Remote Sensing Hands-On Lesson, using CASSINI ============================================== November 20, 2017 Overview -------- In this lesson you will develop a series of simple programs that demonstrate the usage of SpiceyPy to compute a variety of different geometric quantities applicable to experiments carried out by a remote sensing instrument flown on an interplanetary spacecraft. This particular lesson focuses on a framing camera flying on the Cassini spacecraft, but many of the concepts are easily extended and generalized to other scenarios. References ---------- This section lists SPICE documents referred to in this lesson. 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 "cspice/exe" of Toolkit installation tree. Tutorials ^^^^^^^^^ The following SPICE tutorials serve as references for the discussions in this lesson: .. code-block:: text 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) Data These tutorials are available from the NAIF ftp server at JPL: https://naif.jpl.nasa.gov/naif/tutorials.html Required Readings ^^^^^^^^^^^^^^^^^ .. tip:: The `Required Readings `_ are also available on the NAIF website at: https://naif.jpl.nasa.gov/pub/naif/misc/toolkit_docs_N0067/C/req/index.html. The Required Reading documents are provided with the Toolkit and are located under the "cspice/doc" directory in the CSPICE Toolkit installation tree. .. code-block:: text 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 The Permuted Index ^^^^^^^^^^^^^^^^^^ .. tip:: The `Permuted Index `_ is also available on the NAIF website at: https://naif.jpl.nasa.gov/pub/naif/misc/toolkit_docs_N0067/C/info/cspice_idx.html. Another useful document distributed with the Toolkit is the permuted index. This is located under the "cspice/doc" directory in the C installation tree. This text document provides a simple mechanism by which users can discover which SpiceyPy functions perform functions of interest, as well as the names of the source files that contain these functions. SpiceyPy API Documentation ^^^^^^^^^^^^^^^^^^^^^^^^^^ A SpiceyPy function's parameters specification is available using the built-in Python help system. For example, the Python help function .. py-editor:: :env: rsenv :config: pyscript_remote_sensing.json :setup: import spiceypy .. py-editor:: :env: rsenv :config: pyscript_remote_sensing.json import spiceypy help(spiceypy.str2et) describes the ``str2et`` function's parameters, while the document https://naif.jpl.nasa.gov/pub/naif/misc/toolkit_docs_N0067/C/cspice/str2et_c.html describes extensively the ``str2et`` functionality. Kernels Used ------------ The following kernels are used in examples provided in this lesson: .. code-block:: text # 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 Kernel These SPICE kernels are included in the lesson package available from the NAIF server at JPL: ftp://naif.jpl.nasa.gov/pub/naif/misc/toolkit_docs_N0067/Lessons/ In addition to these kernels, the extra credit exercises require the following kernels: .. code-block:: text # FILE NAME TYPE DESCRIPTION -- --------------- ---- --------------------------------------------- 11 jup310_2004.bsp SPK Generic Jovian Satellite Ephemeris These SPICE kernels are available from the NAIF server at JPL: https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/satellites/ SpiceyPy Modules Used --------------------- This section provides a complete list of the functions and kernels that are suggested for usage in each of the exercises in this lesson. (You may wish to not look at this list unless/until you "get stuck" while working on your own.) .. code-block:: text CHAPTER EXERCISE FUNCTIONS NON-VOID KERNELS ------- --------- --------------- --------------- ---------- 1 convtm spiceypy.furnsh spiceypy.str2et 1,2 spiceypy.unload spiceypy.etcal spiceypy.timout spiceypy.sce2s extra (*) spiceypy.unitim 1,2 spiceypy.sct2e spiceypy.et2utc spiceypy.scs2e 2 getsta spiceypy.furnsh spiceypy.str2et 1,3-5 spiceypy.unload spiceypy.spkezr spiceypy.spkpos spiceypy.vnorm spiceypy.convrt extra (*) spiceypy.kclear 1,3-5,11 3 xform spiceypy.furnsh spiceypy.str2et 1-8 spiceypy.unload spiceypy.spkezr spiceypy.sxform spiceypy.mxvg spiceypy.spkpos spiceypy.pxform spiceypy.mxv spiceypy.convrt spiceypy.vsep extra (*) spiceypy.kclear 1-8 4 subpts spiceypy.furnsh spiceypy.str2et 1,3-5,8,9 spiceypy.unload spiceypy.subpnt spiceypy.vnorm spiceypy.subslr extra (*) spiceypy.kclear spiceypy.reclat 1,3-5,8 spiceypy.dpr spiceypy.bodvrd spiceypy.recpgr 5 fovint spiceypy.furnsh spiceypy.str2et 1-10 