In-situ Sensing Hands-On Lesson, using CASSINI

November 20, 2017

Overview

In this lesson you will develop a simple program illustrating how SPICE can be used to compute various kinds of geometry information applicable to the experiments carried out by an in-situ instrument flown on an interplanetary spacecraft.

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 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.

The following SPICE tutorials serve as references for the discussions in this lesson:

Name              Lesson steps/functions it describes
----------------  -----------------------------------------------
Time              UTC to ET and SCLK to ET
Loading Kernels   Loading SPICE kernels
SCLK              SCLK to ET time conversion
SPK               Computing positions and velocities
Frames            Computing transformations between frames

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/toolkit_docs/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
---------------  -----------------------------------------
kernel.req       Loading SPICE kernels
naif_ids.req     Body and reference frame names
spk.req          Computing positions and velocities
sclk.req         SCLK to ET time conversion
time.req         UTC to ET time conversion

The Permuted Index

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

>>> import spiceypy
>>> help(spiceypy.str2et)

describes of the str2et function’s parameters, while the document

https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/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  020514_SE_SAT105.bsp      SPK  Saturnian Satellite Ephemeris SPK
4  030201AP_SK_SM546_T45.bsp SPK  Cassini Spacecraft SPK
5  981005_PLTEPH-DE405S.bsp  SPK  Planetary Ephemeris SPK
6  sat128.bsp                SPK  Saturnian Satellite Ephemeris SPK
7  04135_04171pc_psiv2.bc    CK   Cassini Spacecraft CK
8  cas_v37.tf                FK   Cassini FK
9  cpck05Mar2004.tpc         PCK  Cassini project PCK

These SPICE kernels are included in the lesson package available from the NAIF server at JPL:

https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/Lessons/

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    convrt     spiceypy.furnsh  spiceypy.str2et  1
                   spiceypy.unload

   2    sclket     spiceypy.furnsh  spiceypy.str2et  1,2
                   spiceypy.unload  spiceypy.scs2e

   3    getsta     spiceypy.furnsh  spiceypy.str2et  1-6
                   spiceypy.unload  spiceypy.scs2e
                                    spiceypy.spkezr

   4    soldir     spiceypy.furnsh  spiceypy.str2et  1-8
                   spiceypy.unload  spiceypy.scs2e
                                    spiceypy.spkezr
                                    spiceypy.spkpos
                                    spiceypy.vhat

   5    sscpnt     spiceypy.furnsh  spiceypy.str2et  1-9
                   spiceypy.unload  spiceypy.scs2e
                                    spiceypy.spkezr
                                    spiceypy.spkpos
                                    spiceypy.vhat
                                    spiceypy.subpnt
                                    spiceypy.reclat
                                    spiceypy.pxform
                                    spiceypy.mxv
                                    spiceypy.dpr

   6    scvel      spiceypy.furnsh  spiceypy.str2et  1-9
                   spiceypy.unload  spiceypy.scs2e
                                    spiceypy.spkezr
                                    spiceypy.spkpos
                                    spiceypy.vhat
                                    spiceypy.subpnt
                                    spiceypy.reclat
                                    spiceypy.pxform
                                    spiceypy.mxv
                                    spiceypy.dpr

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.

Step-1: “UTC to ET”

“UTC to ET” Task Statement

Write a program that computes and prints the Ephemeris Time (ET) corresponding to “2004-06-11T19:32:00” UTC, as the number of ephemeris seconds past J2000, .

“UTC to ET” Hints

Find out what SPICE kernel(s) is(are) needed to support this conversion. Reference the “time.req” and/or “Time” tutorial.

Find necessary kernel(s) on the NAIF’s FTP site.

Find out what routine should be called to load necessary kernel(s). Reference the “kernel.req” and/or “Loading Kernels” tutorial.

Find the “loader” routine calling sequence specification. Look at the “time.req”and that routine’s source code header. This routine may be an entry point, in which case there will be no source file with the same name. To find out in which source file this entry point is, search for its name in the “Permuted Index”.

Find the routine(s) used to convert time between UTC and ET. Look at the “time.req” and/or “Time” tutorial.

Find the “converter” routine(s) calling sequence specification. Look in the “time.req” and the routine’s source code header.

Put all calls together in a program, add variable declarations (the routine header’s “Declarations” and “Examples” sections are a good place to look for declaration specification and examples) and output print statements.

“UTC to ET” Solution Steps

Only one kernel file is needed to support this conversion – an LSK file “naif0008.tls”.

As any other SPICE kernel this file can be loaded by the spiceypy.furnsh function. For that, the name of the file can be provided as a sole argument of this routine:

...
lskfile = 'naif0008.tls'

spiceypy.furnsh(lskfile)

or it can be listed in a meta-kernel:

KPL/MK

   The names and contents of the kernels referenced by this
   meta-kernel are as follows:


   File Name                   Description
   --------------------------  ----------------------------------
   naif0008.tls                Generic LSK.

\begindata
   KERNELS_TO_LOAD = (
                     'kernels/lsk/naif0008.tls'
                     )
\begintext

the name of which, let’s call it “convrt.tm”, can be then provided as a sole argument of the spiceypy.spiceypy.furnsh() routine:

mkfile = 'convrt.tm'
spiceypy.furnsh(mkfile)

While the second option seems to involve a bit more work – it requires making an extra file – it is a much better way to go if you plan to load more kernels as you extend the program. With the meta-kernel approach simply adding more kernels to the list in KERNEL_TO_LOAD without changing the program code will accomplish that.

