Other Stuff (Python)¶
November 20, 2017
The extensive scope of the SpiceyPy system’s functionality includes features the average user may not expect or appreciate, features NAIF refers to as “Other Stuff.” This workbook includes a set of lessons to introduce the beginning to moderate user to such features.
The lessons provide a brief description to several related sets of routines, associated reference documents, a programming task designed to teach the use of the routines, and an example solution to the programming problem.
Overview¶
This workbook contains lessons to demonstrate use of the less celebrated SpiceyPy routines.
1. Kernel Management with the Kernel Subsystem
2. The Kernel Pool
3. Coordinate Conversions
4. Advanced Time Manipulation Routines
5. Error Handling
6. Windows and Cells
7. Utility and Constants Routines
References¶
This section lists SPICE documents referred to in this lesson.
The following SPICE tutorials serve as references for the discussions in this lesson:
Name Lesson steps/functions it describes
---------------- -----------------------------------------------
concepts Concepts of space geometry and time
intro_to_kernels Using kernels, meta-kernels
time Time systems, conversions and formats
lsk_and_sclk LSK and SCLK
derived_quant "high-level" observation geometry computations
other_functions Intro to some SPICE "low level" computations
exceptions built-in mechanism for trapping/handling errors
These tutorials are available from the NAIF ftp server at JPL:
http://naif.jpl.nasa.gov/naif/tutorials.html
Required Readings
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
--------------- -----------------------------------------
cells.req The SPICE cell data type
error.req The SPICE error handling system
kernel.req Loading SPICE kernels
time.req Time conversion
windows.req The SPICE window data type
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 de405s.bsp SPK Planet Ephemeris SPK
3 pck00008.tpc PCK Generic PCK
These SPICE kernels are included in the lesson package available from the NAIF server at JPL:
ftp://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 kpool spiceypy.furnsh spiceypy.ktotal 1-3
spiceypy.unload spiceypy.kdata
spiceypy.kclear
2 kervar spiceypy.furnsh spiceypy.gnpool 1-3
spiceypy.kclear spiceypy.dtpool
spiceypy.gdpool
spiceypy.gcpool
3 coord spiceypy.furnsh spiceypy.dpr 1-3
spiceypy.kclear spiceypy.str2et
spiceypy.bodvrd
spiceypy.spkpos
spiceypy.recrad
spiceypy.reclat
spiceypy.recsph
spiceypy.recgeo
4 xtic spiceypy.furnsh spiceypy.str2et 1
spiceypy.tsetyr spiceypy.timout
spiceypy.kclear spiceypy.tpictr
spiceypy.jyear
5 aderr spiceypy.furnsh spiceypy.spkezr 1-3
spiceypy.kclear
6 win spiceypy.furnsh spiceypy.str2et 1-3
spiceypy.wninsd spiceypy.wnvald
spiceypy.kclear spiceypy.wnintd
spiceypy.card
spiceypy.wnfetd
spiceypy.et2utc
spiceypy.wnsumd
7 units spiceypy.tkvrsn
spiceypy.convrt
xconst spiceypy.spd
spiceypy.dpr
spiceypy.rpd
spiceypy.clight
spiceypy.j2100
spiceypy.j2000
spiceypy.tyear
spiceypy.halfpi
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.
NAIF Documentation¶
The technical complexity of the various SPICE subsystems mandates an extensive, user-friendly documentation set. The set differs somewhat depending on your choice of development language but provides the same information with regards to SPICE operation. The sources for a user needing information concerning SPICE are:
-- Required Readings and Users Guides
-- Library Source Code Documentation
-- API Documentation
-- Tutorials
Required Reading and Users Guides
NAIF Required Reading (*.req) documents introduce the functionality of particular SpiceyPy subsystems:
abcorr.req
cells.req
ck.req
daf.req
das.req
dla.req
dsk.req
ek.req
ellipses.req
error.req
frames.req
gf.req
kernel.req
naif_ids.req
pck.req
planes.req
problems.req
rotation.req
scanning.req
sclk.req
sets.req
spc.req
spk.req
symbols.req
time.req
windows.req
NAIF Users Guides (*.ug) describe the proper use of particular SpiceyPy tools:
brief.ug
chronos.ug
ckbrief.ug
commnt.ug
convert.ug
dskbrief.ug
dskexp.ug
frmdiff.ug
inspekt.ug
mkdsk.ug
mkspk.ug
msopck.ug
simple.ug
spacit.ug
spkdiff.ug
spkmerge.ug
states.ug
subpt.ug
tictoc.ug
tobin.ug
toxfr.ug
version.ug
These text documents exist in the ‘doc’ directory of the main CSPICE Toolkit directory:
../cspice/doc/
HTML format documentation
The SpiceyPy distributions include HTML versions of Required Readings and Users Guides, accessible from the HTML documentation directory:
../cspice/doc/html/index.html
Library Source Code Documentation
All SPICELIB and CSPICE source files include usage and design information incorporated in a comment block known as the “header.” (Every toolkit includes either the SPICELIB or CSPICE library.)
A header consists of several marked sections:
-- Procedure: Routine name and one line expansion of the routine's
name.
-- Abstract: A tersely worded explanation describing the routine.
-- Copyright: An identification of the copyright holder for the
routine.
-- Required_Reading: A list of SpiceyPy required reading documents
relating to the routine.
-- Brief_I/O: A table of arguments, identifying each as either
input, output, or both, with a very brief description of the
variable.
-- Detailed_Input & Detailed_Output: An elaboration of the
Brief_I/O section providing comprehensive information on
argument use.
-- Parameters: Description and declaration of any parameters
(constants) specific to the routine.
-- Exceptions: A list of error conditions the routine detects and
signals plus a discussion of any other exceptional conditions
the routine may encounter.
-- Files: A list of other files needed for the routine to operate.
-- Particulars: A discussion of the routine's function (if
needed). This section may also include information relating to
"how" and "why" the routine performs an operation and to
explain functionality of routines that operate by side effects.
-- Examples: Descriptions and code snippets concerning usage of
the routine.
-- Restrictions: Restrictions or warnings concerning use.
-- Literature_References: A list of sources required to understand
the algorithms or data used in the routine.
-- Author_and_Institution: The names and affiliations for authors
of the routine.