spiceypy.unload spiceypy.bodn2c spiceypy.getfov spiceypy.sincpt spiceypy.reclat spiceypy.dpr spiceypy.illumf spiceypy.et2lst (*) Additional APIs and kernels used in Extra Credit tasks. Use the Python built-in help system on the various functions listed above for the API parameters' description, and refer to the headers of their corresponding CSPICE versions for detailed interface specifications. Time Conversion (convtm) ------------------------ Task Statement ^^^^^^^^^^^^^^ Write a program that prompts the user for an input UTC time string, converts it to the following time systems and output formats: #. Ephemeris Time (ET) in seconds past J2000 #. Calendar Ephemeris Time #. Spacecraft Clock Time and displays the results. Use the program to convert “2004 jun 11 19:32:00” UTC into these alternate systems. Learning Goals ^^^^^^^^^^^^^^ Familiarity with the various time conversion and parsing functions available in the Toolkit. Exposure to source code headers and their usage in learning to call functions. Approach ^^^^^^^^ The solution to the problem can be broken down into a series of simple steps: - Decide which SPICE kernels are necessary. Prepare a meta-kernel listing the kernels and load it into the program. - Prompt the user for an input UTC time string. - Convert the input time string into ephemeris time expressed as seconds past J2000 TDB. Display the result. - Convert ephemeris time into a calendar format. Display the result. - Convert ephemeris time into a spacecraft clock string. Display the result. You may find it useful to consult the permuted index, the headers of various source modules, and the "Time Required Reading" (time.req) and "SCLK Required Reading" (sclk.req) documents. When completing the "calendar format" step above, consider using one of two possible methods: :py:func:`spiceypy.etcal ` or :py:func:`spiceypy.timout `. Solution ^^^^^^^^ **Solution Meta-Kernel** The meta-kernel we created for the solution to this exercise is named 'convtm.tm'. Its contents follow: .. py-editor:: :env: rsenv :config: pyscript_remote_sensing.json :src: scripts/remote_sensing/convtm_make_mk.py **Solution Source Code** A sample solution to the problem follows: .. py-editor:: :env: rsenv :src: scripts/remote_sensing/convtm.py **Solution Sample Output** Execute the program: .. code-block:: text 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 ^^^^^^^^^^^^ In this "extra credit" section you will be presented with more complex tasks, aimed at improving your understanding of time conversions, the Toolkit routines that deal with them, and some common errors that may happen during the execution of these conversions. 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** #. Extend your program to convert the input UTC time string to TDB Julian Date. Convert "2004 jun 11 19:32:00" UTC. #. Remove the LSK from the original meta-kernel and run your program again, using the same inputs as before. Has anything changed? Why? #. Remove the SCLK from the original meta-kernel and run your program again, using the same inputs as before. Has anything changed? Why? #. Modify your program to perform conversion of UTC or ephemeris time, to a spacecraft clock string using the NAIF ID for the CASSINI ISS NAC camera. Convert "2004 jun 11 19:32:00" UTC. #. Find the earliest UTC time that can be converted to CASSINI spacecraft clock. #. Extend your program to convert the spacecraft clock time obtained in the regular task back to UTC Time and present it in ISO calendar date format, with a resolution of milliseconds. #. Examine the contents of the generic LSK and the CASSINI SCLK kernels. Can you understand and explain what you see? **Solutions and answers** #. Two methods exist in order to convert ephemeris time to Julian Date: :py:func:`spiceypy.unitim ` and :py:func:`spiceypy.timout `. The difference between them is the type of output produced by each method. :py:func:`spiceypy.unitim ` returns the double precision value of an input epoch, while :py:func:`spiceypy.timout ` returns the string representation of the ephemeris time in Julian Date format (when picture input is set to ``'JULIAND.