March 28, 2005
The extensive scope of the CSPICE 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 a several 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.
This workbook includes several lessons to demonstrate use of the less
celebrated CSPICE routines.
The technical complexity of the various CSPICE subsystems mandates an
extensive, user-friendly documentation set. The set differs somewhat
depending on your choice of development language, FORTRAN, C, or IDL,
but provides the same information with regards to SPICE operation.
The sources for a user needing information concerning the CSPICE System or other NAIF product:
NAIF Required Reading (*.req) documents introduce the functionality of
particular CSPICE subsystems:
cells.req ek.req intrdctn.req problems.req ck.req ellipses.req kernel.req rotation.req cspice.req error.req naif_ids.req scanning.req daf.req frames.req pck.req sclk.req das.req icy.req planes.req sets.req spc.req spk.req symbols.req time.req windows.reqNAIF Users Guides (*.ug) describe the proper use of particular CSPICE tools:
brief.ug convert.ug spacit.ug tictoc.ug chronos.ug inspekt.ug spkmerge.ug tobin.ug ckbrief.ug mkspk.ug states.ug toxfr.ug commnt.ug simple.ug subpt.ug version.ugThese text documents exist in the 'doc' directory of the main Toolkit directory:
../cspice/doc/HTML format documentation
As of delivery N57, the CSPICE distributions include HTML versions of Required Readings and Users Guides, accessible from the HTML documentation directory:
../cspice/doc/html/index.html
All SPICELIB and CSPICE source files include usage and design
information incorporated in a comment block known as the "header."
A header consists of several marked sections:
../cspice/src/Find the CSPICE library source code in:
../cspice/src/cspice/Note: The CSPICE source files have two forms: C files created by the f2c conversion process on a SPICELIB files, indicated with a name of the form "module.c," and wrappers files indicated by names of the form "module_c.c" The f2c converted source code is very difficult to read, refer to the wrapper routines if possible. In some cases, NAIF replaced an f2c converted file with a hand written version.
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.
..cspice/doc/html/cspice/index.html
A set of Microsoft PowerPoint presentations provide a general overview
of the complete CSPICE toolkit. Download the set at:
http://naif.jpl.nasa.gov/naif/tutorials.htmlAccess individual files in the 'office/individual_docs/' directory; an archive of all tutorial files is available in the 'office/packages/' directory.
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:
\begintextand
\begindatato 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:
\begintext ... commentary information on the data assignments ... \begindata ... data assignments ...
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.
The lessons may include kernels a program must load to operate. For
this workbook, a user can download all kernels from the NAIF anonymous
ftp site:
ftp://naif.jpl.nasa.gov/pub/naif/generic_kernels FILE NAME TYPE DESCRIPTION ----------------------- ---- ---------------------- naif0007.tls LSK Generic LSK leapseconds.tls LSK The current leapseconds kernel (naif0007.tls as of May 2004) de405s.bsp SPK Planet Ephemeris SPK pck00007.tpc PCK Generic PCK
The code examples listed in this workbook include corresponding
outputs for the described inputs. The output of a given example on a
particular platform may not exactly match that shown since compilers
and math libraries differ between platform architectures.
Lesson Goals:
This lesson demonstrates us of the kernel subsystem to load, unload, and list loaded kernels. Comprehension of kernel file data access precedence. Data loaded last (later) has precedence over similar data loaded first (earlier).
This lesson requires creation of a SPICE meta kernel.
Knowledge of information in the kernels.req document, the mk.ppt and
intro_to_kernels.ppt tutorial files.
Write a program to load a meta kernel, interrogate the CSPICE system
for the names and types of all loaded kernels, then demonstrate the
unload functionality and the resulting effects.