The highest level SpiceyPy time routine converting UTC to ET is spiceypy.str2et spiceypy.spiceypy.str2et() .

It has two arguments – input time string representing UTC in a variety of formats (see spiceypy.spiceypy.str2et() header’s section “Particulars” for the complete description of input time formats) and output DP number of ET seconds past J2000. A call to spiceypy.str2et converting a given UTC to ET could look like this:

utc =  '2004-06-11T19:32:00'
et = spiceypy.str2et(utc)

By combining spiceypy.spiceypy.furnsh() and spiceypy.spiceypy.str2et() calls and required declarations and by adding a simple print statement, one would get a complete program that prints ET for the given UTC epoch.

Use of SpiceyPy calls in a Python script requires the SpiceyPy package to be installed in your Python distribution, either using pip or conda, and imported within the script.

When you execute the script, “convrt”, it produces the following output:

> python convrt.py
UTC       = 2004-06-11T19:32:00
ET        =     140254384.184625

“UTC to ET” Code

Program “convrt.py”:

from __future__ import print_function
import spiceypy

def convrt():

    mkfile = 'convrt.tm'
    spiceypy.furnsh(mkfile)

    utc =  '2004-06-11T19:32:00'
    et = spiceypy.str2et(utc)

    print('UTC       = {:s}'.format(utc))
    print('ET        = {:20.6f}'.format(et))

    spiceypy.unload(mkfile)


if __name__ == '__main__':
    convrt()

Meta-kernel file “convrt.tm”:

KPL/MK

   The names and contents of the kernels referenced by this
   meta-kernel are as follows:


   File Name                   Description
   --------------------------  ----------------------------------
   naif0008.tls                Generic LSK.

\begindata
   KERNELS_TO_LOAD = (
                     'kernels/lsk/naif0008.tls'
                     )
\begintext

Step-2: “SCLK to ET”

“SCLK to ET” Task Statement

Extend the program from Step-1 to compute and print ET for the following CASSINI on-board clock epoch “1465674964.105”.

“SCLK to ET” Hints

Find out what additional (to those already loaded in Step-1) SPICE kernel(s) is(are) needed to support SCLK to ET conversion. Look at the “sclk.req” and/or “SCLK” tutorial.

Find necessary kernel(s) on the NAIF’s FTP site.

Modify the program or meta-kernel to load this (these) kernels.

Find the routine(s) needed to convert time between SCLK and ET. Look at the “sclk.req” and/or “Time” and “SCLK” tutorials.

Find the “converter” routine’s calling sequence specification. Look in the “sclk.req” and the routine’s source code header.

Look at “naif_ids.req” and the comments in the additional kernel(s) that you have loaded for information on proper values of input arguments of this routine.

Add calls to the “converter” routine(s), necessary variable declarations (the routine header’s” Declarations”and “Examples” sections are a good place to look for declaration specification and examples), and output print statements to the program.

“SCLK to ET” Solution Steps

A CASSINI SCLK file is needed additionally to the LSK file loaded in the Step-1 to support this conversion.

No code change is needed in the loading portion of the program if a meta-kernel approach was used in the Step-1. The program will load the file if it will be added to the list of kernels in the KERNELS_TO_LOAD variable:

KPL/MK

   The names and contents of the kernels referenced by this
   meta-kernel are as follows:


   File Name                   Description
   --------------------------  ----------------------------------
   naif0008.tls                Generic LSK.
   cas00084.tsc                Cassini SCLK.

\begindata
   KERNELS_TO_LOAD = (
                     'kernels/lsk/naif0008.tls'
                     'kernels/sclk/cas00084.tsc'
                     )
\begintext

The highest level SpiceyPy routine converting SCLK to ET is spiceypy.scs2e spiceypy.spiceypy.scs2e() .

It has three arguments – NAIF ID for CASSINI s/c (-82 as described by “naif_ids.req” document), input time string representing CASSINI SCLK, and output DP number of ET seconds past J2000. A call to spiceypy.str2et converting given SCLK to ET could look like this:

scid = -82
sclk = '1465674964.105'
et = spiceypy.scs2e(scid, sclk)

By adding the spiceypy.scs2e call, required declarations and a simple print statement, one would get a complete program that prints ET for the given SCLK epoch.

When you execute the script, “sclket”, it produces the following output:

> python convrt.py
UTC       = 2004-06-11T19:32:00
ET        =     140254384.184625
SCLK      = 1465674964.105
ET        =     140254384.183426

“SCLK to ET” Code

Program “sclket.py”:

from __future__ import print_function
import spiceypy

def sclket():

    mkfile = 'sclket.tm'
    spiceypy.furnsh(mkfile)

    utc =  '2004-06-11T19:32:00'
    et = spiceypy.str2et(utc)

    print('UTC       = {:s}'.format(utc))
    print('ET        = {:20.6f}'.format(et))

    scid = -82
    sclk = '1465674964.105'
    et = spiceypy.scs2e(scid, sclk)

    print('SCLK      = {:s}'.format(sclk))
    print('ET        = {:20.6f}'.format(et))

    spiceypy.unload(mkfile)


if __name__ == '__main__':
    sclket()

Meta-kernel file “sclket.tm”:

KPL/MK

   The names and contents of the kernels referenced by this
   meta-kernel are as follows:


   File Name                   Description
   --------------------------  ----------------------------------
   naif0008.tls                Generic LSK.
   cas00084.tsc                Cassini SCLK.