######### ::TDB'``). Refer to the function header for further details. The solution for the requested input UTC string is: ``Julian Date TDB: 2453168.3146318`` #. When running the original program without the LSK kernel, an error is produced: .. code-block:: text spiceypy.utils.support_types.SpiceyError: ================================================================================ Toolkit version: N0067 SPICE(NOLEAPSECONDS) -- 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 via the routine FURNSH. str2et_c --> STR2ET --> TTRANS ================================================================================ This error is triggered by :py:func:`spiceypy.str2et ` because the variable that points to the leapseconds is not present in the kernel pool and therefore the program lacks data required to perform the requested UTC to ephemeris time conversion. By default, SPICE will report, as a minimum, a short descriptive message and an expanded form of this short message where more details about the error are provided. If this error message is not sufficient for you to understand what has happened, you could go to the "Exceptions" section in the SPICELIB or CSPICE headers of the function that has triggered the error and find out more information about the possible causes. #. When running the original program without the SCLK kernel, an error is produced: .. code-block:: text spiceypy.utils.support_types.SpiceyError: ================================================================================ Toolkit version: N0067 SPICE(KERNELVARNOTFOUND) -- The Variable Was not Found in the Kernel Pool. SCLK_DATA_TYPE_82 not found. Did you load the SCLK kernel? sce2s_c --> SCE2S --> SCE2T --> SCTYPE --> SCLI01 ================================================================================ This error is triggered by :py:func:`spiceypy.sce2s `. In this case the error message may not give you enough information to understand what has actually happened. Nevertheless, the expanded form of this short message clearly indicates that the SCLK kernel for the spacecraft ID -82 has not been loaded. The UTC string to ephemeris time conversion and the conversion of ephemeris time into a calendar format worked normally as these conversions only require the LSK kernel to be loaded. #. The first thing you need to do is to find out what the NAIF ID is for the CASSINI ISS NAC camera. In order to do so, examine the ISS instrument kernel listed above and look for the "NAIF ID Code to Name Mapping" and there, for the NAIF ID given to CASSINI_ISS_NAC (which is -82360). Then replace in your code the SCLK ID -82 with -82360. After executing the program using the original meta-kernel, you will be getting the same error as in the previous task. Despite the error being exactly the same, this case is different. Generally, spacecraft clocks are associated with the spacecraft ID and not with its payload, sensors or structures IDs. Therefore, in order to do conversions from/to spacecraft clock for payload, sensors or spacecraft structures, the spacecraft ID must be used. Note that this does not need to be true for all missions or payloads, as SPICE does not restrict the SCLKs to spacecraft IDs only. Please refer to your mission's SCLK kernels for particulars. #. Use :py:func:`spiceypy.sct2e ` with the encoding of the Cassini spacecraft clock time set to 0.0 ticks and convert the resulting ephemeris time to UTC using either :py:func:`spiceypy.timout ` or :py:func:`spiceypy.et2utc `. The solution for the requested SCLK string is: ``Earliest UTC convertible to SCLK: 1980-01-01T00:00:00.000`` #. Use :py:func:`spiceypy.scs2e ` with the SCLK string obtained in the computations performed in the regular tasks and convert the resulting ephemeris time to UTC using either :py:func:`spiceypy.et2utc `, with ``'ISOC'`` format and 3 digits precision, or using :py:func:`spiceypy.timout ` using the time picture ``'YYYY-MM-DDTHR:MN:SC.### ::RND'``. The solution of the requested conversion is: .. code-block:: text 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-rs-1: Task Statement ^^^^^^^^^^^^^^ Write a program that prompts the user for an input UTC time string, computes the following quantities at that epoch: #. The apparent state of Phoebe as seen from CASSINI in the J2000 frame, in kilometers and kilometers/second. This vector itself is not of any particular interest, but it is a useful intermediate quantity in some geometry calculations. #. The apparent position of the Earth as seen from CASSINI in the J2000 frame, in kilometers. #. The one-way light time between CASSINI and the apparent position of Earth, in seconds. #. The apparent position of the Sun as seen from Phoebe in the J2000 frame (J2000), in kilometers. #. The actual (geometric) distance between the Sun and Phoebe, in astronomical units. and displays the results. Use the program to compute these quantities at “2004 jun 11 