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:

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.

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

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:

#  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:

#  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.)

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:

  1. Ephemeris Time (ET) in seconds past J2000

  2. Calendar Ephemeris Time

  3. 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: spiceypy.etcal or spiceypy.timout.

Solution

Solution Meta-Kernel

The meta-kernel we created for the solution to this exercise is named 'convtm.tm'. Its contents follow:

Solution Source Code

A sample solution to the problem follows:

Solution Sample Output

Execute the program:

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

  1. Extend your program to convert the input UTC time string to TDB Julian Date. Convert "2004 jun 11 19:32:00" UTC.

  2. Remove the LSK from the original meta-kernel and run your program again, using the same inputs as before. Has anything changed? Why?

  3. Remove the SCLK from the original meta-kernel and run your program again, using the same inputs as before. Has anything changed? Why?

  4. 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.

  5. Find the earliest UTC time that can be converted to CASSINI spacecraft clock.

  6. 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.

  7. Examine the contents of the generic LSK and the CASSINI SCLK kernels. Can you understand and explain what you see?

Solutions and answers

  1. Two methods exist in order to convert ephemeris time to Julian Date: spiceypy.unitim and spiceypy.timout. The difference between them is the type of output produced by each method. spiceypy.unitim returns the double precision value of an input epoch, while 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

  2. When running the original program without the LSK kernel, an error is produced:

    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 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.

  3. When running the original program without the SCLK kernel, an error is produced:

    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 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.

  4. 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.

  5. Use 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 spiceypy.timout or spiceypy.et2utc. The solution for the requested SCLK string is: Earliest UTC convertible to SCLK: 1980-01-01T00:00:00.000

  6. Use 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 spiceypy.et2utc, with 'ISOC' format and 3 digits precision, or using spiceypy.timout using the time picture 'YYYY-MM-DDTHR:MN:SC.### ::RND'. The solution of the requested conversion is:

    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

Write a program that prompts the user for an input UTC time string, computes the following quantities at that epoch:

  1. 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.

  2. The apparent position of the Earth as seen from CASSINI in the J2000 frame, in kilometers.

  3. The one-way light time between CASSINI and the apparent position of Earth, in seconds.

  4. The apparent position of the Sun as seen from Phoebe in the J2000 frame (J2000), in kilometers.

  5. 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

Understand the anatomy of an spiceypy.spkezr call. Discover the difference between spiceypy.spkezr and spiceypy.spkpos. Familiarity with the Toolkit utility "brief". Exposure to unit conversion with SpiceyPy.

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

Solution Meta-Kernel

The meta-kernel we created for the solution to this exercise is named 'getsta.tm'. Its contents follow:

Solution Source Code

A sample solution to the problem follows:

Solution Sample Output

Execute the program:

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

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 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

  1. 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?

  2. Extend your program to compute the geometric position of Jupiter as seen from Saturn in the J2000 frame (J2000), in kilometers.

  3. 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.

  4. Examine the CASSINI frames definition kernel and the ISS instrument kernel to find the SPICE ID/name definitions.

Solutions and answers

  1. When running the original program without the Solar System ephemerides SPK, an error is produced by spiceypy.spkezr:

    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":

    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

  2. If you run your extended program with the original meta-kernel, the SPICE(SPKINSUFFDATA) error should be produced by the 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:

    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:

    Actual position of Jupiter as seen from Saturn in the
   J2000 frame (km):
   X =   -436016583.291
   Y =  -1094176737.323
   Z =   -446585337.431

  3. When using 'NONE' aberration corrections, 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:

    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

Write a program that prompts the user for an input time string, computes and displays the following at the epoch of interest:

  1. 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.

  2. 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

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 spiceypy.pxform and spiceypy.sxform.

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 spiceypy.pxform and spiceypy.sxform.

You may find it useful to consult the permuted index, the headers of various source modules, and the following toolkit documentation:

  1. Frames Required Reading (frames.req)

  2. PCK Required Reading (pck.req)

  3. SPK Required Reading (spk.req)

  4. 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

Solution Meta-Kernel

The meta-kernel we created for the solution to this exercise is named 'xform.tm'. Its contents follow:

Solution Source Code

A sample solution to the problem follows:

Solution Sample Output

Execute the program:

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

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

  1. Run the original program using the input UTC time "2004 jun 11 18:25:00". Explain what happens.

  2. 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

  1. When running the original software using as input the UTC time string "2004 jun 11 18:25:00":

    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

================================================================================

    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:

    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):

    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.

  2. 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:

    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

Write a program that prompts the user for an input UTC time string and computes the following quantities at that epoch:

  1. The apparent sub-observer point of CASSINI on Phoebe, in the body fixed frame IAU_PHOEBE, in kilometers.

  2. 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

Discover higher level geometry calculation functions in SpiceyPy and their usage as it relates to CASSINI.

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

Solution Meta-Kernel

The meta-kernel we created for the solution to this exercise is named 'subpts.tm'. Its contents follow:

Solution Source Code

A sample solution to the problem follows:

Solution Sample Output

Execute the program:

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

In this "extra credit" section you will be presented with more complex tasks, aimed at improving your understanding of spiceypy.subpnt and 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

  1. 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.

  2. 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".

  3. 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 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

  1. 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:

    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

  2. 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:

    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

  3. The sub-spacecraft point of CASSINI on Phoebe in planetocentric and planetographic coordinates at "2004 jun 11 19:32:00" UTC epoch is:

    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 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

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

  1. A Cartesian vector in the IAU_PHOEBE frame

  2. 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:

  1. Phase angle

  2. Solar incidence angle

  3. 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

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

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

Solution Meta-Kernel

The meta-kernel we created for the solution to this exercise is named 'fovint.tm'. Its contents follow:

Solution Source Code

A sample solution to the problem follows:

Solution Sample Output

Execute the program:

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

There are no "extra credit" tasks for this step of the lesson.