-- Version: A list of edits and the authors of those edits made to
the routine since initial delivery to the SpiceyPy system.
The source code for SpiceyPy products is stored in ‘src’ sub-directory of the main SpiceyPy directory:
API Documentation
The SpiceyPy package is documented in “readthedocs” website:
https://spiceypy.readthedocs.io/en/master/index.html
Each API documentation page is in large part copied from the “Abstract” and” Brief_I/O” sections of the corresponding CSPICE function documentation. Each API page includes a link to the API documentation for the CSPICE routine called by the SpiceyPy interface.
This SpiceyPy API documentation (the same information as in the website but without hyperlinks) is also available from the Python built-in help system:
>>> help ( spiceypy.str2et )
Help on function str2et in module spiceypy.spiceypy:
str2et(*args, **kwargs)
Convert a string representing an epoch to a double precision
value representing the number of TDB seconds past the J2000
epoch corresponding to the input epoch.
...
:param time: A string representing an epoch.
:type time: str
:return: The equivalent value in seconds past J2000, TDB.
:rtype: float
In order to have offline access to the documentation it is recommended to have the CSPICE Toolkit installed locally. The CSPICE package includes the CSPICE Reference Guide, an index of all CSPICE wrapper APIs with hyperlinks to API specific documentation. Each API documentation page includes cross-links to any other wrapper API mentioned in the document and links to the wrapper source code.
...cspice/doc/html/cspice/index.html
Text kernels¶
Several workbooks use SPICE text kernels. SPICE identifies a text kernel as an ASCII text file containing the mark-up tags the kernel subsystem requires to identify data assignments in that file, and “name=value” data assignments.
The subsystem uses two tags:
\begintext
and
\begindata
to mark information blocks within the text kernel. The \begintext tag specifies all text following the tag as comment information to be ignored by the subsystem.
Things to know:
1. The \begindata tag marks the start of a data definition block.
The subsystem processes all text following this marker as SPICE
kernel data assignments until finding a \begintext marker.
2. The kernel subsystem defaults to the \begintext mode until the
parser encounters a \begindata tag. Once in \begindata mode the
subsystem processes all text as variable assignments until the
next \begintext tag.
3. Enter the tags as the only text on a line, i.e.:
\begintext
... commentary information on the data assignments ...
\begindata
... data assignments ...
4. CSPICE delivery N0059 added to the CSPICE and Icy text kernel
parsers the functionality to read non native text kernels, i.e.
a Unix compiled library can read a MS Windows native text
kernel, a MS Windows compiled library can read a Unix native
text kernel. Mice acquires this capability from CSPICE.
5. With regards to the FORTRAN distribution, as of delivery N0057
the spiceypy.furnsh call includes a line terminator check,
signaling an error on any attempt to read non-native text
kernels.
Text kernel format
Scalar assignments.
VAR_NAME_DP = 1.234
VAR_NAME_INT = 1234
VAR_NAME_STR = 'FORBIN'
Please note the use of a single quote in string assignments.
Vector assignments. Vectors must contain the same type data.
VEC_NAME_DP = ( 1.234 , 45.678 , 901234.5 )
VEC_NAME_INT = ( 1234 , 456 , 789 )
VEC_NAME_STR = ( 'FORBIN', 'FALKEN', 'ROBUR' )
also
VEC_NAME_DP = ( 1.234,
45.678,
901234.5 )
VEC_NAME_STR = ( 'FORBIN',
'FALKEN',
'ROBUR' )
Time assignments.
TIME_VAL = @31-JAN-2003-12:34:56.798
TIME_VEC = ( @01-DEC-2004, @15-MAR-2004 )
The at-sign character ‘@’ indicates a time string. The pool subsystem converts the strings to double precision TDB (a numeric value). Please note, the time strings must not contain embedded blanks. WARNING - a TDB string is not the same as a UTC string.
The above examples depict direct assignments via the ‘=’ operator. The kernel pool also permits incremental assignments via the ‘+=’ operator.
Please refer to the kernels required reading, kernel.req, for additional information.
Lesson 1: Kernel Management with the Kernel Subsystem¶
Task Statement¶
Write a program to load a meta kernel, interrogate the SpiceyPy system for the names and types of all loaded kernels, then demonstrate the unload functionality and the resulting effects.
Learning Goals¶
This lesson demonstrates use of the kernel subsystem to load, unload, and list loaded kernels.
This lesson requires creation of a SPICE meta kernel.
Code Solution¶
First, create a meta text kernel:
You can use two versions of a meta kernel with code examples (kpool.tm) in this lesson. Either a kernel with explicit path information:
KPL/MK
\begindata
KERNELS_TO_LOAD = ( 'kernels/spk/de405s.bsp',
'kernels/pck/pck00008.tpc',
'kernels/lsk/naif0008.tls' )
\begintext
… or a more generic meta kernel using the PATH_VALUES/PATH_SYMBOLS functionality to declare path names as variables:
KPL/MK
Define the paths to the kernel directory. Use the PATH_SYMBOLS
as aliases to the paths.
The names and contents of the kernels referenced by this
meta-kernel are as follows:
File Name Description
--------------- ------------------------------
naif0008.tls Generic LSK.
de405s.bsp Planet Ephemeris SPK.
pck00008.tpc Generic PCK.
\begindata
PATH_VALUES = ( 'kernels/lsk',
'kernels/spk',
'kernels/pck' )
PATH_SYMBOLS = ( 'LSK', 'SPK', 'PCK' )
KERNELS_TO_LOAD = ( '$LSK/naif0008.tls',
'$SPK/de405s.bsp',
'$PCK/pck00008.tpc' )
\begintext
Now the solution source code:
from __future__ import print_function
#
# Import the CSPICE-Python interface.
#
import spiceypy
def kpool():
#
# Assign the path name of the meta kernel to META.
#
META = 'kpool.tm'
#
# Load the meta kernel then use KTOTAL to interrogate the SPICE
# kernel subsystem.
#
spiceypy.furnsh( META )
count = spiceypy.ktotal( 'ALL' );
print( 'Kernel count after load: {0}\n'.format(count))
