET seconds past J2000: %16.3f\n', et ) for mi = 1:2 if mi == 1 % % Use the "near point" sub-point definition % and an ellipsoidal model. % method = 'NEAR POINT/Ellipsoid'; else % % Use the "nadir" sub-point definition % and a DSK model. % method = 'NADIR/DSK/Unprioritized'; end fprintf ( '\n Sub-point/target shape model: %s\n\n', ... method ) % % Compute the apparent sub-observer point of BepiColombo MPO % on Mercury. % [spoint, trgepc, srfvec ] = ... cspice_subpnt ( method, 'MERCURY', et, ... 'IAU_MERCURY', 'LT+S', 'MPO' ); fprintf ( [ ' Apparent sub-observer point of ', ... 'BepiColombo MPO on Mercury \n', ... ' in the IAU_MERCURY frame (km):\n' ] ) fprintf ( ' X = %16.3f\n', spoint(1) ) fprintf ( ' Y = %16.3f\n', spoint(2) ) fprintf ( ' Z = %16.3f\n', spoint(3) ) fprintf ( ' ALT = %16.3f\n', norm(srfvec) ) % % Compute the apparent sub-solar point on Mercury % as seen from BepiColombo MPO. % [spoint, trgepc, srfvec ] = ... cspice_subslr ( method, 'MERCURY', et, ... 'IAU_MERCURY', 'LT+S', 'MPO' ); fprintf ( [ ' Apparent sub-solar point ', ... 'on Mercury as seen from BepiColombo\n', ... ' MPO in the IAU_MERCURY frame (km):\n' ] ) fprintf ( ' X = %16.3f\n', spoint(1) ) fprintf ( ' Y = %16.3f\n', spoint(2) ) fprintf ( ' Z = %16.3f\n', spoint(3) ) end fprintf( '\n' ) % % Unload all kernels. % cspice_kclear; % % End of function subpts % Solution Sample Output
Input UTC Time: 2027 JAN 05 02:04:36 Converting UTC Time: 2027 JAN 05 02:04:36 ET seconds past J2000: 852386745.184 Sub-point/target shape model: NEAR POINT/Ellipsoid Apparent sub-observer point of BepiColombo MPO on Mercury in the IAU_MERCURY frame (km): X = 1978.726 Y = 640.793 Z = 1275.611 ALT = 463.634 Apparent sub-solar point on Mercury as seen from BepiColombo MPO in the IAU_MERCURY frame (km): X = 1526.831 Y = 1903.936 Z = -1.436 Sub-point/target shape model: NADIR/DSK/Unprioritized Apparent sub-observer point of BepiColombo MPO on Mercury in the IAU_MERCURY frame (km): X = 1979.558 Y = 641.062 Z = 1276.148 ALT = 462.608 Apparent sub-solar point on Mercury as seen from BepiColombo MPO in the IAU_MERCURY frame (km): X = 1525.673 Y = 1902.492 Z = -1.434 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 Mercury as seen from BepiColombo MPO in the IAU_MERCURY frame using the 'Near Point: ellipsoid' method (km): X = 1526.828 Y = 1903.939 Z = -1.435 Apparent sub-solar point on Mercury as seen from BepiColombo MPO in the IAU_MERCURY frame using the 'Intercept: ellipsoid' method (km): X = 1526.828 Y = 1903.939 Z = -1.438
Additional kernels required for this task: 1. Generic Jovian Satellite Ephemeris SPK: jup365_2027.bsp available in the NAIF server at: https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/ satellites/a_old_versions
Geometric sub-spacecraft point of BepiColombo MPO on Europa in the IAU_EUROPA frame using the 'Near Point: ellipsoid' method (km): X = -753.484 Y = -1366.703 Z = -24.296
Planetocentric coordinates of the BepiColombo MPO sub-spacecraft point on Europa (degrees, km): LAT = -0.892 LON = -118.869 R = 1560.835 Planetographic coordinates of the BepiColombo MPO sub-spacecraft point on Europa (degrees, km): LAT = -0.895 LON = 118.869 ALT = -1.764
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 spectrometer aperture boresight with the surface of Mercury, using both ellipsoidal and DSK shape models. Use this program to compute values at the UTC epoch:
Learning Goals