You can use two versions of a meta kernel with code examples
(meta.ker) in this lesson. Either a kernel with explicit path
information:
\begindata KERNELS_TO_LOAD = ( 'kernels/spk/de405s.bsp', 'kernels/pck/pck00007.tpc', 'kernels/lsk/leapseconds.tls') \begintext... or a more generic meta kernel using the PATH_VALUES/PATH_SYMBOLS functionality to declare path names as variables:
\begintext Define the paths to the kernel directory. Use the PATH_SYMBOLS as aliases to the paths. \begindata PATH_VALUES = ( 'kernels/lsk', 'kernels/spk', 'kernels/pck' ) PATH_SYMBOLS = ( 'LSK', 'SPK', 'PCK' ) KERNELS_TO_LOAD = ( '$LSK/naif0007.tls', '$SPK/de405s.bsp', '$PCK/pck00007.tpc' ) \begintext
#include <stdlib.h> #include <stdio.h> #include <strings.h> #include "SpiceUsr.h" /* Define the maximum length for any string, 80 characters plus one null terminator. */ #define LENOUT 81 int main( int argc, char **argv ) { /* Declare the needed variables: */ SpiceChar file [LENOUT]; SpiceChar type [LENOUT]; SpiceChar source [LENOUT]; SpiceInt i; SpiceInt count; SpiceInt handle; SpiceBoolean found; /* Assign the path name of the meta kernel to META. */ SpiceChar * META = "meta.ker"; /* Load the meta kernel then use KTOTAL to interrogate the SPICE kernel subsystem for the total number of loaded kernel files. */ furnsh_c ( META ); ktotal_c ("ALL", &count ); printf( "Kernel count after load: %ld\n", count ); /* Loop over the number of files; interrogate the SPICE system with kdata_c 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 = 0L; i < count; i++ ) { kdata_c( i, "ALL", LENOUT, LENOUT, LENOUT, file, type, source, &handle, &found ); printf ( "File %s\n", file ); printf ( "Type %s\n", type ); printf ( "Source %s\n", source ); printf ( "\n" ); } /* Unload one kernel then check the count. */ unload_c ( "kernels/spk/de405s.bsp" ); ktotal_c ( "ALL", &count ); /* The subsystem should report one less kernel. */ printf ( "Kernel count after one unload: %ld\n", count ); /* Now unload the meta kernel. This action unloads all files listed in the meta kernel. */ unload_c ( META ); /* Check the count. SPICE should return a count of zero. */ ktotal_c ( "ALL", &count ); printf ( "Kernel count after meta unload: %ld\n", count ); exit(0); }
First we see the number of all loaded kernels returned from the
ktotal_c call:
Kernel count after load: 4Now the kdata_c 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 furnsh_c call.
File meta.ker Type META Source File kernels/spk/de405s.bsp Type SPK Source meta.ker File kernels/pck/pck00007.tpc Type TEXT Source meta.ker File kernels/lsk/naif0007.tls Type TEXT Source meta.ker Kernel count after one unload: 3 Kernel count after meta unload: 0
Lesson Goals:
The lesson demonstrates the CSPICE 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 (cassini.ker) containing PCK-type data, kernels to load, and example time strings:
\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 Name the kernels to load. Use path symbols. \begindata PATH_VALUES = ('kernels/spk', 'kernels/pck', 'kernels/lsk') PATH_SYMBOLS = ('SPK' , 'PCK' , 'LSK' ) KERNELS_TO_LOAD = ( '$SPK/de405s.bsp', '$PCK/pck00007.tpc', '$LSK/leapseconds.tls') \begintext
Knowledge of the material in the kernels.req document and the
intro_to_kernels.ppt tutorial file.
The main references for pool routines are found in the source files or API documentation for the particular routines.
Write a program to retrieve particular string and numeric text kernel
variables, both scalars and arrays. Interrogate the kernel pool for
assigned variable names.