19:32:00” UTC. .. _learning-goals-rs-1: Learning Goals ^^^^^^^^^^^^^^ Understand the anatomy of an :py:func:`spiceypy.spkezr ` call. Discover the difference between :py:func:`spiceypy.spkezr ` and :py:func:`spiceypy.spkpos `. Familiarity with the Toolkit utility "brief". Exposure to unit conversion with SpiceyPy. .. _approach-rs-1: Approach ^^^^^^^^ The solution to the problem can be broken down into a series of simple steps: - Decide which SPICE kernels are necessary. Prepare a meta-kernel listing the kernels and load it into the program. - Prompt the user for an input time string. - Convert the input time string into ephemeris time expressed as seconds past J2000 TDB. - Compute the state of Phoebe relative to CASSINI in the J2000 reference frame, corrected for aberrations. - Compute the position of Earth relative to CASSINI in the J2000 reference frame, corrected for aberrations. (The function in the library that computes this also returns the one-way light time between CASSINI and Earth.) - Compute the position of the Sun relative to Phoebe in the J2000 reference frame, corrected for aberrations. - Compute the position of the Sun relative to Phoebe without correcting for aberration. Compute the length of this vector. This provides the desired distance in kilometers. - Convert the distance in kilometers into AU. You may find it useful to consult the permuted index, the headers of various source modules, and the "SPK Required Reading" (spk.req) document. When deciding which SPK files to load, the Toolkit utility "brief" may be of some use. "brief" is located in the "cspice/exe" directory for C toolkits. Consult its user's guide available in "cspice/doc/brief.ug" for details. .. _solution-rs-1: Solution ^^^^^^^^ **Solution Meta-Kernel** The meta-kernel we created for the solution to this exercise is named 'getsta.tm'. Its contents follow: .. py-editor:: :env: rsenv :src: scripts/remote_sensing/getsta_make_mk.py **Solution Source Code** A sample solution to the problem follows: .. py-editor:: :env: rsenv :src: scripts/remote_sensing/getsta.py **Solution Sample Output** Execute the program: .. code-block:: text 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-rs-1: Extra Credit ^^^^^^^^^^^^ In this "extra credit" section you will be presented with more complex tasks, aimed at improving your understanding of state computations, particularly the application of the different light time and stellar aberration corrections available in the :py:func:`spiceypy.spkezr ` function, and some common errors that may happen when computing these states. 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** #. Remove the Solar System ephemerides SPK from the original meta-kernel and run your program again, using the same inputs as before. Has anything changed? Why? #. Extend your program to compute the geometric position of Jupiter as seen from Saturn in the J2000 frame (J2000), in kilometers. #. Extend, or modify, your program to compute the position of the Sun as seen from Saturn in the J2000 frame (J2000), in kilometers, using the following light time and aberration corrections: NONE, LT and LT+S. Explain the differences. #. Examine the CASSINI frames definition kernel and the ISS instrument kernel to find the SPICE ID/name definitions. **Solutions and answers** #. When running the original program without the Solar System ephemerides SPK, an error is produced by :py:func:`spiceypy.spkezr `: .. code-block:: text spiceypy.utils.support_types.SpiceyError: ================================================================================ 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 epoch 2004 JUN 11 19:33:04.184. spkezr_c --> SPKEZR --> SPKEZ --> SPKACS --> SPKGEO ================================================================================ This error is generated when trying to compute the apparent state of Phoebe as seen from CASSINI in the J2000 frame because despite both Phoebe and CASSINI ephemeris data being relative to the Saturn Barycenter, the state of the spacecraft with respect to the solar system barycenter is required to compute the light time and stellar aberrations. The loaded SPK data are enough to compute geometric states of CASSINI with respect to the Saturn Barycenter, and geometric states of Phoebe with respect to the Saturn Barycenter, but insufficient to compute the state of the spacecraft relative to the Solar System Barycenter because the SPK data needed to compute geometric states of Saturn Barycenter relative to the Solar System barycenter