#
# Loop over the number of files; interrogate the SPICE system
# with spiceypy.kdata for the kernel names and the type.
# 'found' returns a boolean indicating whether any kernel files
# of the specified type were loaded by the kernel subsystem.
# This example ignores checking 'found' as kernels are known
# to be loaded.
#
for i in range(0, count):
[ file, type, source, handle] = spiceypy.kdata(i, 'ALL');
print( 'File {0}'.format(file) )
print( 'Type {0}'.format(type) )
print( 'Source {0}\n'.format(source) )
#
# Unload one kernel then check the count.
#
spiceypy.unload( 'kernels/spk/de405s.bsp')
count = spiceypy.ktotal( 'ALL' );
#
# The subsystem should report one less kernel.
#
print( 'Kernel count after one unload: {0}'.format(count))
#
# Now unload the meta kernel. This action unloads all
# files listed in the meta kernel.
#
spiceypy.unload( META )
#
# Check the count; spiceypy should return a count of zero.
#
count = spiceypy.ktotal( 'ALL');
print( 'Kernel count after meta unload: {0}'.format(count))
#
# Done. Unload the kernels.
#
spiceypy.kclear
if __name__ == '__main__':
kpool()
Run the code example
First we see the number of all loaded kernels returned from the spiceypy.ktotal call.
Then the spiceypy.kdata loop returns the name of each loaded kernel, the type of kernel (SPK, CK, TEXT, etc.) and the source of the kernel - the mechanism that loaded the kernel. The source either identifies a meta kernel, or contains an empty string. An empty source string indicates a direct load of the kernel with a spiceypy.furnsh call.
Kernel count after load: 4
File kpool.tm
Type META
Source
File kernels/lsk/naif0008.tls
Type TEXT
Source kpool.tm
File kernels/spk/de405s.bsp
Type SPK
Source kpool.tm
File kernels/pck/pck00008.tpc
Type TEXT
Source kpool.tm
Kernel count after one unload: 3
Kernel count after meta unload: 0
Lesson 2: The Kernel Pool¶
Task Statement¶
Write a program to retrieve particular string and numeric text kernel variables, both scalars and arrays. Interrogate the kernel pool for assigned variable names.
Learning Goals¶
The lesson demonstrates the SpiceyPy system’s facility to retrieve different types of data (string, numeric, scalar, array) from the kernel pool.
For the code examples, use this generic text kernel (kervar.tm) containing PCK-type data, kernels to load, and example time strings:
KPL/MK
Name the kernels to load. Use path symbols.
The names and contents of the kernels referenced by this
meta-kernel are as follows:
File Name Description
--------------- ------------------------------
naif0008.tls Generic LSK.
de405s.bsp Planet Ephemeris SPK.
pck00008.tpc Generic PCK.
\begindata
PATH_VALUES = ('kernels/spk',
'kernels/pck',
'kernels/lsk')
PATH_SYMBOLS = ('SPK' , 'PCK' , 'LSK' )
KERNELS_TO_LOAD = ( '$SPK/de405s.bsp',
'$PCK/pck00008.tpc',
'$LSK/naif0008.tls')
\begintext
Ring model data.
\begindata
BODY699_RING1_NAME = 'A Ring'
BODY699_RING1 = (122170.0 136780.0 0.1 0.1 0.5)
BODY699_RING1_1_NAME = 'Encke Gap'
BODY699_RING1_1 = (133405.0 133730.0 0.0 0.0 0.0)
BODY699_RING2_NAME = 'Cassini Division'
BODY699_RING2 = (117580.0 122170.0 0.0 0.0 0.0)
\begintext
The kernel pool recognizes values preceded by '@' as time
values. When read, the kernel subsystem converts these
representations into double precision ephemeris time.
Caution: The kernel subsystem interprets the time strings
identified by '@' as TDB. The same string passed as input
to @STR2ET is processed as UTC.
The three expressions stored in the EXAMPLE_TIMES array represent
the same epoch.
\begindata
EXAMPLE_TIMES = ( @APRIL-1-2004-12:34:56.789,
@4/1/2004-12:34:56.789,
@JD2453097.0242684
)
\begintext
The main references for pool routines are found in the help command, the CSPICE source files or the API documentation for the particular routines.
Code Solution¶
from __future__ import print_function
#
# Import the CSPICE-Python interface.
#
import spiceypy
from spiceypy.utils.support_types import SpiceyError
def kervar():
#
# Define the max number of kernel variables
# of concern for this examples.
#
N_ITEMS = 20
#
# Load the example kernel containing the kernel variables.
# The kernels defined in KERNELS_TO_LOAD load into the
# kernel pool with this call.
#
spiceypy.furnsh( 'kervar.tm' )
#
# Initialize the start value. This value indicates
# index of the first element to return if a kernel
# variable is an array. START = 0 indicates return everything.
# START = 1 indicates return everything but the first element.
#
START = 0
#
# Set the template for the variable names to find. Let's
# look for all variables containing the string RING.
# Define this with the wildcard template '*RING*'. Note:
# the template '*RING' would match any variable name
# ending with the RING string.
#
tmplate = '*RING*'
#
# We're ready to interrogate the kernel pool for the
# variables matching the template. spiceypy.gnpool tells us:
#
# 1. Does the kernel pool contain any variables that
# match the template (value of found).
# 2. If so, how many variables?
# 3. The variable names. (cvals, an array of strings)
#
try:
cvals = spiceypy.gnpool( tmplate, START, N_ITEMS )
print( 'Number variables matching template: {0}'.\
format( len(cvals)) )
except SpiceyError:
print( 'No kernel variables matched template.' )
return
#
# Okay, now we know something about the kernel pool
# variables of interest to us. Let's find out more...
#
for cval in cvals:
#
# Use spiceypy.dtpool to return the dimension and type,
# C (character) or N (numeric), of each pool
# variable name in the cvals array. We know the
# kernel data exists.
#
[dim, type] = spiceypy.dtpool( cval )
print( '\n' + cval )
print( ' Number items: {0} Of type: {1}\n'.\
format(dim, type) )
#
# Test character equality, 'N' or 'C'.
#
if type == 'N':
#
# If 'type' equals 'N', we found a numeric array.
# In this case any numeric array will be an array
# of double precision numbers ('doubles').
# spiceypy.gdpool retrieves doubles from the
# kernel pool.
#
dvars = spiceypy.gdpool( cval, START, N_ITEMS )
for dvar in dvars:
print(' Numeric value: {0:20.6f}'.format(dvar))
elif type == 'C':
#
# If 'type' equals 'C', we found a string array.
# spiceypy.gcpool retrieves string values from the
# kernel pool.
#
cvars = spiceypy.gcpool( cval, START, N_ITEMS )
for cvar in cvars:
print(' String value: {0}\n'.format(cvar))
else:
#
# This block should never execute.
#
print('Unknown type. Code error.')