#include <stdlib.h> #include <stdio.h> #include <strings.h> #include "SpiceUsr.h" /* Define the max number of kernel variables of concern for this examples. */ #define N_ITEMS 20 /* Define the maximum length for any string, 80 characters plus one null terminator. */ #define STRLEN 81 int main( int argc, char **argv ) { /* Note, the pool routines return a boolean to 'found' signaling whether the requested variable name exists in the kernel pool. The code solutions do not check the boolean value since the solutions use variables known to exist. In general, code should always check the boolean value to ensure return of valid data. */ /* As usual, type our variables... */ SpiceInt i; SpiceInt j; SpiceInt dim; SpiceInt n_var; SpiceInt n_val; SpiceInt start; SpiceBoolean found; SpiceDouble dvars [N_ITEMS]; SpiceChar cvals [N_ITEMS][STRLEN]; SpiceChar cvars [N_ITEMS][STRLEN]; SpiceChar type; SpiceChar tmplate[12]; /* Load the example kernel containing the kernel variables. The kernels defined in KERNELS_TO_LOAD load into the kernel pool with this call. */ furnsh_c ( "cassini.ker" ); /* Initialize the start value. This values 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. */ strcpy ( tmplate, "*RING*"); /* We're ready to interrogate the kernel pool for the variables matching the template. gnpool_c tells us: 1. Does the kernel pool contain any variables that match the template (value of found). 2. If so, how many variables? (value of n_val) 3. The variable names. (cvals, an array of strings) */ gnpool_c ( tmplate, start, N_ITEMS, STRLEN, &n_val, cvals, &found ); if ( found ) { printf( "No. variables matching template: %ld\n", n_val); } else { puts ( "No kernel variables matched template" ); exit(0); } /* Okay, now we know something about the kernel pool variables of interest to us. Let's find out more... */ for (i=0; i<n_val; ++i ) { /* Use dtpool_c to return the dimension and type, C (character) or N (numeric), of each pool variable name in the cvals array. */ dtpool_c ( cvals[i], &found, &dim, &type ); printf ( "\n%s\n", cvals[i]); printf ( " No. items: %ld Of type: %c\n\n", dim, type ); /* Use the EQSTR routine to test character equality, 'N' or 'C'. */ if ( eqstr_c( "N", &type ) ) { /* If 'type' equals "N", we found a numeric array. In this case any numeric array will be an array of double precision numbers ("doubles"). gdpool_c retrieves doubles from the kernel pool. 'dvars' contains the array of 'n_vars' values. */ gdpool_c ( cvals[i], start, N_ITEMS, &n_var, dvars , &found ); for( j=0; j<n_var; ++j ) { printf( " Numeric value: %f\n", dvars[j] ); } } else if ( eqstr_c( "C", &type ) ) { /* If 'type' equals "C", we found a string array. gcpool_c retrieves string values from the kernel pool. cvars[i] contains the array of 'n_var' values. */ gcpool_c ( cvals[i], start , N_ITEMS, STRLEN , &n_var, cvars , &found ); for( j=0; j<n_var; ++j ) { printf( " String value: %s\n", cvars[j] ); } } } puts( " " ); /* Now look at the kernel variable EXAMPLE_TIMES. Extract this value as an array of doubles. */ gdpool_c ( "EXAMPLE_TIMES", start, N_ITEMS, &n_var, dvars, &found ); puts( "EXAMPLE_TIMES"); for( j=0; j<n_var; ++j ) { printf( " Time value: %f\n", dvars[j] ); } exit(0); }
The program runs and first reports the number of kernel pool variables
matching the template, 6.
No. variables matching template: 6The program then loops over the dtpool_c 6 times, reporting the name of each pool variable, the number of data items assigned to that variable, and the variable type. Within the dtpool_c loop, a second loop outputs the contents of the data variable using gcpool_c or gdpool_c.
BODY699_RING1 No. items: 5 Of type: N Numeric value: 122170.00000000 Numeric value: 136780.00000000 Numeric value: 1.0000000000000D-01 Numeric value: 1.0000000000000D-01 Numeric value: 0.50000000000000 BODY699_RING2 No. items: 5 Of type: N Numeric value: 117580.00000000 Numeric value: 122170.00000000 Numeric value: 0. Numeric value: 0. Numeric value: 0. BODY699_RING1_1_NAME No. items: 1 Of type: C String value: Encke Gap BODY699_RING2_NAME No. items: 1 Of type: C String value: Cassini Division BODY699_RING1_NAME No. items: 1 Of type: C String value: A Ring BODY699_RING1_1 No. items: 5 Of type: N Numeric value: 133405.00000000 Numeric value: 133730.00000000 Numeric value: 0. Numeric value: 0. Numeric value: 0.Note the final time value differs from the previous values in the final two 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.
EXAMPLE_TIMES Time value: 134094896.78900 Time value: 134094896.78900 Time value: 134094896.78975
Lesson Goals:
The CSPICE 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.