Approach
SolutionSolution Meta-Kernel
KPL/MK This is the meta-kernel used in the solution of the ``Intersecting Vectors with an Ellipsoid and a DSK'' task in the Remote Sensing Hands On Lesson. The names and contents of the kernels referenced by this meta-kernel are as follows: 1. Generic LSK: naif0012.tls 2. BepiColombo MPO SCLK: bc_mpo_step_20230117.tsc 3. Solar System Ephemeris SPK, subsetted to cover only the time range of interest: de432s.bsp 4. BepiColombo MPO Spacecraft Trajectory SPK, subsetted to cover only the time range of interest: bc_mpo_mlt_50037_20260314_20280529_v05.bsp 5. BepiColombo MPO FK: bc_mpo_v32.tf 6. BepiColombo MPO Spacecraft CK, subsetted to cover only the time range of interest: bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc 7. Generic PCK: pck00011.tpc 8. SIMBIO-SYS IK: bc_mpo_simbio-sys_v08.ti 9. Low-resolution Mercury DSK: mercury_lowres.bds \begindata KERNELS_TO_LOAD = ( 'kernels/lsk/naif0012.tls', 'kernels/sclk/bc_mpo_step_20230117.tsc', 'kernels/spk/de432s.bsp', 'kernels/spk/bc_mpo_mlt_50037_20260314_20280529_v05.bsp', 'kernels/fk/bc_mpo_v32.tf', 'kernels/ck/bc_mpo_sc_slt_50028_20260314_20280529_f20181127_v03.bc', 'kernels/pck/pck00011.tpc', 'kernels/ik/bc_mpo_simbio-sys_v08.ti' 'kernels/dsk/mercury_lowres.bds' ) \begintext Solution Source Code
% % Remote sensing lesson: Intersecting Vectors % with an Ellipsoid and a DSK % function fovint() % % Local Parameters % METAKR = 'fovint.tm'; % % BCVLEN is the maximum number of boundary corner % vectors we can retrieve. We've extended this array by 1 % element to make room for the boresight vector. % BCVLEN = 5; % % Use strings to represent boolean values: % boolstr = { 'false', 'true' }; % % We use a cell array to store our vector names, which % have unequal lengths. % vecnam = { 'Boundary Corner 1', 'Boundary Corner 2', 'Boundary Corner 3', 'Boundary Corner 4', 'MPO SIMBIO-SYS HRIC Boresight' }; % % Load the kernels that this program requires. We will need: % % A leapseconds kernel. % A SCLK kernel for BepiColombo MPO. % Any necessary ephemerides. % The BepiColombo MPO frame kernel. % An BepiColombo MPO C-kernel. % A PCK file with Mercury constants. % The BepiColombo MPO SIMBIO-SYS I-kernel. % A DSK file containing Mercury shape data. % cspice_furnsh ( METAKR ); % % Prompt the user for the input time string. % utctim = input ( 'Input UTC Time: ', 's' ); fprintf ( 'Converting UTC Time: %s\n', utctim ) % % Convert utctim to ET. % et = cspice_str2et ( utctim ); fprintf ( ' ET seconds past J2000: %16.3f\n', et ) % % Now we need to obtain the FOV configuration of % the SIMBIO-SYS HRIC channel. % [shape, insfrm, bsight, bounds] = ... cspice_getfvn ( 'MPO_SIMBIO-SYS_HRIC_FPA', BCVLEN ); % % Rather than treat 'bsight' as a separate vector, % copy it and 'bounds' to 'scan_vecs'. % scan_vecs = [ bounds, bsight ]; % % Set values of "method" string that specify use of % ellipsoidal and DSK (topographic) shape models. % % In this case, we can use the same methods for calls to both % cspice_sincpt and cspice_ilumin. Note that some SPICE routines % require different "method" inputs from those shown here. See the % API documentation of each routine for details. % method = { 'Ellipsoid', 'DSK/Unprioritized' }; % % The ID code for MERCURY is built in to the library. % However, it is good programming practice to get % in the habit of checking your found-flags. % [ marsid, found ] = cspice_bodn2c ( 'MERCURY' ); % % Return if the code was not found. % if ~found fprintf ( 'Unable to locate the ID code for Mercury.' ) return end % % Now perform the same set of calculations for each % vector listed in the "bounds" array. Use both % ellipsoidal and detailed (DSK) shape models. % for vi = 1:5 fprintf ( '\nVector: %s\n', vecnam{vi} ) for mi = 1:2 fprintf ( '\n Target shape model: %s\n\n', method{mi} ) % % Call sincpt to determine coordinates of the % intersection of this vector with the surface % of Mercury. % [ point, trgepc, srfvec, found ] = ... cspice_sincpt ( method{mi}, 'MERCURY', et, ... 'IAU_MERCURY', 'LT+S', 'MPO', ... insfrm, scan_vecs(:,vi) ); % % Check the found flag. Display a message if % the point of intersection was not found, % otherwise continue with the calculations. % if ~found fprintf ( 'No intersection point found at this epoch.' ) else % % Now, we have discovered a point of intersection. % Start by displaying the position vector in the % IAU_MERCURY frame of the intersection. % fprintf ( [ ' Position vector of surface intercept ', ... 'in the IAU_MERCURY\n', ... ' frame (km):\n' ] ) fprintf ( ' X = %16.3f\n', point(1) ) fprintf ( ' Y = %16.3f\n', point(2) ) fprintf ( ' Z = %16.3f\n', point(3) ) % % Display the planetocentric latitude and longitude % of the intercept. % [ radius, lon, lat ] = cspice_reclat ( point ); fprintf ( [ ' Planetocentric coordinates of the ', ... 'intercept (degrees):\n' ] ) fprintf ( ' LAT = %16.3f\n', lat * cspice_dpr ) fprintf ( ' LON = %16.3f\n', lon * cspice_dpr ) % % Compute the illumination angles at this point. % [trgepc, srfvec, phase, solar, emissn, visibl, lit] = ... cspice_illumf ( method{mi}, 'MERCURY', 'SUN', ... et, 'IAU_MERCURY', 'LT+S', ... 'MPO', point ); fprintf ( [ ' Phase angle (degrees):', ... ' %14.3f\n' ], ... phase * cspice_dpr ) fprintf ( [ ' Solar incidence angle (degrees):', ... ' %14.3f\n' ], ... solar * cspice_dpr ) fprintf ( [ ' Emission angle (degrees):', ... ' %14.3f\n' ], ... emissn * cspice_dpr ) fprintf ( ' Observer visible: %s\n', ... boolstr{visibl+1} ) fprintf ( ' Sun visible: %s\n', ... boolstr{lit+1} ) if vi == 5 % % Compute local solar time corresponding to the TDB % light time corrected epoch at the boresight % intercept. % [ hr, min, sc, time, ampm ] = ... cspice_et2lst ( trgepc, marsid, ... lon, 'PLANETOCENTRIC' ); fprintf( [ '\n Local Solar Time at boresight', ... ' intercept (24 Hour Clock):\n', ... ' %s\n' ], ... time ) end % % End of LST computation block. % end % % End of shape model loop. % end % % End of vector loop. % end fprintf ( '\n' ); % % Unload kernels we loaded at the start of the function. % cspice_unload ( METAKR ); % % End of function fovint % Solution Sample Output
Input UTC Time: 2027 JAN 05 02:04:36 Converting UTC Time: 2027 JAN 05 02:04:36 ET seconds past J2000: 852386745.184 Vector: Boundary Corner 1 Target shape model: Ellipsoid Position vector of surface intercept in the IAU_MERCURY frame (km): X = 1973.717 Y = 645.436 Z = 1281.009 Planetocentric coordinates of the intercept (degrees): LAT = 31.670 LON = 18.109 Phase angle (degrees): 44.735 Solar incidence angle (degrees): 44.622 Emission angle (degrees): 1.280 Observer visible: true Sun visible: true Target shape model: DSK/Unprioritized Position vector of surface intercept in the IAU_MERCURY frame (km): X = 1974.257 Y = 645.602 Z = 1281.346 Planetocentric coordinates of the