\begindata
   KERNELS_TO_LOAD = (
                     'kernels/lsk/naif0008.tls'
                     'kernels/sclk/cas00084.tsc'
                     )
\begintext

Step-3: “Spacecraft State”

“Spacecraft State” Task Statement

Extend the program from Step-2 to compute geometric state – position and velocity – of the CASSINI spacecraft with respect to the Sun in the Ecliptic frame at the epoch specified by SCLK time from Step-2.

“Spacecraft State” Hints

Find out what additional (to those already loaded in Steps-1&2) SPICE kernel(s) is(are) needed to support state computation. Look at the “spk.req” and/or “SPK” tutorial.

Find necessary kernel(s) on the NAIF’s FTP site.

Verify that the kernels contain enough data to compute the state of interest. Use “brief” utility program located under “toolkit/exe” directory for that.

Modify the meta-kernel to load this(these) kernels.

Determine the routine(s) needed to compute states. Look at the “spk.req” and/or “SPK” tutorial presentation.

Find the the routine(s) calling sequence specification. Look in the “spk.req” and the routine’s source code header.

Reference the “naif_ids.req” and “frames.req”and the routine(s) header “Inputs” and “Particulars” sections to determine proper values of the input arguments of this routine.

Add calls to the routine(s), necessary variable declarations and output print statements to the program.

“Spacecraft State” Solution Steps

A CASSINI spacecraft trajectory SPK and generic planetary ephemeris SPK files are needed to support computation of the state of interest.

The file names can be added to the meta-kernel to get them loaded into the program:

KPL/MK

   The names and contents of the kernels referenced by this
   meta-kernel are as follows:


   File Name                   Description
   --------------------------  ----------------------------------
   naif0008.tls                Generic LSK.
   cas00084.tsc                Cassini SCLK.
   020514_SE_SAT105.bsp        Saturnian Satellite Ephemeris SPK.
   030201AP_SK_SM546_T45.bsp   Cassini Spacecraft SPK.
   981005_PLTEPH-DE405S.bsp    Planetary Ephemeris SPK.
   sat128.bsp                  Saturnian Satellite Ephemeris SPK.

\begindata
   KERNELS_TO_LOAD = (
                     'kernels/lsk/naif0008.tls'
                     'kernels/sclk/cas00084.tsc'
                     'kernels/spk/020514_SE_SAT105.bsp'
                     'kernels/spk/030201AP_SK_SM546_T45.bsp'
                     'kernels/spk/981005_PLTEPH-DE405S.bsp'
                     'kernels/spk/sat128.bsp'
                     )
\begintext

The highest level SpiceyPy routine computing states is spiceypy.spkezr spiceypy.spiceypy.spkezr() .

We are interested in computing CASSINI position and velocity with respect to the Sun, therefore the target and observer names should be set to ‘CASSINI’ and ‘Sun’ (both names can be found in “naif_ids.req”).

The state should be in ecliptic frame, therefore the name of the frame in which the state should be computed is ‘ECLIPJ2000’ (see “frames.req” document.)

Since we need only the geometric position, the ‘abcorr’ argument of the routine should be set to ‘NONE’ (see aberration correction discussion in the spiceypy.spiceypy.spkezr() .

Putting it all together, we get:

target = 'CASSINI'
frame  = 'ECLIPJ2000'
corrtn = 'NONE'
observ = 'SUN'

state, ltime = spiceypy.spkezr(target, et, frame,
                               corrtn, observ)

When you execute the script, “getsta”, it produces the following output:

> python getsta.py
UTC       = 2004-06-11T19:32:00
ET        =     140254384.184625
SCLK      = 1465674964.105
ET        =     140254384.183426
 X        =    -376599061.916539
 Y        =    1294487780.929154
 Z        =      -7064853.054698
VX        =            -5.164226
VY        =             0.801719
VZ        =             0.040603

“Spacecraft State” Code

Program “getsta.py”:

from __future__ import print_function
import spiceypy

def getsta():

    mkfile = 'getsta.tm'
    spiceypy.furnsh(mkfile)

    utc =  '2004-06-11T19:32:00'
    et = spiceypy.str2et(utc)

    print('UTC       = {:s}'.format(utc))
    print('ET        = {:20.6f}'.format(et))

    scid = -82
    sclk = '1465674964.105'
    et = spiceypy.scs2e(scid, sclk)

    print('SCLK      = {:s}'.format(sclk))
    print('ET        = {:20.6f}'.format(et))

    target = 'CASSINI'
    frame  = 'ECLIPJ2000'
    corrtn = 'NONE'
    observ = 'SUN'

    state, ltime = spiceypy.spkezr(target, et, frame,
                                   corrtn, observ)

    print(' X        = {:20.6f}'.format(state[0]))
    print(' Y        = {:20.6f}'.format(state[1]))
    print(' Z        = {:20.6f}'.format(state[2]))
    print('VX        = {:20.6f}'.format(state[3]))
    print('VY        = {:20.6f}'.format(state[4]))
    print('VZ        = {:20.6f}'.format(state[5]))

    spiceypy.unload(mkfile)


if __name__ == '__main__':
    getsta()

Meta-kernel file “getsta.tm”:

KPL/MK

   The names and contents of the kernels referenced by this
   meta-kernel are as follows:


   File Name                   Description
   --------------------------  ----------------------------------
   naif0008.tls                Generic LSK.
   cas00084.tsc                Cassini SCLK.
   020514_SE_SAT105.bsp        Saturnian Satellite Ephemeris SPK.
   030201AP_SK_SM546_T45.bsp   Cassini Spacecraft SPK.
   981005_PLTEPH-DE405S.bsp    Planetary Ephemeris SPK.
   sat128.bsp                  Saturnian Satellite Ephemeris SPK.