Basic knowledge of the standard coordinate systems used in celestial
mechanics. The contents of concepts.ppt and derived_quant.ppt tutorial
files.
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.
#include <stdlib.h> #include <stdio.h> #include <strings.h> #include "SpiceUsr.h" /* Define the length of the time string, 32 characters plus 1 for the null terminator. */ #define LENOUT 33 int main( int argc, char **argv ) { /* Type the variables. */ SpiceInt dim; /* Define the inertial and non inertial frame names. */ SpiceChar inrfrm [] = "J2000"; SpiceChar nonfrm [] = "IAU_EARTH"; SpiceChar timstr [LENOUT]; SpiceDouble et; SpiceDouble range; SpiceDouble ra; SpiceDouble dec; SpiceDouble lat; SpiceDouble colat; SpiceDouble lon; SpiceDouble ltime; SpiceDouble flat; SpiceDouble rad [3]; SpiceDouble pos [3]; /* Load the needed kernels using a furnsh_c call on the meta kernel. */ furnsh_c ( "meta.ker" ); /* Prompt the user for a time string. Convert the time string to ephemeris time J2000 (ET). */ prompt_c ( "Time of interest: ", LENOUT, timstr ); str2et_c ( timstr, &et ); /* Access the kernel pool data for the triaxial radii of the Earth, rad[0] holds the equatorial radius, rad[2] the polar radius. */ bodvrd_c ( "Earth", "RADII", 3, &dim, rad); /* Calculate the flattening factor for the Earth. equatorial_radius - polar_radius flat = ________________________________ equatorial_radius */ flat = (rad[0] - rad[2])/rad[0]; /* Make the spkpos_c call to determine the apparent position of the Moon w.r.t. to the Earth at 'et' in the inertial frame. */ spkpos_c ( "MOON", et, inrfrm, "LT+S","EARTH", pos, <ime); /* Show the current frame and time. */ printf ( " Time : %s\n" , timstr ); printf ( " Inertial Frame: %s\n", inrfrm ); /* First convert the position vector X = pos[0], Y = pos[1], Z = pos[2], to RA/DEC. */ recrad_c ( pos, &range, &ra, &dec ); printf ( " Range/Ra/Dec\n" ); printf ( " Range: %f\n", range ); printf ( " RA : %f\n", ra * dpr_c() ); printf ( " DEC : %f\n", dec* dpr_c() ); /* ...latitudinal coordinates... */ reclat_c ( pos, &range, &lon, &lat ); printf ( " Latitudinal\n" ); printf ( " Rad : %f\n", range); printf ( " Lon : %f\n", lon * dpr_c() ); printf ( " Lat : %f\n", lat * dpr_c() ); /* ...spherical coordinates use the colatitude, the angle from the Z axis. */ recsph_c ( pos, &range, &colat, &lon ); printf ( " Spherical\n"); printf ( " Rad : %f\n", range ); printf ( " Lon : %f\n", lon * dpr_c() ); printf ( " Colat: %f\n", colat * dpr_c() ); /* Make the spkpos_c call to determine the apparent position of the Moon w.r.t. to the Earth at 'et' in the non-inertial, body fixed, frame. */ spkpos_c ( "MOON", et, nonfrm, "LT+S","EARTH", pos, <ime); puts ( " " ); printf ( " Non-inertial Frame: %s\n", nonfrm ); /* ...latitudinal coordinates... */ reclat_c ( pos, &range, &lon, &lat ); printf ( " Latitudinal\n" ); printf ( " Rad : %f\n", range ); printf ( " Lon : %f\n", lon * dpr_c() ); printf ( " Lat : %f\n", lat * dpr_c() ); /* ...spherical coordinates... */ recsph_c ( pos, &range, &colat, &lon ); printf ( " Spherical\n" ); printf ( " Rad : %f\n", range ); printf ( " Lon : %f\n", lon * dpr_c() ); printf ( " Colat: %f\n", colat * dpr_c() ); /* ...finally, convert the position to geodetic coordinates. */ recgeo_c ( pos, rad[0], flat, &lon, &lat, &range ); printf ( " Geodetic\n" ); printf ( " Rad : %f\n", range ); printf ( " Lon : %f\n", lon * dpr_c() ); printf ( " Lat : %f\n", lat * dpr_c() ); puts ( " " ); exit(0); }
Input a time/date at which to calculate the Moon's position. (the
'TDB' tag indicates a Barycentric Dynamical Time value).