intercept (degrees): LAT = 31.670 LON = 18.108 Phase angle (degrees): 44.735 Solar incidence angle (degrees): 46.703 Emission angle (degrees): 4.145 Observer visible: true Sun visible: true Vector: Boundary Corner 2 Target shape model: Ellipsoid Position vector of surface intercept in the IAU_MERCURY frame (km): X = 1979.643 Y = 647.354 Z = 1270.875 Planetocentric coordinates of the intercept (degrees): LAT = 31.391 LON = 18.108 Phase angle (degrees): 45.641 Solar incidence angle (degrees): 44.447 Emission angle (degrees): 1.198 Observer visible: true Sun visible: true Target shape model: DSK/Unprioritized Position vector of surface intercept in the IAU_MERCURY frame (km): X = 1980.449 Y = 647.601 Z = 1271.407 Planetocentric coordinates of the intercept (degrees): LAT = 31.391 LON = 18.108 Phase angle (degrees): 45.641 Solar incidence angle (degrees): 43.796 Emission angle (degrees): 1.894 Observer visible: true Sun visible: true Vector: Boundary Corner 3 Target shape model: Ellipsoid Position vector of surface intercept in the IAU_MERCURY frame (km): X = 1983.307 Y = 636.037 Z = 1270.876 Planetocentric coordinates of the intercept (degrees): LAT = 31.391 LON = 17.781 Phase angle (degrees): 44.501 Solar incidence angle (degrees): 44.666 Emission angle (degrees): 1.195 Observer visible: true Sun visible: true Target shape model: DSK/Unprioritized Position vector of surface intercept in the IAU_MERCURY frame (km): X = 1984.034 Y = 636.285 Z = 1271.361 Planetocentric coordinates of the intercept (degrees): LAT = 31.391 LON = 17.781 Phase angle (degrees): 44.501 Solar incidence angle (degrees): 45.429 Emission angle (degrees): 2.027 Observer visible: true Sun visible: true Vector: Boundary Corner 4 Target shape model: Ellipsoid Position vector of surface intercept in the IAU_MERCURY frame (km): X = 1977.381 Y = 634.119 Z = 1281.010 Planetocentric coordinates of the intercept (degrees): LAT = 31.670 LON = 17.780 Phase angle (degrees): 43.576 Solar incidence angle (degrees): 44.840 Emission angle (degrees): 1.278 Observer visible: true Sun visible: true Target shape model: DSK/Unprioritized Position vector of surface intercept in the IAU_MERCURY frame (km): X = 1978.158 Y = 634.384 Z = 1281.499 Planetocentric coordinates of the intercept (degrees): LAT = 31.670 LON = 17.781 Phase angle (degrees): 43.576 Solar incidence angle (degrees): 45.349 Emission angle (degrees): 1.920 Observer visible: true Sun visible: true Vector: MPO SIMBIO-SYS HRIC Boresight Target shape model: Ellipsoid Position vector of surface intercept in the IAU_MERCURY frame (km): X = 1978.524 Y = 640.740 Z = 1275.950 Planetocentric coordinates of the intercept (degrees): LAT = 31.530 LON = 17.944 Phase angle (degrees): 44.609 Solar incidence angle (degrees): 44.644 Emission angle (degrees): 0.059 Observer visible: true Sun visible: true Local Solar Time at boresight intercept (24 Hour Clock): 09:46:41 Target shape model: DSK/Unprioritized Position vector of surface intercept in the IAU_MERCURY frame (km): X = 1979.357 Y = 641.010 Z = 1276.487 Planetocentric coordinates of the intercept (degrees): LAT = 31.530 LON = 17.944 Phase angle (degrees): 44.609 Solar incidence angle (degrees): 45.349 Emission angle (degrees): 1.138 Observer visible: true Sun visible: true Local Solar Time at boresight intercept (24 Hour Clock): 09:46:41 Extra Credit
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