\begindata
   KERNELS_TO_LOAD = (
                     'kernels/lsk/naif0008.tls'
                     'kernels/sclk/cas00084.tsc'
                     'kernels/spk/020514_SE_SAT105.bsp'
                     'kernels/spk/030201AP_SK_SM546_T45.bsp'
                     'kernels/spk/981005_PLTEPH-DE405S.bsp'
                     'kernels/spk/sat128.bsp'
                     )
\begintext

Step-4: “Sun Direction”

“Sun Direction” Task Statement

Extend the program from Step-3 to compute apparent direction of the Sun in the INMS frame at the epoch specified by SCLK time from Step-2.

“Sun Direction” Hints

Determine the additional SPICE kernels needed to support the direction computation, knowing that they should provide the s/c and instrument frame orientation. Retrieve these kernels from the NAIF’s FTP site.

Verify that the orientation data in the kernels have adequate coverage to support computation of the direction of interest. Use “ckbrief” utility program located under” toolkit/exe” directory for that.

Modify the meta-kernel to load this(these) kernels.

Determine the proper input arguments for the spiceypy.spkpos call to calculate the direction (which is the position portion of the output state). Look through the Frames Kernel find the name of the frame to used.

Add calls to the routine(s), necessary variable declarations and output print statements to the program.

“Sun Direction” Solution Steps

A CASSINI spacecraft orientation CK file, providing s/c orientation with respect to an inertial frame, and CASSINI FK file, providing orientation of the INMS frame with respect to the s/c frame, are needed additionally to already loaded kernels to support computation of this direction.

The file names can be added to the meta-kernel to get them loaded into the program:

KPL/MK

   The names and contents of the kernels referenced by this
   meta-kernel are as follows:


   File Name                   Description
   --------------------------  ----------------------------------
   naif0008.tls                Generic LSK.
   cas00084.tsc                Cassini SCLK.
   020514_SE_SAT105.bsp        Saturnian Satellite Ephemeris SPK.
   030201AP_SK_SM546_T45.bsp   Cassini Spacecraft SPK.
   981005_PLTEPH-DE405S.bsp    Planetary Ephemeris SPK.
   sat128.bsp                  Saturnian Satellite Ephemeris SPK.
   04135_04171pc_psiv2.bc      Cassini Spacecraft CK.
   cas_v37.tf                  Cassini FK.


\begindata
   KERNELS_TO_LOAD = (
                     'kernels/lsk/naif0008.tls'
                     'kernels/sclk/cas00084.tsc'
                     'kernels/spk/020514_SE_SAT105.bsp'
                     'kernels/spk/030201AP_SK_SM546_T45.bsp'
                     'kernels/spk/981005_PLTEPH-DE405S.bsp'
                     'kernels/spk/sat128.bsp'
                     'kernels/ck/04135_04171pc_psiv2.bc'
                     'kernels/fk/cas_v37.tf'
                     )
\begintext

The same highest level SpiceyPy routine computing positions, spiceypy.spkpos, can be used to compute this direction.

Since this is the direction of the Sun as seen from the s/c, the target argument should be set to ‘Sun’ and the observer argument should be set to ‘CASSINI’. The name of the INMS frame is ‘CASSINI_INMS’, the definition and description of this frame are provided in the CASSINI FK file, “cassini_v02.tf”.

Since the apparent, or ‘as seen’, position is sought for, the ‘abcorr’ argument of the routine should be set to ‘LT+S’ (see aberration correction discussion in the (”cspice/src/cspice/spkpos_c.c”)

If desired, the position can then be turned into a unit vector using spiceypy.vhat function (https://spiceypy.readthedocs.io/en/main/documentation.html#spiceypy.spiceypy.vhat). Putting it all together, we get:

target = 'SUN'
frame  = 'CASSINI_INMS'
corrtn = 'LT+S'
observ = 'CASSINI'

sundir, ltime = spiceypy.spkpos(target, et, frame,
                                corrtn, observ)
sundir = spiceypy.vhat(sundir)

When you execute the script, “soldir”, it produces the following output:

> python soldir.py
UTC       = 2004-06-11T19:32:00
ET        =     140254384.184625
SCLK      = 1465674964.105
ET        =     140254384.183426
 X        =    -376599061.916539
 Y        =    1294487780.929154
 Z        =      -7064853.054698
VX        =            -5.164226
VY        =             0.801719
VZ        =             0.040603
SUNDIR(X) =            -0.290204
SUNDIR(Y) =             0.881631
SUNDIR(Z) =             0.372167