Time of interest: Feb 3 2002 TDBExamine the Moon position in the J2000 inertial frame, display the time and frame:
Time : Feb 3 2002 TDB Inertial Frame: J2000Convert the Moon Cartesian coordinates to right ascension declination.
Range/Ra/Dec Range: 369340.815193 RA : 203.643686 DEC : -4.979010Latitudinal. 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 : -4.979010Spherical. 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: 94.979010The same position look-up in a body fixed (non-inertial) frame, IAU_EARTH.
Non-inertial Frame: IAU_EARTHLatitudinal coordinates return the geocentric latitude.
Latitudinal Rad : 369340.815193 Lon : 70.973950 Lat : -4.989675Spherical.
Spherical Rad : 369340.815193 Lon : 70.973950 Colat: 94.989675Geodetic. The cartographic lat/lon.
Geodetic Rad : 362962.836755 Lon : 70.973950 Lat : -4.990249
Lesson Goals:
Introduce the routines used for advanced manipulation of time strings. Understand the concept of ephemeris time (ET) as used in CSPICE.
Knowledge of the time.req document, the time.ppt, lsk_and_sclk.ppt,
and other_functions.ppt tutorial files.
Also, examine the header of timout_c for a list of the string markers used by timout_c and tpictr_c to describe time string format. Always keep in mind str2et_c assumes 'UTC' unless indicated otherwise.
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 CSPICE-supported formats.
Caution: Be sure to assign sufficient string lengths for time
formats/pictures.
#include <stdlib.h> #include <stdio.h> #include <strings.h> #include "SpiceUsr.h" /* Define the maximum length for any string, 80 characters plus one null terminator. */ #define STRLEN 81 int main( int argc, char **argv ) { /* Declare the needed variables: */ SpiceDouble et; SpiceDouble et1; SpiceDouble et2; SpiceBoolean ok; SpiceChar error [STRLEN]; SpiceChar pictr [STRLEN]; SpiceChar timstr[STRLEN]; /* Assign the LSK variable to the name of the leapsecond, kernel and create an arbitrary time string. */ SpiceChar * CALSTR = "Mar 15, 2003 12:34:56.789 AM PST"; SpiceChar * LSK = "kernels/lsk/leapseconds.tls"; SpiceChar * AMBIGSTR = "Mar 15, 79 12:34:56"; /* Load the leapseconds kernel. */ furnsh_c ( LSK ); printf ( "Original time string : %s\n", 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). */ str2et_c ( CALSTR, &et ); printf ( "Corresponding ET : %f\n", et ); /* Make a picture of an output format. Describe a Unix-like time string then send the picture and the 'et' value through timout_c to format and convert the ET representation of the time string into the form described in timout_c. 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. */ timout_c ( et, "Wkd Mon DD HR:MN:SC PDT YYYY ::UTC-7", STRLEN, timstr ); printf ( "Time in string format 1 : %s\n", timstr ); /* Create another picture, this time combine a calendar, 2 digit year , with Julian Day format. */ timout_c ( et, "Wkd Mon DD HR:MN ::UTC-7 YR (JULIAND.##### JDUTC)", STRLEN, timstr ); printf ( "Time in string format 2 : %s\n", timstr ); /* Why create a picture by hand when CSPICE can do it for you? Input a string to tpictr_c 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 'error'. In this example, no need exists to check the error flag since the picture string is known as correct.. */ tpictr_c ( "12:34:56.789 P.M. PDT January 1, 2006", STRLEN, STRLEN, pictr, &ok, error); timout_c ( et, pictr, STRLEN, timstr ); printf ("Time in string format 3 : %s\n", timstr ); /* Two digit year representations often cause problems due to the ambiguity of the century. The routine tsetyr_c 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. */ str2et_c ( AMBIGSTR, &et1 ); /* Set 1980 as the base year causes CSPICE to interpret the time string's "79" as 2079. */ tsetyr_c ( 1980 ); str2et_c ( AMBIGSTR, &et2 ); /* Calculate the number of years between the two ET representations, ~100. */ printf ( "Years between evaluations : %f\n", (et2 - et1)/jyear_c() ); exit(0); }
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 Goal:
This lesson introduces the basics of the error subsystem and its various the response modes: DEFAULT, RETURN, ABORT, RETURN, IGNORE, the error output modes: SHORT, LONG, EXPLAIN TRACEBACK, DEFAULT, ALL, NONE, and the error traceback message.