#
# Now look at the time variable EXAMPLE_TIMES. Extract this
# value as an array of doubles.
#
dvars = spiceypy.gdpool( 'EXAMPLE_TIMES', START, N_ITEMS )
print( 'EXAMPLE_TIMES' )
for dvar in dvars:
print(' Time value: {0:20.6f}'.format(dvar))
#
# Done. Unload the kernels.
#
spiceypy.kclear
if __name__ == '__main__':
kervar()
Run the code example
The program runs and first reports the number of kernel pool variables matching the template, 6.
The program then loops over the spiceypy.dtpool 6 times, reporting the name of each pool variable, the number of data items assigned to that variable, and the variable type. Within the spiceypy.dtpool loop, a second loop outputs the contents of the data variable using spiceypy.gcpool or spiceypy.gdpool.
Number variables matching template: 6
BODY699_RING1_1
Number items: 5 Of type: N
Numeric value: 133405.000000
Numeric value: 133730.000000
Numeric value: 0.000000
Numeric value: 0.000000
Numeric value: 0.000000
BODY699_RING1
Number items: 5 Of type: N
Numeric value: 122170.000000
Numeric value: 136780.000000
Numeric value: 0.100000
Numeric value: 0.100000
Numeric value: 0.500000
BODY699_RING2
Number items: 5 Of type: N
Numeric value: 117580.000000
Numeric value: 122170.000000
Numeric value: 0.000000
Numeric value: 0.000000
Numeric value: 0.000000
BODY699_RING1_1_NAME
Number items: 1 Of type: C
String value: Encke Gap
BODY699_RING2_NAME
Number items: 1 Of type: C
String value: Cassini Division
BODY699_RING1_NAME
Number items: 1 Of type: C
String value: A Ring
EXAMPLE_TIMES
Time value: 134094896.789000
Time value: 134094896.789000
Time value: 134094896.789753
Note the final time value differs from the previous values in the final three decimal places despite the intention that all three strings represent the same time. This results from round-off when converting a decimal Julian day representation to the seconds past J2000 ET representation.
Lesson 3: Coordinate Conversions¶
Task Statement¶
Write a program to convert a Cartesian 3-vector representing some location to the other coordinate representations. Use the position of the Moon with respect to Earth in an inertial and non-inertial reference frame as the example vector.
Learning Goals¶
The SpiceyPy system provides functions to convert coordinate tuples between Cartesian and various non Cartesian coordinate systems including conversion between geodetic and rectangular coordinates.
This lesson presents these coordinate transform routines for rectangular, cylindrical, and spherical systems.
Code Solution¶
from __future__ import print_function
from builtins import input
import sys
#
# Import the CSPICE-Python interface.
#
import spiceypy
def coord():
#
# Define the inertial and non inertial frame names.
#
# Initialize variables or set type. All variables
# used in a PROMPT construct must be initialized
# as strings.
#
INRFRM = 'J2000'
NONFRM = 'IAU_EARTH'
r2d = spiceypy.dpr()
#
# Load the needed kernels using a spiceypy.furnsh call on the
# meta kernel.
#
spiceypy.furnsh( 'coord.tm' )
#
# Prompt the user for a time string. Convert the
# time string to ephemeris time J2000 (ET).
#
timstr = input( 'Time of interest: ')
et = spiceypy.str2et( timstr )
#
# Access the kernel pool data for the triaxial radii of the
# Earth, rad[1][0] holds the equatorial radius, rad[1][2]
# the polar radius.
#
rad = spiceypy.bodvrd( 'EARTH', 'RADII', 3 )
#
# Calculate the flattening factor for the Earth.
#
# equatorial_radius - polar_radius
# flat = ________________________________
#
# equatorial_radius
#
flat = (rad[1][0] - rad[1][2])/rad[1][0]
#
# Make the spiceypy.spkpos call to determine the apparent
# position of the Moon w.r.t. to the Earth at 'et' in the
# inertial frame.
#
[pos, ltime] = spiceypy.spkpos('MOON', et, INRFRM,
'LT+S','EARTH' )
#
# Show the current frame and time.
#
print( ' Time : {0}'.format(timstr) )
print( ' Inertial Frame: {0}\n'.format(INRFRM) )
#
# First convert the position vector
# X = pos(1), Y = pos(2), Z = pos(3), to RA/DEC.
#
[ range, ra, dec ] = spiceypy.recrad( pos )
print(' Range/Ra/Dec' )
print(' Range: {0:20.6f}'.format(range) )
print(' RA : {0:20.6f}'.format(ra * r2d) )
print(' DEC : {0:20.6f}'.format(dec* r2d) )
#
# ...latitudinal coordinates...
#
[ range, lon, lat ] = spiceypy.reclat( pos )
print(' Latitudinal ' )
print(' Rad : {0:20.6f}'.format(range) )
print(' Lon : {0:20.6f}'.format(lon * r2d) )
print(' Lat : {0:20.6f}'.format(lat * r2d) )
#
# ...spherical coordinates use the colatitude,
# the angle from the Z axis.
#
[ range, colat, lon ] = spiceypy.recsph( pos )
print( ' Spherical' )
print(' Rad : {0:20.6f}'.format(range) )
print(' Lon : {0:20.6f}'.format(lon * r2d) )
print(' Colat: {0:20.6f}'.format(colat * r2d) )
#
# Make the spiceypy.spkpos call to determine the apparent
# position of the Moon w.r.t. to the Earth at 'et' in the
# non-inertial, body fixed, frame.
#
[pos, ltime] = spiceypy.spkpos('MOON', et, NONFRM,
'LT+S','EARTH')
print()
print( ' Non-inertial Frame: {0}'.format(NONFRM) )