“Sun Direction” Code

Program “soldir.py”:

from __future__ import print_function
import spiceypy

def soldir():

    mkfile = 'soldir.tm'
    spiceypy.furnsh(mkfile)

    utc =  '2004-06-11T19:32:00'
    et = spiceypy.str2et(utc)

    print('UTC       = {:s}'.format(utc))
    print('ET        = {:20.6f}'.format(et))

    scid = -82
    sclk = '1465674964.105'
    et = spiceypy.scs2e(scid, sclk)

    print('SCLK      = {:s}'.format(sclk))
    print('ET        = {:20.6f}'.format(et))

    target = 'CASSINI'
    frame  = 'ECLIPJ2000'
    corrtn = 'NONE'
    observ = 'SUN'

    state, ltime = spiceypy.spkezr(target, et, frame,
                                   corrtn, observ)

    print(' X        = {:20.6f}'.format(state[0]))
    print(' Y        = {:20.6f}'.format(state[1]))
    print(' Z        = {:20.6f}'.format(state[2]))
    print('VX        = {:20.6f}'.format(state[3]))
    print('VY        = {:20.6f}'.format(state[4]))
    print('VZ        = {:20.6f}'.format(state[5]))

    target = 'SUN'
    frame  = 'CASSINI_INMS'
    corrtn = 'LT+S'
    observ = 'CASSINI'

    sundir, ltime = spiceypy.spkpos(target, et, frame,
                                    corrtn, observ)
    sundir = spiceypy.vhat(sundir)

    print('SUNDIR(X) = {:20.6f}'.format(sundir[0]))
    print('SUNDIR(Y) = {:20.6f}'.format(sundir[1]))
    print('SUNDIR(Z) = {:20.6f}'.format(sundir[2]))

    spiceypy.unload(mkfile)


if __name__ == '__main__':
    soldir()

Meta-kernel file “soldir.tm”:

KPL/MK

   The names and contents of the kernels referenced by this
   meta-kernel are as follows:


   File Name                   Description
   --------------------------  ----------------------------------
   naif0008.tls                Generic LSK.
   cas00084.tsc                Cassini SCLK.
   020514_SE_SAT105.bsp        Saturnian Satellite Ephemeris SPK.
   030201AP_SK_SM546_T45.bsp   Cassini Spacecraft SPK.
   981005_PLTEPH-DE405S.bsp    Planetary Ephemeris SPK.
   sat128.bsp                  Saturnian Satellite Ephemeris SPK.
   04135_04171pc_psiv2.bc      Cassini Spacecraft CK.
   cas_v37.tf                  Cassini FK.


\begindata
   KERNELS_TO_LOAD = (
                     'kernels/lsk/naif0008.tls'
                     'kernels/sclk/cas00084.tsc'
                     'kernels/spk/020514_SE_SAT105.bsp'
                     'kernels/spk/030201AP_SK_SM546_T45.bsp'
                     'kernels/spk/981005_PLTEPH-DE405S.bsp'
                     'kernels/spk/sat128.bsp'
                     'kernels/ck/04135_04171pc_psiv2.bc'
                     'kernels/fk/cas_v37.tf'
                     )
\begintext

Step-5: “Sub-Spacecraft Point”

“Sub-Spacecraft Point” Task Statement

Extend the program from Step-4 to compute planetocentric longitude and and latitude of the sub-spacecraft point on Phoebe, and the direction from the spacecraft to that point in the INMS frame.

“Sub-Spacecraft Point” Hints

Find the SpiceyPy routine that computes sub-observer point coordinates. Use “Most Used SpiceyPy APIs” or” subpt” cookbook program for that.

Refer to the routine’s header to determine the additional kernels needed for this direction computation. Get these kernels from the NAIF’s FTP site. Modify the meta-kernel to load this(these) kernels.

Determine the proper input arguments for the routine. Refer to the routine’s header for that information.

Convert the surface point Cartesian vector returned by this routine to latitudinal coordinates. Use “Permuted Index” to find the routine that does this conversion. Refer to the routine’s header for input/output argument specifications.

Since the Cartesian vector from the spacecraft to the sub-spacecraft point is computed in the Phoebe body-fixed frame, it should be transformed into the instrument frame get the direction we are looking for. Refer to “frames.req” and/or” Frames” tutorial to determine the name of the routine computing transformations and use it to compute transformation from Phoebe body-fixed to the INMS frame.

Using “Permuted Index” find the routine that multiplies 3x3 matrix by 3d vector and use it to rotate the vector to the instrument frame.

Add calls to the routine(s), necessary variable declarations and output print statements to the program.

“Sub-Spacecraft Point” Solution Steps

The spiceypy.spiceypy.subpnt() routine can be used to compute the sub-observer point and the vector from the observer to that point with a single call. To determine this point as the closest point on the Phoebe ellipsoid, the ‘method’ argument has to be set to ‘NEAR POINT: ELLIPSOID’. For our case the ‘target’ is ‘PHOEBE’, the target body-fixed frame is ‘IAU_PHOEBE’, and the observer is ‘CASSINI’.

Since the s/c is close to Phoebe, light time does not need to be taken into account and, therefore, the ‘abcorr’ argument can be set to ‘NONE’.

In order for spiceypy.subpnt to compute the nearest point location, a PCK file containing Phoebe radii has to be loaded into the program (see “Files” section of the routine’s header.) All other files required for this computation are already being loaded by the program. With PCK file name added to it, the updated meta-kernel will look like this:

KPL/MK

   The names and contents of the kernels referenced by this
   meta-kernel are as follows:


   File Name                   Description
   --------------------------  ----------------------------------
   naif0008.tls                Generic LSK.
   cas00084.tsc                Cassini SCLK.
   020514_SE_SAT105.bsp        Saturnian Satellite Ephemeris SPK.
   030201AP_SK_SM546_T45.bsp   Cassini Spacecraft SPK.
   981005_PLTEPH-DE405S.bsp    Planetary Ephemeris SPK.
   sat128.bsp                  Saturnian Satellite Ephemeris SPK.
   04135_04171pc_psiv2.bc      Cassini Spacecraft CK.
   cas_v37.tf                  Cassini FK.
   cpck05Mar2004.tpc           Cassini project PCK.