Knowledge of material in the error.req document and the exceptions.ppt
tutorial file. Comprehension of the catch/throw concept.
Show the behavior of the various error modes by writing a program to
signal an error, check for an error signal, set the long and short
error strings, set error behavior (DEFAULT, RETURN, ABORT, RETURN).
#include <stdlib.h> #include <stdio.h> #include <strings.h> #include "SpiceUsr.h" /* Define the maximum length for any string, 80 characters plus one null terminator. */ #define STRLEN 81 void doerr(); int main( int argc, char **argv ) { /* Declare the needed variables: */ SpiceChar errcon[STRLEN]; SpiceBoolean doloop = SPICETRUE; /* Check into the error subsystem to create a traceback showing the call tree. A chkout_c must balance every chkin_c. */ chkin_c ( "ERRSYSC" ); /* Before we start, what's the initial (default) error state? erract_c both sets the state and reports the state. */ erract_c ( "GET", STRLEN, errcon ); printf ( "Default error state: %s\n", errcon ); /* Now start an input loop so we can try different settings for error response. */ do { /* Again use ERRACT to retrieve the current error mode. */ erract_c ( "GET", STRLEN, errcon ); printf ( "Current error state: %s\n", errcon ); /* Okay, input one of the response settings strings then set the error subsystem response to that value. */ prompt_c ( "Set error condition (DEFAULT, REPORT, " "ABORT, RETURN, IGNORE) :", STRLEN, errcon ); erract_c ( "SET", STRLEN, errcon ); /* Cause an error signal. */ doerr(); /* Check for an error signal via a call to FAILED. At this point we see an important difference between the error mode's response to an error signal. */ if ( !failed_c() ) { puts( "No error signal noted." ); } else { puts( "Error signal noted." ); } } while ( doloop ); /* Check out of the error subsystem tho' we'll never hit this call. */ chkout_c ( "ERRSYSC" ); exit(0); } /* This subroutine initiates a SPICE error signal. */ void doerr () { /* Check into the error subsystem as before. */ chkin_c ("DOERR"); /* Let's signal an error. The string passed by setmsg_c is the long error message. You may place markers in the long message string then later substitute other data items for those markers. */ setmsg_c ( "A truly horrendous event occurred " "during execution of this program. " "Data added to long error message string: " "A double #, an int #, and a string #." ); /* Now substitute other data into the long message string. Note the substitutions work on the first found marker. */ errdp_c ( "#", 186282.397 ); errint_c ( "#", 666 ); errch_c ( "#", "A STRING" ); /* SIGERR causes the error signal with the string passed from SETMSG. Set the error flag in the SPICE error subsystem and execute the proper error response. */ sigerr_c ( "OOPS(SOMETHINGBAD)" ); chkout_c ( "DOERR" ); }
o- Demo the DEFAULT mode:
Default error state: DEFAULT Current error state: DEFAULTThe subsystem is in error state DEFAULT. Let the subsystem run to the error signal in DEFAULT mode:
Set error condition (DEFAULT,REPORT,ABORT,RETURN,IGNORE):defaultWhat subsystem reaction occurs in this state?