#
# ...latitudinal coordinates...
#
[ range, lon, lat ] = spiceypy.reclat( pos )
print(' Latitudinal ' )
print(' Rad : {0:20.6f}'.format(range) )
print(' Lon : {0:20.6f}'.format(lon * r2d) )
print(' Lat : {0:20.6f}'.format(lat * r2d) )
#
# ...spherical coordinates use the colatitude,
# the angle from the Z axis.
#
[ range, colat, lon ] = spiceypy.recsph( pos )
print( ' Spherical' )
print(' Rad : {0:20.6f}'.format(range) )
print(' Lon : {0:20.6f}'.format(lon * r2d) )
print(' Colat: {0:20.6f}'.format(colat * r2d) )
#
# ...finally, convert the position to geodetic coordinates.
#
[ lon, lat, range ] = spiceypy.recgeo( pos, rad[1][0], flat )
print( ' Geodetic' )
print(' Rad : {0:20.6f}'.format(range) )
print(' Lon : {0:20.6f}'.format(lon * r2d) )
print(' Lat : {0:20.6f}'.format(lat * r2d) )
print()
#
# Done. Unload the kernels.
#
spiceypy.kclear
if __name__ == '__main__':
coord()
Run the code example
Input “Feb 3 2002 TDB” to calculate the Moon’s position. (the ‘TDB’ tag indicates a Barycentric Dynamical Time value).
Time of interest: Feb 3 2002 TDB
Examine the Moon position in the J2000 inertial frame, display the time and frame:
Time : Feb 3 2002 TDB
Inertial Frame: J2000
Convert the Moon Cartesian coordinates to right ascension declination.
Range/Ra/Dec
Range: 369340.815193
RA : 203.643686
DEC : -4.979010
Latitudinal. Note the difference in the expressions for longitude and right ascension though they represent a measure of the same quantity. The RA/DEC system measures RA in the interval [0,2Pi). Latitudinal coordinates measures longitude in the interval (-Pi,Pi].
Latitudinal
Rad : 369340.815193
Lon : -156.356314
Lat : -4.979010
Spherical. Note the difference between the expression of latitude in the Latitudinal system and the corresponding Spherical colatitude. The spherical coordinate system uses the colatitude, the angle measure away from the positive Z axis. Latitude is the angle between the position vector and the x-y (equatorial) plane with positive angle defined as toward the positive Z direction
Spherical
Rad : 369340.815193
Lon : -156.356314
Colat: 94.979010
The same position look-up in a body fixed (non-inertial) frame, IAU_EARTH.
Non-inertial Frame: IAU_EARTH
Latitudinal coordinates return the geocentric latitude.
Latitudinal
Rad : 369340.815193
Lon : 70.986950
Lat : -4.989675
Spherical.
Spherical
Rad : 369340.815193
Lon : 70.986950
Colat: 94.989675
Geodetic. The cartographic lat/lon.
Geodetic
Rad : 362962.836755
Lon : 70.986950
Lat : -4.990249
Lesson 4: Advanced Time Manipulation Routines¶
Task Statement¶
Demonstrate the advanced functions of the time utilities with regard to formatting of time strings for output. Formatting options include altering calendar representations of the time strings. Convert time-date strings between different SpiceyPy-supported formats.
Learning Goals¶
Introduce the routines used for advanced manipulation of time strings. Understand the concept of ephemeris time (ET) as used in SpiceyPy.
Code Solution¶
Caution: Be sure to assign sufficient string lengths for time formats/pictures.
from __future__ import print_function
#
# Import the CSPICE-Python interface.
#
import spiceypy
def xtic():
#
# Assign the META variable to the name of the meta-kernel
# that contains the LSK kernel and create an arbitrary
# time string.
#
CALSTR = 'Mar 15, 2003 12:34:56.789 AM PST'
META = 'xtic.tm'
AMBIGSTR = 'Mar 15, 79 12:34:56'
T_FORMAT1 = 'Wkd Mon DD HR:MN:SC PDT YYYY ::UTC-7'
T_FORMAT2 = 'Wkd Mon DD HR:MN ::UTC-7 YR (JULIAND.##### JDUTC)'
#
# Load the meta-kernel.
#
spiceypy.furnsh( META )
print( 'Original time string : {0}'.format(CALSTR) )
#
# Convert the time string to the number of ephemeris
# seconds past the J2000 epoch. This is the most common
# internal time representation used by the CSPICE
# system; CSPICE refers to this as ephemeris time (ET).
#
et = spiceypy.str2et( CALSTR )
print( 'Corresponding ET : {0:20.6f}\n'.format(et) )
#
# Make a picture of an output format. Describe a Unix-like
# time string then send the picture and the 'et' value through
# spiceypy.timout to format and convert the ET representation
# of the time string into the form described in
# spiceypy.timout. The '::UTC-7' token indicates the time
# zone for the `timstr' output - PDT. 'PDT' is part of the
# output, but not a time system token.
#
timstr = spiceypy.timout( et, T_FORMAT1)
print( 'Time in string format 1 : {0}'.format(timstr) )
timstr = spiceypy.timout( et, T_FORMAT2)
print( 'Time in string format 2 : {0}'.format(timstr) )
#
# Why create a picture by hand when spiceypy can do it for
# you? Input a string to spiceypy.tpictr with the format of
# interest. `ok' returns a boolean indicating whether an
# error occurred while parsing the picture string, if so,
# an error diagnostic message returns in 'xerror'. In this
# example the picture string is known as correct.
#
pic = '12:34:56.789 P.M. PDT January 1, 2006'
[ pictr, ok, xerror] = spiceypy.tpictr(pic)
if not bool(ok):
print( xerror )
exit
timstr = spiceypy.timout( et, pictr)
print( 'Time in string format 3 : {0}'.format( timstr ) )