\begindata
   KERNELS_TO_LOAD = (
                     'kernels/lsk/naif0008.tls'
                     'kernels/sclk/cas00084.tsc'
                     'kernels/spk/020514_SE_SAT105.bsp'
                     'kernels/spk/030201AP_SK_SM546_T45.bsp'
                     'kernels/spk/981005_PLTEPH-DE405S.bsp'
                     'kernels/spk/sat128.bsp'
                     'kernels/ck/04135_04171pc_psiv2.bc'
                     'kernels/fk/cas_v37.tf'
                     'kernels/pck/cpck05Mar2004.tpc'
                     )
\begintext

The sub-spacecraft point Cartesian vector can be converted to planetocentric radius, longitude and latitude using the spiceypy.reclat routine spiceypy.spiceypy.reclat() .

The vector from the spacecraft to the sub-spacecraft point returned by spiceypy.subpnt has to be rotated from the body-fixed frame to the instrument frame. The name of the routine that computes 3x3 matrices rotating vectors from one frame to another is spiceypy.pxform spiceypy.spiceypy.pxform() .

In our case the “from’ argument should be set to ‘IAU_PHOEBE’ and the ‘to’ argument should be set to ‘CASSINI_INMS’

The vector should be then multiplied by this matrix to rotate it to the instrument frame. The spiceypy.mxv routine performs that function spiceypy.spiceypy.mxv() .

After applying the rotation, normalize the resultant vector using the spiceypy.vhat function.

For output the longitude and latitude angles returned by spiceypy.reclat in radians can be converted to degrees by multiplying by spiceypy.dpr function spiceypy.spiceypy.dpr() .

Putting it all together, we get:

method = 'NEAR POINT: ELLIPSOID'
target = 'PHOEBE'
frame  = 'IAU_PHOEBE'
corrtn = 'NONE'
observ = 'CASSINI'

spoint, trgepc, srfvec = spiceypy.subpnt(method, target, et,
                                         frame, corrtn, observ)

srad, slon, slat = spiceypy.reclat(spoint)

fromfr = 'IAU_PHOEBE'
tofr   = 'CASSINI_INMS'

m2imat = spiceypy.pxform(fromfr, tofr, et)

sbpdir = spiceypy.mxv(m2imat, srfvec)
sbpdir = spiceypy.vhat(sbpdir)

print('LON       = {:20.6f}'.format(slon * spiceypy.dpr()))
print('LAT       = {:20.6f}'.format(slat * spiceypy.dpr()))

When you execute the script, “sscpnt”, it produces the following output:

> python sscpnt.py
UTC       = 2004-06-11T19:32:00
ET        =     140254384.184625
SCLK      = 1465674964.105
ET        =     140254384.183426
 X        =    -376599061.916539
 Y        =    1294487780.929154
 Z        =      -7064853.054698
VX        =            -5.164226
VY        =             0.801719
VZ        =             0.040603
SUNDIR(X) =            -0.290204
SUNDIR(Y) =             0.881631
SUNDIR(Z) =             0.372167
LON       =            23.423158
LAT       =             3.709797
SBPDIR(X) =            -0.000776
SBPDIR(Y) =            -0.999873
SBPDIR(Z) =            -0.015905

“Sub-Spacecraft Point” Code

Program

from __future__ import print_function
import spiceypy

def sscpnt():

    mkfile = 'sscpnt.tm'
    spiceypy.furnsh(mkfile)

    utc =  '2004-06-11T19:32:00'
    et = spiceypy.str2et(utc)

    print('UTC       = {:s}'.format(utc))
    print('ET        = {:20.6f}'.format(et))

    scid = -82
    sclk = '1465674964.105'
    et = spiceypy.scs2e(scid, sclk)

    print('SCLK      = {:s}'.format(sclk))
    print('ET        = {:20.6f}'.format(et))

    target = 'CASSINI'
    frame  = 'ECLIPJ2000'
    corrtn = 'NONE'
    observ = 'SUN'

    state, ltime = spiceypy.spkezr(target, et, frame,
                                   corrtn, observ)

    print(' X        = {:20.6f}'.format(state[0]))
    print(' Y        = {:20.6f}'.format(state[1]))
    print(' Z        = {:20.6f}'.format(state[2]))
    print('VX        = {:20.6f}'.format(state[3]))
    print('VY        = {:20.6f}'.format(state[4]))
    print('VZ        = {:20.6f}'.format(state[5]))

    target = 'SUN'
    frame  = 'CASSINI_INMS'
    corrtn = 'LT+S'
    observ = 'CASSINI'

    sundir, ltime = spiceypy.spkpos(target, et, frame,
                                    corrtn, observ)
    sundir = spiceypy.vhat(sundir)

    print('SUNDIR(X) = {:20.6f}'.format(sundir[0]))
    print('SUNDIR(Y) = {:20.6f}'.format(sundir[1]))
    print('SUNDIR(Z) = {:20.6f}'.format(sundir[2]))

    method = 'NEAR POINT: ELLIPSOID'
    target = 'PHOEBE'
    frame  = 'IAU_PHOEBE'
    corrtn = 'NONE'
    observ = 'CASSINI'