are no longer loaded. Run "brief" on the SPKs used in the original task to find out which ephemeris objects are available from those kernels. If you want to find out what is the 'center of motion' for the ephemeris object(s) included in an SPK, use the ``-c`` option when running "brief": .. code-block:: text BRIEF -- Version 4.0.0, September 8, 2010 -- Toolkit Version N0066 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 #. If you run your extended program with the original meta-kernel, the ``SPICE(SPKINSUFFDATA)`` error should be produced by the :py:func:`spiceypy.spkpos ` function because you have not loaded enough ephemeris data to compute the position of Jupiter with respect to Saturn. The loaded SPKs contain data for Saturn relative to the Solar System Barycenter, and for the Jupiter System Barycenter relative to the Solar System Barycenter, but the data for Jupiter relative to the Jupiter System Barycenter are missing: .. code-block:: text 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/ Download the relevant SPK, add it to the meta-kernel and run again your extended program. The solution for the input UTC time "2004 jun 11 19:32:00" when using the downloaded Jovian Satellite Ephemeris SPK: .. code-block:: text Actual position of Jupiter as seen from Saturn in the J2000 frame (km): X = -436016583.291 Y = -1094176737.323 Z = -446585337.431 #. When using ``'NONE'`` aberration corrections, :py:func:`spiceypy.spkpos ` returns the geometric position of the target body relative to the observer. If ``'LT'`` is used, the returned vector corresponds to the position of the target at the moment it emitted photons arriving at the observer at ``et``. If ``'LT+S'`` is used instead, the returned vector takes into account the observer's velocity relative to the solar system barycenter. The solution for the input UTC time "2004 jun 11 19:32:00" is: .. code-block:: text 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-rs-2: Task Statement ^^^^^^^^^^^^^^ Write a program that prompts the user for an input time string, computes and displays the following at the epoch of interest: #. The apparent state of Phoebe as seen from CASSINI in the IAU_PHOEBE body-fixed frame. This vector itself is not of any particular interest, but it is a useful intermediate quantity in some geometry calculations. #. The angular separation between the apparent position of Earth as seen from CASSINI and the nominal boresight of the CASSINI high gain antenna (HGA). The HGA boresight direction is provided by the kernel variable TKFRAME\_-82101_BORESIGHT, which is defined in the Cassini frame kernel cited above in the section “Kernels Used.” In this kernel, the HGA boresight vector is expressed relative to the CASSINI_HGA reference frame. Use the program to compute these quantities at the epoch “2004 jun 11 19:32:00” UTC. .. _learning-goals-2: Learning Goals ^^^^^^^^^^^^^^ Familiarity with the different types of kernels involved in chaining reference frames together, both inertial and non-inertial. Discover some of the matrix and vector math functions. Understand the difference between :py:func:`spiceypy.pxform ` and :py:func:`spiceypy.sxform `. .. _approach-2: Approach ^^^^^^^^ The solution to the problem can be broken down into a series of simple steps: - Decide which SPICE kernels are necessary. Prepare a meta-kernel listing the kernels and load it into the program. - Prompt the user for an input time string. - Convert the input time string into ephemeris time expressed as seconds past J2000 TDB. - Compute the state of Phoebe relative to CASSINI in the J2000 reference frame, corrected for aberrations. - Compute the state transformation matrix from J2000 to IAU_PHOEBE at the epoch, adjusted for light time. - Multiply the state of Phoebe relative to CASSINI in the J2000 reference frame by the state transformation matrix computed in the previous step. - Compute the position of Earth relative to CASSINI in the J2000 reference frame, corrected for aberrations. - Determine what the nominal boresight of the CASSINI high gain antenna is by examining the frame kernel's content. - Compute the rotation matrix from the CASSINI high gain antenna frame to J2000. - Multiply the nominal boresight expressed in the CASSINI high gain antenna frame by the rotation matrix from the previous step. - Compute the separation between the result of the previous step and the apparent position of the Earth relative to CASSINI in the J2000 frame. HINT: Several of the steps above may be compressed into