#
# Two digit year representations often cause problems due to
# the ambiguity of the century. The routine spiceypy.tsetyr
# gives the user the ability to set a default range for 2
# digit year representation. SPICE uses 1969AD as the default
# start year so the numbers inclusive of 69 to 99 represent
# years 1969AD to 1999AD, the numbers inclusive of 00 to 68
# represent years 2000AD to 2068AD.
#
# The defined time string 'AMBIGSTR' contains a two-digit
# year. Since the SPICE base year is 1969, the time subsystem
# interprets the string as 1979.
#
et1 = spiceypy.str2et( AMBIGSTR )
#
# Set 1980 as the base year causes SPICE to interpret the
# time string's "79" as 2079.
#
spiceypy.tsetyr( 1980 )
et2 = spiceypy.str2et( AMBIGSTR )
#
# Calculate the number of years between the two ET
# representations, ~100.
#
print( 'Years between evaluations: {0:20.6f}'.\
format( (et2 - et1)/spiceypy.jyear()))
#
# Reset the default year to 1969.
#
spiceypy.tsetyr( 1969 )
#
# Done. Unload the kernels.
#
spiceypy.kclear
if __name__ == '__main__':
xtic()
Run the code example
Original time string : Mar 15, 2003 12:34:56.789 AM PST
Corresponding ET : 100989360.974561
Time in string format 1 : Sat Mar 15 01:34:56 PDT 2003
Time in string format 2 : Sat Mar 15 01:34 03 (2452713.85760 JDUTC)
Time in string format 3 : 01:34:56.789 A.M. PDT March 15, 2003
Years between evaluations: 100.000000
Lesson 5: Error Handling¶
Task Statement¶
Write an interactive program to return a state vector based on a user’s input. Code the program with the capability to recover from user input mistakes, inform the user of the mistake, then continue to run.
Learning Goals¶
Learn how to write a program that has the capability to recover from expected SPICE errors.
The SpiceyPy error subsystem differs from CSPICE and SPICELIB packages in that the user cannot alter the state of the error subsystem, rather the user can respond to an error signal using try-except blocks. This block natively receives and processes any SpiceyError exception signaled from SpiceyPy. The user can therefore “catch” an error signal so as to respond in an appropriate manner.
Code Solution¶
from __future__ import print_function
from builtins import input
#
# Import the CSPICE-Python interface.
#
import spiceypy
from spiceypy.utils.support_types import SpiceyError
def aderr():
#
# Set initial parameters.
#
SPICETRUE = True
SPICEFALSE= False
doloop = SPICETRUE
#
# Load the data we need for state evaluation.
#
spiceypy.furnsh( 'aderr.tm' )
#
# Start our input query loop to the user.
#
while (doloop):
#
# For simplicity, we request only one input.
# The program calculates the state vector from
# Earth to the user specified target 'targ' in the
# J2000 frame, at ephemeris time zero, using
# aberration correction LT+S (light time plus
# stellar aberration).
#
targ = input( 'Target: ' )
if targ == 'NONE':
#
# An exit condition. If the user inputs NONE
# for a target name, set the loop to stop...
#
doloop = SPICEFALSE
else:
#
# ...otherwise evaluate the state between the Earth
# and the target. Initialize an error handler.
#
try:
#
# Perform the state lookup.
#
[state, ltime] = spiceypy.spkezr(targ, 0., 'J2000',
'LT+S', 'EARTH')
#
# No error, output the state.
#
print( 'R : {0:20.6f} {1:20.6f} '
'{2:20.5f}'.format(*state[0:3]))
print( 'V : {0:20.6f} {1:20.6f} '
'{2:20.6f}'.format(*state[3:6]) )
print( 'LT: {0:20.6f}\n'.format(float(ltime)))
except SpiceyError as err:
#
# What if spiceypy.spkezr signaled an error?
# Then spiceypy signals an error to python.
#
# Examine the value of 'e' to retrieve the
# error message.
#
print( err )
print( )
#
# Done. Unload the kernels.
#
spiceypy.kclear
if __name__ == '__main__':
aderr()
Run the code example
Now run the code with various inputs to observe behavior. Begin the run using known astronomical bodies, e.g. “Moon”, “Mars”, “Pluto barycenter” and “Puck”. Recall the SpiceyPy default units are kilometers, kilometers per second, kilograms, and seconds. The ‘R’ marker identifies the (X,Y,Z) position of the body in kilometers, the ‘V’ marker identifies the velocity of the body in kilometers per second, and the ‘LT’ marker identifies the one-way light time between the bodies at the requested evaluation time.
Target: Moon
R : -291584.616595 -266693.402359 -76095.64756
V : 0.643439 -0.666066 -0.301310
LT: 1.342311
Target: Mars
R : 234536077.419136 -132584383.595569 -63102685.70619
V : 30.961373 28.932996 13.113031
LT: 923.001080
Target: Pluto barycenter
R : -1451304742.838526 -4318174144.406321 -918251433.58736
V : 35.079843 3.053138 -0.036762
LT: 15501.258293
Target: Puck
=====================================================================
===========
Toolkit version: N0066
SPICE(SPKINSUFFDATA) --
Insufficient ephemeris data has been loaded to compute the state of 7
15 (PUCK) relative to 0 (SOLAR SYSTEM BARYCENTER) at the ephemeris ep
och 2000 JAN 01 12:00:00.000.
spkezr_c --> SPKEZR --> SPKEZ --> SPKACS --> SPKAPS --> SPKLTC --> SP
KGEO
=====================================================================
===========
Target:
Perplexing. What happened?
The kernel files named in meta.tm did not include ephemeris data for Puck. When the SPK subsystem tried to evaluate Puck’s position, the evaluation failed due to lack of data, so an error signaled.
The above error signifies an absence of state information at ephemeris time 2000 JAN 01 12:00:00.000 (the requested time, ephemeris time zero).
Try another look-up, this time for “Casper”
Target: Casper
=====================================================================
===========
Toolkit version: N0066
SPICE(IDCODENOTFOUND) --
The target, 'Casper', is not a recognized name for an ephemeris objec
t. The cause of this problem may be that you need an updated version
of the SPICE Toolkit. Alternatively you may call SPKEZ directly if yo
u know the SPICE ID codes for both 'Casper' and 'EARTH'
spkezr_c --> SPKEZR
=====================================================================
===========
Target:
An easy to understand error. The SPICE system does not contain information on a body named ‘Casper.’
Another look-up, this time, “Venus”.
Target: Venus
R : -80970027.540532 -139655772.573898 -53860125.95820
V : 31.166910 -27.001056 -12.316514
LT: 567.655074
Target:
The look-up succeeded despite two errors in our run. The SpiceyPy system can respond to error conditions (not system errors) in much the same fashion as languages with catch/throw instructions.