    spoint, trgepc, srfvec = spiceypy.subpnt(method, target, et,
                                             frame, corrtn, observ)

    srad, slon, slat = spiceypy.reclat(spoint)

    fromfr = 'IAU_PHOEBE'
    tofr   = 'CASSINI_INMS'

    m2imat = spiceypy.pxform(fromfr, tofr, et)

    sbpdir = spiceypy.mxv(m2imat, srfvec)
    sbpdir = spiceypy.vhat(sbpdir)

    print('LON       = {:20.6f}'.format(slon * spiceypy.dpr()))
    print('LAT       = {:20.6f}'.format(slat * spiceypy.dpr()))
    print('SBPDIR(X) = {:20.6f}'.format(sbpdir[0]))
    print('SBPDIR(Y) = {:20.6f}'.format(sbpdir[1]))
    print('SBPDIR(Z) = {:20.6f}'.format(sbpdir[2]))

    spiceypy.unload(mkfile)


if __name__ == '__main__':
    sscpnt()

Meta-kernel file “sscpnt.tm”:

KPL/MK

   The names and contents of the kernels referenced by this
   meta-kernel are as follows:


   File Name                   Description
   --------------------------  ----------------------------------
   naif0008.tls                Generic LSK.
   cas00084.tsc                Cassini SCLK.
   020514_SE_SAT105.bsp        Saturnian Satellite Ephemeris SPK.
   030201AP_SK_SM546_T45.bsp   Cassini Spacecraft SPK.
   981005_PLTEPH-DE405S.bsp    Planetary Ephemeris SPK.
   sat128.bsp                  Saturnian Satellite Ephemeris SPK.
   04135_04171pc_psiv2.bc      Cassini Spacecraft CK.
   cas_v37.tf                  Cassini FK.
   cpck05Mar2004.tpc           Cassini project PCK.


\begindata
   KERNELS_TO_LOAD = (
                     'kernels/lsk/naif0008.tls'
                     'kernels/sclk/cas00084.tsc'
                     'kernels/spk/020514_SE_SAT105.bsp'
                     'kernels/spk/030201AP_SK_SM546_T45.bsp'
                     'kernels/spk/981005_PLTEPH-DE405S.bsp'
                     'kernels/spk/sat128.bsp'
                     'kernels/ck/04135_04171pc_psiv2.bc'
                     'kernels/fk/cas_v37.tf'
                     'kernels/pck/cpck05Mar2004.tpc'
                     )
\begintext

Step-6: “Spacecraft Velocity”

“Spacecraft Velocity” Task Statement

Extend the program from Step-5 to compute the spacecraft velocity with respect to Phoebe in the INMS frame.

“Spacecraft Velocity” Hints

Compute velocity of the spacecraft with respect to Phoebe in some inertial frame, for example J2000. Recall that velocity is the last three components of the state vector returned by spiceypy.spkezr.

Since the velocity vector is computed in the inertial frame, it should be rotated to the instrument frame. Look at the previous step the routine that compute necessary rotation and rotate vectors.

Add calls to the routine(s), necessary variable declarations and output print statements to the program.

“Spacecraft Velocity” Solution Steps

All kernels required for computations in this step are already being loaded by the program, therefore, the meta-kernel does not need to be changed.

The spacecraft velocity vector is the last three components of the state returned by spiceypy.spkezr. To compute velocity of CASSINI with respect to Phoebe in the J2000 inertial frame the spiceypy.spkezr arguments should be set to ‘CASSINI’ (TARG), ‘PHOEBE’ (OBS), ‘J2000’ (REF) and ‘NONE’ (ABCORR).

The computed velocity vector has to be rotated from the J2000 frame to the instrument frame. The spiceypy.pxform routine used in the previous step can be used to compute the rotation matrix needed for that. In this case the frame name arguments should be set to ‘J2000’ (FROM) and ‘CASSINI_INMS’ (TO).

As in the previous step the difference vector should be then multiplied by this rotation matrix using the spiceypy.mxv routine. After applying the rotation, normalize the resultant vector using the spiceypy.vhat routine.

Putting it all together, we get:

target = 'CASSINI'
frame  = 'J2000'
corrtn = 'NONE'
observ = 'PHOEBE'

state, ltime = spiceypy.spkezr(target, et, frame,
                               corrtn, observ)
scvdir = state[3:6]

fromfr = 'J2000'
tofr   = 'CASSINI_INMS'
j2imat = spiceypy.pxform(fromfr, tofr, et)

scvdir = spiceypy.mxv(j2imat, scvdir)
scvdir = spiceypy.vhat(scvdir)

When you execute the script, “scvel”, it produces the following output:

> python scvel.py
UTC       = 2004-06-11T19:32:00
ET        =     140254384.184625
SCLK      = 1465674964.105
ET        =     140254384.183426
 X        =    -376599061.916539
 Y        =    1294487780.929154
 Z        =      -7064853.054698
VX        =            -5.164226
VY        =             0.801719
VZ        =             0.040603
SUNDIR(X) =            -0.290204
SUNDIR(Y) =             0.881631
SUNDIR(Z) =             0.372167
LON       =            23.423158
LAT       =             3.709797
SBPDIR(X) =            -0.000776
SBPDIR(Y) =            -0.999873
SBPDIR(Z) =            -0.015905
SCVDIR(X) =             0.395785
SCVDIR(Y) =            -0.292808
SCVDIR(Z) =             0.870413

Note that computing the spacecraft velocity in the instrument frame by a single call to spiceypy.spkezr by specifying ‘CASSINI_INMS’ in the ‘ref’ argument returns an incorrect result. Such computation will take into account the spacecraft angular velocity from the CK files, which should not be considered in this case.