=================================================================== Toolkit version: N0057 OOPS(SOMETHINGBAD) -- A truly horrendous event occurred during execution of this program. Data added to long error message string: A double 1.8628239700000E+05, an int 666, and a string A STRING. A traceback follows. The name of the highest level module is first. ERRSYSF --> DOERR Oh, by the way: The SPICELIB error handling actions are USER-TAILORABLE. You can choose whether the Toolkit aborts or continues when errors occur, which error messages to output, and where to send the output. Please read the ERROR "Required Reading" file, or see the routines ERRACT, ERRDEV, and ERRPRT. ===================================================================Notice we see no error signal status line. The program quit when it signaled an error. The program output the error messages, an additional information blurb ("Oh by the way"), the Toolkit version, and the traceback list.
o- Rerun the program in REPORT mode:
Default error state: DEFAULT Current error state: DEFAULT Set error condition (DEFAULT,REPORT,ABORT,RETURN,IGNORE) :reportHow does the REPORT reaction differ from DEFAULT? A demo to illustrate...
=================================================================== Toolkit version: N0057 OOPS(SOMETHINGBAD) -- A truly horrendous event occurred during execution of this program. Data added to long error message string: A double 1.8628239700000E+05, an int 666, and a string A STRING. A traceback follows. The name of the highest level module is first. ERRSYSF --> DOERR =================================================================== Error signal noted. Current error state: REPORT Set error condition (DEFAULT, REPORT, ABORT, RETURN, IGNORE) :The error output ceases after the traceback then returns into the calling routine. Note the error signal marker indicates detection of the signal. The subsystem in REPORT mode does not print the information blurb. The CSPICE system can continue to run after an error signal with the error state set to REPORT - this mode flags an error then allows the program to continue the run. It may happen that the cause of the error condition causes instability in the CSPICE system.
o- Rerun to test ABORT mode:
Default error state: DEFAULT Current error state: DEFAULT Set error condition (DEFAULT,REPORT,ABORT,RETURN,IGNORE) :abortHow does the subsystem respond in ABORT mode?
=================================================================== Toolkit version: N0057 OOPS(SOMETHINGBAD) -- A truly horrendous event occurred during execution of this program. Data added to long error message string: A double 1.8628239700000E+05, an int 666, and a string A STRING. A traceback follows. The name of the highest level module is first. ERRSYSF --> DOERR ===================================================================ABORT responds quite like DEFAULT except the error output does not include the information blurb shown in the DEFAULT output. All execution stops when the error signals.
o- Run the program to demo the RETURN mode:
Default error state: DEFAULT Current error state: DEFAULT Set error condition (DEFAULT,REPORT,ABORT,RETURN,IGNORE) :returnRETURN mode provides the highest measure of flexibility to deal with error signals. On output:
=================================================================== Toolkit version: N0057 OOPS(SOMETHINGBAD) -- A truly horrendous event occurred during execution of this program. Data added to long error message string: A double 1.8628239700000E+05, an int 666, and a string A STRING. A traceback follows. The name of the highest level module is first. ERRSYSF --> DOERR =================================================================== Error signal noted. Current error state: RETURNThe subroutine signals an error then returns similar to REPORT mode. However, this mode includes another property. If we make another pass through the command loop:
Set error condition (DEFAULT, REPORT, ABORT, RETURN, IGNORE):return Error signal noted. Current error state: RETURNWe see no error output. The main property of the RETURN mode is to allow program execution to continue but immediately return from all CSPICE routines that check the state of the return_c function. This mode restricts program flow after an error signal.
o- And the final mode to test, IGNORE:
Default error state: DEFAULT Current error state: DEFAULT Set error condition (DEFAULT,REPORT,ABORT,RETURN,IGNORE) :ignore No error signal noted. Current error state: IGNORE Set error condition (DEFAULT,REPORT,ABORT,RETURN,IGNORE) :No error output, no error signal. IGNORE mode prevents expression of all error subsystem functions; the subsystem does not set RETURN or FAILED. While using IGNORE mode the user cannot identify an error signal. Carefully consider program requirements before any use of IGNORE mode.
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.