Lesson 6: Windows, and Cells¶
Programming task¶
Given the times of line-of-sight for a vehicle from a ground station and the times for an acceptable Sun-station-vehicle phase angle, write a program to determine the time intervals common to both configurations.
Learning Goals¶
SpiceyPy implementation of SPICE cells consists of a class that provides an interface to the underlying CSPICE cell structure.
A user should create cells by use of the appropriate SpiceyPy calls. NAIF recommends against manual creation of cells.
A ‘window’ is a type of cell containing ordered, double precision values describing a collection of zero or more intervals.
We define an interval, ‘i’, as all double precision values bounded by and including an ordered pair of numbers,
[ a , b ]
i i
where
a < b
i - i
The intervals within a window are both ordered and disjoint. That is, the beginning of each interval is greater than the end of the previous interval:
b < a
i i+1
A common use of the windows facility is to calculate the intersection set of a number of time intervals.
Code Solution¶
from __future__ import print_function
#
# Import the CSPICE-Python interface.
#
import spiceypy
def win():
MAXSIZ = 8
#
# Define a set of time intervals. For the purposes of this
# tutorial program, define time intervals representing
# an unobscured line of sight between a ground station
# and some body.
#
los = [ 'Jan 1, 2003 22:15:02', 'Jan 2, 2003 4:43:29',
'Jan 4, 2003 9:55:30', 'Jan 4, 2003 11:26:52',
'Jan 5, 2003 11:09:17', 'Jan 5, 2003 13:00:41',
'Jan 6, 2003 00:08:13', 'Jan 6, 2003 2:18:01' ]
#
# A second set of intervals representing the times for which
# an acceptable phase angle exists between the ground station,
# the body and the Sun.
#
phase = [ 'Jan 2, 2003 00:03:30', 'Jan 2, 2003 19:00:00',
'Jan 3, 2003 8:00:00', 'Jan 3, 2003 9:50:00',
'Jan 5, 2003 12:00:00', 'Jan 5, 2003 12:45:00',
'Jan 6, 2003 00:30:00', 'Jan 6, 2003 23:00:00' ]
#
# Load our meta kernel for the leapseconds data.
#
spiceypy.furnsh( 'win.tm' )
#
# SPICE windows consist of double precision values; convert
# the string time tags defined in the 'los'and 'phase'
# arrays to double precision ET. Store the double values
# in the 'loswin' and 'phswin' windows.
#
los_et = spiceypy.str2et( los )
phs_et = spiceypy.str2et( phase )
loswin = spiceypy.stypes.SPICEDOUBLE_CELL( MAXSIZ )
phswin = spiceypy.stypes.SPICEDOUBLE_CELL( MAXSIZ )
for i in range(0, int( MAXSIZ/2 ) ):
spiceypy.wninsd( los_et[2*i], los_et[2*i+1], loswin )
spiceypy.wninsd( phs_et[2*i], phs_et[2*i+1], phswin )
spiceypy.wnvald( MAXSIZ, MAXSIZ, loswin )
spiceypy.wnvald( MAXSIZ, MAXSIZ, phswin )
#
# The issue for consideration, at what times do line of
# sight events coincide with acceptable phase angles?
# Perform the set operation AND on loswin, phswin,
# (the intersection of the time intervals)
# place the results in the window 'sched'.
#
sched = spiceypy.wnintd( loswin, phswin )
print( 'Number data values in sched : '
'{0:2d}'.format(spiceypy.card(sched)) )
#
# Output the results. The number of intervals in 'sched'
# is half the number of data points (the cardinality).
#
print( ' ' )
print( 'Time intervals meeting defined criterion.' )
for i in range( spiceypy.card(sched)//2):
#
# Extract from the derived 'sched' the values defining the
# time intervals.
#
[left, right ] = spiceypy.wnfetd( sched, i )
#
# Convert the ET values to UTC for human comprehension.
#
utcstr_l = spiceypy.et2utc( left , 'C', 3 )
utcstr_r = spiceypy.et2utc( right, 'C', 3 )
#
# Output the UTC string and the corresponding index
# for the interval.
#
print( '{0:2d} {1} {2}'.format(i, utcstr_l, utcstr_r))
#
# Summarize the 'sched' window.
#
[meas, avg, stddev, small, large] = spiceypy.wnsumd( sched )
print( '\nSummary of sched window\n' )
print( 'o Total measure of sched : {0:16.6f}'.format(meas))
print( 'o Average measure of sched : {0:16.6f}'.format(avg))
print( 'o Standard deviation of ' )
print( ' the measures in sched : '
'{0:16.6f}'.format(stddev))
#
# The values for small and large refer to the indexes of the
# values in the window ('sched'). The shortest interval is
#
# [ sched.base[ sched.data + small]
# sched.base[ sched.data + small +1] ];
#
# the longest is
#
# [ sched.base[ sched.data + large]
# sched.base[ sched.data + large +1] ];
#
# Output the interval indexes for the shortest and longest
# intervals. As Python bases an array index on 0, the interval
# index is half the array index.
#
print( 'o Index of shortest interval: '
'{0:2d}'.format(int(small/2)) )
print( 'o Index of longest interval : '
'{0:2d}'.format(int(large/2)) )
#
# Done. Unload the kernels.
#
spiceypy.kclear
if __name__ == '__main__':
win()
Run the code example
The output window has the name `sched’ (schedule).
Output the amount of data held in `sched’ compared to the maximum possible amount.
Number data values in sched : 6
List the time intervals for which a line of sight exists during the time of a proper phase angle.
Time intervals meeting defined criterion.
0 2003 JAN 02 00:03:30.000 2003 JAN 02 04:43:29.000
1 2003 JAN 05 12:00:00.000 2003 JAN 05 12:45:00.000
2 2003 JAN 06 00:30:00.000 2003 JAN 06 02:18:01.000
Finally, an analysis of the `sched’ data. The measure of an interval [a,b] (a <= b) equals b-a. Real values output in units of seconds.