“Spacecraft Velocity” Code Program “scvel.py”:

from __future__ import print_function
import spiceypy

def scvel():

    mkfile = 'scvel.tm'
    spiceypy.furnsh(mkfile)

    utc =  '2004-06-11T19:32:00'
    et = spiceypy.str2et(utc)

    print('UTC       = {:s}'.format(utc))
    print('ET        = {:20.6f}'.format(et))

    scid = -82
    sclk = '1465674964.105'
    et = spiceypy.scs2e(scid, sclk)

    print('SCLK      = {:s}'.format(sclk))
    print('ET        = {:20.6f}'.format(et))

    target = 'CASSINI'
    frame  = 'ECLIPJ2000'
    corrtn = 'NONE'
    observ = 'SUN'

    state, ltime = spiceypy.spkezr(target, et, frame,
                                   corrtn, observ)

    print(' X        = {:20.6f}'.format(state[0]))
    print(' Y        = {:20.6f}'.format(state[1]))
    print(' Z        = {:20.6f}'.format(state[2]))
    print('VX        = {:20.6f}'.format(state[3]))
    print('VY        = {:20.6f}'.format(state[4]))
    print('VZ        = {:20.6f}'.format(state[5]))

    target = 'SUN'
    frame  = 'CASSINI_INMS'
    corrtn = 'LT+S'
    observ = 'CASSINI'

    sundir, ltime = spiceypy.spkpos(target, et, frame,
                                    corrtn, observ)
    sundir = spiceypy.vhat(sundir)

    print('SUNDIR(X) = {:20.6f}'.format(sundir[0]))
    print('SUNDIR(Y) = {:20.6f}'.format(sundir[1]))
    print('SUNDIR(Z) = {:20.6f}'.format(sundir[2]))

    method = 'NEAR POINT: ELLIPSOID'
    target = 'PHOEBE'
    frame  = 'IAU_PHOEBE'
    corrtn = 'NONE'
    observ = 'CASSINI'

    spoint, trgepc, srfvec = spiceypy.subpnt(method, target, et,
                                             frame, corrtn, observ)

    srad, slon, slat = spiceypy.reclat(spoint)

    fromfr = 'IAU_PHOEBE'
    tofr   = 'CASSINI_INMS'

    m2imat = spiceypy.pxform(fromfr, tofr, et)

    sbpdir = spiceypy.mxv(m2imat, srfvec)
    sbpdir = spiceypy.vhat(sbpdir)

    print('LON       = {:20.6f}'.format(slon * spiceypy.dpr()))
    print('LAT       = {:20.6f}'.format(slat * spiceypy.dpr()))
    print('SBPDIR(X) = {:20.6f}'.format(sbpdir[0]))
    print('SBPDIR(Y) = {:20.6f}'.format(sbpdir[1]))
    print('SBPDIR(Z) = {:20.6f}'.format(sbpdir[2]))

    target = 'CASSINI'
    frame  = 'J2000'
    corrtn = 'NONE'
    observ = 'PHOEBE'

    state, ltime = spiceypy.spkezr(target, et, frame,
                                   corrtn, observ)
    scvdir = state[3:6]

    fromfr = 'J2000'
    tofr   = 'CASSINI_INMS'
    j2imat = spiceypy.pxform(fromfr, tofr, et)

    scvdir = spiceypy.mxv(j2imat, scvdir)
    scvdir = spiceypy.vhat(scvdir)

    print('SCVDIR(X) = {:20.6f}'.format(scvdir[0]))
    print('SCVDIR(Y) = {:20.6f}'.format(scvdir[1]))
    print('SCVDIR(Z) = {:20.6f}'.format(scvdir[2]))

    spiceypy.unload(mkfile)


if __name__ == '__main__':
    scvel()

Meta-kernel file “scvel.tm”:

KPL/MK

   The names and contents of the kernels referenced by this
   meta-kernel are as follows:


   File Name                   Description
   --------------------------  ----------------------------------
   naif0008.tls                Generic LSK.
   cas00084.tsc                Cassini SCLK.
   020514_SE_SAT105.bsp        Saturnian Satellite Ephemeris SPK.
   030201AP_SK_SM546_T45.bsp   Cassini Spacecraft SPK.
   981005_PLTEPH-DE405S.bsp    Planetary Ephemeris SPK.
   sat128.bsp                  Saturnian Satellite Ephemeris SPK.
   04135_04171pc_psiv2.bc      Cassini Spacecraft CK.
   cas_v37.tf                  Cassini FK.
   cpck05Mar2004.tpc           Cassini project PCK.


\begindata
   KERNELS_TO_LOAD = (
                     'kernels/lsk/naif0008.tls'
                     'kernels/sclk/cas00084.tsc'
                     'kernels/spk/020514_SE_SAT105.bsp'
                     'kernels/spk/030201AP_SK_SM546_T45.bsp'
                     'kernels/spk/981005_PLTEPH-DE405S.bsp'
                     'kernels/spk/sat128.bsp'
                     'kernels/ck/04135_04171pc_psiv2.bc'
                     'kernels/fk/cas_v37.tf'
                     'kernels/pck/cpck05Mar2004.tpc'
                     )
\begintext