a single step using SpiceyPy functions with which you are already familiar. The "long way" presented above is intended to facilitate the introduction of the functions :py:func:`spiceypy.pxform ` and :py:func:`spiceypy.sxform `. You may find it useful to consult the permuted index, the headers of various source modules, and the following toolkit documentation: #. Frames Required Reading (frames.req) #. PCK Required Reading (pck.req) #. SPK Required Reading (spk.req) #. CK Required Reading (ck.req) This particular example makes use of many of the different types of SPICE kernels. You should spend a few moments thinking about which kernels you will need and what data they provide. .. _solution-2: Solution ^^^^^^^^ **Solution Meta-Kernel** The meta-kernel we created for the solution to this exercise is named 'xform.tm'. Its contents follow: .. py-editor:: :env: rsenv :src: scripts/remote_sensing/xform_make_mk.py **Solution Source Code** A sample solution to the problem follows: .. py-editor:: :env: rsenv :src: scripts/remote_sensing/xform.py **Solution Sample Output** Execute the program: .. code-block:: text 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-2: Extra Credit ^^^^^^^^^^^^ In this "extra credit" section you will be presented with more complex tasks, aimed at improving your understanding of frame transformations, and some common errors that may happen when computing them. 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** #. Run the original program using the input UTC time "2004 jun 11 18:25:00". Explain what happens. #. Compute the angular separation between the apparent position of the Sun as seen from CASSINI and the nominal boresight of the CASSINI high gain antenna (HGA). Is the HGA illuminated? **Solutions and answers** #. When running the original software using as input the UTC time string "2004 jun 11 18:25:00": .. code-block:: text spiceypy.utils.support_types.SpiceyError: ================================================================================ Toolkit version: N0067 SPICE(NOFRAMECONNECT) -- At epoch 1.4025036418463E+08 TDB (2004 JUN 11 18:26:04.184 TDB), there is insufficient information available to transform from reference frame -82101 (CASSINI_HGA) to reference frame 1 (J2000). Frame CASSINI_HGA could be transformed to frame -82000 (CASSINI_SC_COORD). The latter is a CK frame; a CK file containing data pxform_c --> PXFORM --> REFCHG ================================================================================ :py:func:`spiceypy.pxform ` returns the ``SPICE(NOFRAMECONNECT)`` error, which indicates that there are not sufficient data to perform the transformation from the CASSINI_HGA frame to J2000 at the requested epoch. If you summarize the CASSINI spacecraft CK using the "ckbrief" utility program with the ``-dump`` option (display interpolation intervals boundaries) you will find that the CK contains gaps within its segment: .. code-block:: text CKBRIEF -- Version 6.1.0, June 27, 2014 -- Toolkit Version N0066 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 whereas if you had used ckbrief without ``-dump`` you would have gotten the following information (only CK segment begin/end times): .. code-block:: text CKBRIEF -- Version 6.1.0, June 27, 2014 -- Toolkit Version N0066 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 which has insufficient detail to reveal the problem. #. By computing the apparent position of the Sun as seen from CASSINI in the CASSINI_HGA frame, and the angular separation between this vector and the nominal boresight of the CASSINI high gain antenna (+Z-axis of the CASSINI_HGA frame), you will find whether the HGA is illuminated. The solution for the input UTC time "2004 jun 11 19:32:00" is: .. code-block:: text 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. since the angular separation is smaller than 90 degrees. Computing Sub-s/c and Sub-solar Points on an Ellipsoid and a DSK (subpts) ------------------------------------------------------------------------- .. _task-statement-rs-3: Task Statement ^^^^^^^^^^^^^^ Write a program that prompts the user for an input UTC time string and computes the following quantities at that epoch: #. The apparent sub-observer point of CASSINI on Phoebe, in the body fixed frame IAU_PHOEBE, in kilometers. #. The apparent sub-solar point on Phoebe, as seen from CASSINI in the body fixed frame IAU_PHOEBE, in kilometers. The program computes each point twice: once using an ellipsoidal shape model and the ``near point/ellipsoid`` definition, and