Summary of sched window
o Total measure of sched : 25980.000009
o Average measure of sched : 8660.000003
o Standard deviation of
the measures in sched : 5958.550217
o Index of shortest interval: 1
o Index of longest interval : 0
Lesson 7: Utility and Constants Routines¶
Task Statement¶
Write an interactive program to convert values between various units. Demonstrate the flexibility of the unit conversion routine, the string equality function, and show the version ID function.
Learning Goals¶
SpiceyPy provides several routines to perform commonly needed tasks. Among these:
SpiceyPy also includes a set of functions that return constant values often used in astrodynamics, time calculations, and geometry.
Code Solution¶
from __future__ import print_function
from builtins import input
#
# Import the CSPICE-Python interface.
#
import spiceypy
def tostan(alias):
value = alias
#
# As a convenience, let's alias a few common terms
# to their appropriate counterpart.
#
if alias == 'meter':
#
# First, a 'meter' by any other name is a
# 'METER' and smells as sweet ...
#
value = 'METERS'
elif (alias == 'klicks') \
or (alias == 'kilometers') \
or (alias =='kilometer'):
#
# ... 'klicks' and 'KILOMETERS' and 'KILOMETER'
# identifies 'KM'....
#
value = 'KM'
elif alias == 'secs':
#
# ... 'secs' to 'SECONDS'.
#
value = 'SECONDS'
elif alias == 'miles':
#
# ... and finally 'miles' to 'STATUTE_MILES'.
# Normal people think in statute miles.
# Only sailors think in nautical miles - one
# minute of arc at the equator.
#
value = 'STATUTE_MILES'
else:
pass
#
# Much better. Now return. If the input matched
# none of the aliases, this function did nothing.
#
return value
def units():
#
# Display the Toolkit version string with a spiceypy.tkvrsn
# call.
#
vers = spiceypy.tkvrsn( 'TOOLKIT' )
print('\nConvert demo program compiled against CSPICE '
'Toolkit ' + vers)
#
# The user first inputs the name of a unit of measure.
# Send the name through tostan for de-aliasing.
#
funits = input( 'From Units : ' )
funits = tostan( funits )
#
# Input a double precision value to express in a new
# unit format.
#
fvalue = float(input( 'From Value : ' ))
#
# Now the user inputs the name of the output units.
# Again we send the units name through tostan for
# de-aliasing.
#
tunits = input( 'To Units : ' )
tunits = tostan( tunits )
tvalue = spiceypy.convrt( fvalue, funits, tunits)
print( '{0:12.5f} {1}'.format(tvalue, tunits) )
if __name__ == '__main__':
units()
Run the code example
Run a few conversions through the application to ensure it works. The intro banner gives us the Toolkit version against which the application was linked:
Convert demo program compiled against CSPICE Toolkit CSPICE_N0066
From Units : klicks
From Value : 3
To Units : miles
1.86411 STATUTE_MILES
Now we know. Three kilometers equals 1.864 miles.
Legend states Pheidippides ran from the Marathon Plain to Athens. The modern marathon race (inspired by this event) spans 26.2 miles. How far in kilometers?
Convert demo program compiled against CSPICE Toolkit CSPICE_N0066
From Units : miles
From Value : 26.2
To Units : km
42.16481 km
Task Statement¶
Write a program to output SpiceyPy constants and use those constants to calculate some rudimentary values.
Code Solution¶
from __future__ import print_function
#
# Import the CSPICE-Python interface.
#
import spiceypy
def xconst():
#
# All the function have the same calling sequence:
#
# VALUE = function_name()
#
# some_procedure( function_name() )
#
# First a simple example using the seconds per day
# constant...
#
print( 'Number of (S)econds (P)er (D)ay : '
'{0:19.12f}'.format(spiceypy.spd() ))
#
# ...then show the value of degrees per radian, 180/Pi...
#
print( 'Number of (D)egrees (P)er (R)adian : '
'{0:19.16f}'.format(spiceypy.dpr() ))
#
# ...and the inverse, radians per degree, Pi/180.
# It is obvious spiceypy.dpr() equals 1.d/spiceypy.rpd(), or
# more simply spiceypy.dpr() * spiceypy.rpd() equals 1
#
print( 'Number of (R)adians (P)er (D)egree : '
'{0:19.16f}'.format(spiceypy.rpd() ))
#
# What's the value for the astrophysicist's favorite
# physical constant (in a vacuum)?
#
print( 'Speed of light in KM per second : '
'{0:19.12f}'.format(spiceypy.clight() ))
#
# How long (in Julian days) from the J2000 epoch to the
# J2100 epoch?
#
print( 'Number of days between epochs J2000')
print( ' and J2100 : '
'{0:19.12f}'.format( spiceypy.j2100()
- spiceypy.j2000() ))
#
# Redo the calculation returning seconds...
#
print( 'Number of seconds between epochs' )
print( ' J2000 and J2100 : '
'{0:19.5f}'.format(spiceypy.spd() * \
(spiceypy.j2100() - spiceypy.j2000() ) ))
#
# ...then tropical years.
#
val =(spiceypy.spd()/spiceypy.tyear() ) * \
(spiceypy.j2100()- spiceypy.j2000() )
print( 'Number of tropical years between' )
print( ' epochs J2000 and J2100 : '
'{0:19.12f}'.format(val))
#
# Finally, how can I convert a radian value to degrees.
#
print( 'Number of degrees in Pi/2 radians of arc: '
'{0:19.16f}'.format( spiceypy.halfpi()
* spiceypy.dpr() ))
#
# and degrees to radians.
#
print( 'Number of radians in 250 degrees of arc : '
'{0:19.16f}'.format(250. * spiceypy.rpd() ))
if __name__ == '__main__':
xconst()
Run the code example
Number of (S)econds (P)er (D)ay : 86400.000000000000
Number of (D)egrees (P)er (R)adian : 57.2957795130823229
Number of (R)adians (P)er (D)egree : 0.0174532925199433
Speed of light in KM per second : 299792.457999999984
Number of days between epochs J2000
and J2100 : 36525.000000000000
Number of seconds between epochs
J2000 and J2100 : 3155760000.00000
Number of tropical years between
epochs J2000 and J2100 : 100.002135902909
Number of degrees in Pi/2 radians of arc: 90.0000000000000000
Number of radians in 250 degrees of arc : 4.3633231299858242