once using a DSK shape model and the ``nadir/dsk/unprioritized`` definition. The program displays the results. Use the program to compute these quantities at “2004 jun 11 19:32:00” UTC. .. _learning-goals-3: Learning Goals ^^^^^^^^^^^^^^ Discover higher level geometry calculation functions in SpiceyPy and their usage as it relates to CASSINI. .. _approach-3: Approach ^^^^^^^^ This particular problem is more of an exercise in searching the permuted index to find the appropriate functions and then reading their headers to understand how to call them. One point worth considering: how would the results change if the sub-solar and sub-observer points were computed using the ``intercept/ellipsoid`` and ``intercept/dsk/unprioritized`` definitions? Which definition is appropriate? .. _solution-3: Solution ^^^^^^^^ **Solution Meta-Kernel** The meta-kernel we created for the solution to this exercise is named 'subpts.tm'. Its contents follow: .. py-editor:: :env: rsenv :src: scripts/remote_sensing/subpts_make_mk.py **Solution Source Code** A sample solution to the problem follows: .. py-editor:: :env: rsenv :src: scripts/remote_sensing/subpts.py **Solution Sample Output** Execute the program: .. code-block:: text 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-3: Extra Credit ^^^^^^^^^^^^ In this "extra credit" section you will be presented with more complex tasks, aimed at improving your understanding of :py:func:`spiceypy.subpnt ` and :py:func:`spiceypy.subslr ` functions. 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** #. Recompute the apparent sub-solar point on Phoebe as seen from CASSINI in the body fixed frame IAU_PHOEBE in kilometers using the 'Intercept/ellipsoid' method at "2004 jun 11 19:32:00". Explain the differences. #. Compute the geometric sub-spacecraft point of CASSINI on Phoebe in the body fixed frame IAU_PHOEBE in kilometers using the 'Near point/ellipsoid' method at "2004 jun 11 19:32:00". #. Transform the sub-spacecraft Cartesian coordinates obtained in the previous task to planetocentric and planetographic coordinates. When computing planetographic coordinates, retrieve Phoebe's radii by calling :py:func:`spiceypy.bodvrd ` and use the first element of the returned radii values as Phoebe's equatorial radius. Explain why planetocentric and planetographic latitudes and longitudes are different. Explain why the planetographic altitude for a point on the surface of Phoebe is not zero and whether this is correct or not. **Solutions and answers** #. The differences observed are due to the computation method. The "Intercept/ellipsoid" method defines the sub-solar point as the target surface intercept of the line containing the Sun and the target's center, while the "Near point/ellipsoid" method defines the sub-solar point as the nearest point on the target relative to the Sun. Since Phoebe is not spherical, these two points are not the same: .. code-block:: text 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 #. The geometric sub-spacecraft point of CASSINI on Phoebe in the body fixed frame IAU_PHOEBE in kilometers at "2004 jun 11 19:32:00" UTC epoch is: .. code-block:: text 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 #. The sub-spacecraft point of CASSINI on Phoebe in planetocentric and planetographic coordinates at "2004 jun 11 19:32:00" UTC epoch is: .. code-block:: text 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 The planetocentric and planetographic longitudes are different ("graphic" = 360 - "centric") because planetographic longitudes on Phoebe are measured positive west as defined by Phoebe's rotation direction. The planetocentric and planetographic latitudes are different because the planetocentric latitude was computed as the angle between the direction from the center of the body to the point and the equatorial plane, while the planetographic latitude was computed as the angle between the surface normal at the point and the equatorial plane. The planetographic altitude is non zero because it was computed using a different and incorrect Phoebe surface model: a spheroid with equal equatorial radii. The surface point returned by :py:func:`spiceypy.subpnt ` was computed by treating Phoebe as a triaxial ellipsoid with different equatorial radii. The planetographic latitude is also incorrect because it is based on the normal to the surface of the spheroid rather than the ellipsoid. In general planetographic coordinates cannot be used for bodies with shapes modeled as triaxial ellipsoids. Intersecting Vectors with an Ellipsoid and a DSK (fovint) --------------------------------------------------------- .. _task-statement-rs-4: Task Statement ^^^^^^^^^^^^^^ Write a program that prompts the user for an input UTC time string and, for that time, computes the intersection of the CASSINI ISS NAC camera boresight and field of view (FOV) boundary vectors with the surface of Phoebe. Compute each intercept twice: once with Phoebe's shape modeled as an ellipsoid, and once with Phoebe's shape modeled by DSK data. The program presents each point of intersection as #. A Cartesian vector in the IAU_PHOEBE frame #. Planetocentric (latitudinal) coordinates in the IAU_PHOEBE frame. For each of the camera FOV boundary and boresight vectors, if an intersection is found, the program displays the results of the above computations, otherwise it indicates no intersection exists. At each point of intersection compute the following: 3. Phase angle 4. Solar incidence angle 5. Emission angle These angles should be computed using both ellipsoidal and DSK shape models. 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 ``"2004 jun 11 19:32:00"`` UTC. .. _learning-goals-4: Learning Goals ^^^^^^^^^^^^^^ Understand how field of view parameters are retrieved from instrument kernels. Learn how various standard planetary constants are retrieved from text PCKs. Discover how to compute the intersection of field of view vectors with target bodies whose shapes are modeled as ellipsoids or provided by DSKs. Discover another high level geometry function and another time conversion function in SpiceyPy. .. _approach-4: Approach ^^^^^^^^ This problem can be broken down into several simple, small steps: - Decide which SPICE kernels are necessary. Prepare a meta-kernel listing the kernels and load it into the program. Remember, you will need to find a kernel with information about the CASSINI NAC camera. - Prompt the user for an input time string. - Convert the input time string into ephemeris time expressed as seconds past J2000 TDB. - Retrieve the FOV (field of view) configuration for the CASSINI NAC camera. For each vector in the set of boundary corner vectors, and for the boresight vector, perform the following operations: - Compute the intercept of the vector with Phoebe modeled as an ellipsoid or using DSK data - If this intercept is found, convert the position vector of the intercept into planetocentric coordinates. Then compute the phase, solar incidence, and emission angles at the intercept. Otherwise indicate to the user no intercept was found for this vector. - Compute the planetocentric longitude of the boresight intercept. Finally - Compute the local solar time at the boresight intercept longitude on a 24-hour clock. The input time for this computation should be the TDB observation epoch minus one-way light time from the boresight intercept to the spacecraft. It may be useful to consult the CASSINI ISS instrument kernel to determine the name of the NAC camera as well as its configuration. This exercise may make use of some of the concepts and (loosely) code from the "Spacecraft Orientation and Reference Frames" task. .. _solution-4: Solution ^^^^^^^^ **Solution Meta-Kernel** The meta-kernel we created for the solution to this exercise is named 'fovint.tm'. Its contents follow: .. py-editor:: :env: rsenv :src: scripts/remote_sensing/fovint_make_mk.py **Solution Source Code** A sample solution to the problem follows: .. py-editor:: :env: rsenv :src: scripts/remote_sensing/fovint.py **Solution Sample Output** Execute the program: .. code-block:: text 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: true Sun visible: true 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: true Sun visible: true 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: true Sun visible: true 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: true Sun visible: true 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: true Sun visible: true 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: true Sun visible: true 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: true Sun visible: true 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: true Sun visible: true 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: true Sun visible: true 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: true Sun visible: true Local Solar Time at boresight intercept (24 Hour Clock): 11:39:55 .. _extra-credit-4: Extra Credit ^^^^^^^^^^^^ There are no "extra credit" tasks for this step of the lesson.