#include <stdlib.h> #include <stdio.h> #include <strings.h> #include "SpiceUsr.h" /* Define the maximum length for any string, 80 characters plus one null terminator. */ #define STRLEN 81 int main( int argc, char **argv ) { /* Declare the needed variables: */ SpiceChar targ [STRLEN]; /* Set a flag to start/stop and continue the inquiry loop. */ SpiceBoolean doloop = SPICETRUE; SpiceDouble state[6]; SpiceDouble ltime; /* The RETURN mode signals an error then returns to the caller. Just what we need. REPORT mode performs almost the same function as RETURN, however RETURN mode sets the return_c() value to TRUE and so the program does not execute those CSPICE routines that check the return_c() value. Consider REPORT mode useful for debugging. */ erract_c ( "SET", STRLEN, "RETURN" ); /* Load the data we need for state evaluation. */ furnsh_c ( "meta.ker" ); /* 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). */ prompt_c ( "Target: ", STRLEN, targ ); if ( eqstr_c( 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. */ spkezr_c ( targ, 0., "J2000", "LT+S", "EARTH", state, <ime ); /* What if the program can't perform the evaluation? Since we set the error subsystem to REPORT we know a failed spkezr_c call sets the failed_c flag to SPICETRUE then returns control to the calling routine. The CSPICE system also outputs an error message informing the user of the problem's cause. Examine the state of failed_c() to determine if we output a state vector or not. */ if ( ! failed_c() ) { printf ( "R : %17.5f %17.5f %17.5f\n", state[0] , state[1], state[2] ); printf ( "V : %17.5f %17.5f %17.5f\n", state[3] , state[4], state[5] ); printf ( "LT: %f\n", ltime ); } else { /* Problem. Something went wrong. Reset the error subsystem for another pass. */ reset_c(); } } } exit(0); }
Now run the code with various inputs to observe behavior. Begin the
run using known astronomical bodies. Recall the CSPICE 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 : -291584.61659 -266693.40236 -76095.64756 V : 0.64353 -0.66608 -0.30132 LT: 1.342311 Target: Mars R : 234536077.41914 -132584383.59557 -63102685.70619 V : 30.95976 28.93646 13.11449 LT: 923.001080 Target: Pluto barycenter R : -1451304742.83853 -4318174144.40632 -918251433.58736 V : 35.03838 3.06560 -0.01514 LT: 15501.258293 Target: Puck =================================================================== Toolkit version: N0057 SPICE(SPKINSUFFDATA) -- Insufficient ephemeris data has been loaded to compute the state of 715 (PUCK) relative to 0 (SOLAR SYSTEM BARYCENTER) at the ephemeris epoch 2000 JAN 01 12:00:00.000. A traceback follows. The name of the highest level module is first. spkezr_c --> SPKEZR --> SPKEZ --> SPKAPP --> SPKSSB --> S ===================================================================Perplexing. What happened?
The kernel files named in meta.ker 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). Since the program set the error mode to RETURN, program execution continues.
Try another look-up.
Target: Casper =================================================================== Toolkit version: N0057 SPICE(IDCODENOTFOUND) -- The target, 'Casper', is not a recognized name for an ephemeris object. The cause of this problem may be that you need an updated version of the SPICE Toolkit. Alternatively you may call SPKEZ directly if you know the SPICE ID codes for both 'Casper' and 'EARTH' A traceback follows. The name of the highest level module is first. spkezr_c --> SPKEZR ===================================================================An easy to understand error. The SPICE system does not contain information on a body named 'Casper.'
Another look-up, this time, something easy.
Target: Venus R : -80970027.54053 -139655772.57390 -53860125.95820 V : 31.16969 -27.00018 -12.31622 LT: 567.655074The look-up succeeded despite two errors in our run. The CSPICE system can respond to error conditions (not system errors) in much the same fashion as languages with catch/throw instructions.
Lesson Goal:
This lesson introduces the concepts of the CSPICE data types 'cell' and 'window. A 'cell' is as the basis for set calculations in CSPICE. A 'window' permits a user to manipulate continuous intervals of the real line. A 'window' is nothing more than an ordered, double precision cell that contains zero or more intervals
An interval being an ordered pair of numbers,
[ a(i), b(i) ]where
a(i) < b(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(i) < a(i+1)A common use of a window is to calculate when the time intervals covering known events, eclipses, occultation, right ascension within a certain value, etc intersect.
Knowledge of cells.req, sets.req, and windows.req documents, as well
as the other_functions.ppt tutorial file.
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.
#include <stdio.h> #include "SpiceUsr.h" #include <stdlib.h> #include <string.h> #define MAXSIZ 8 /* Define the maximum length for a UTC string, 25 characters plus one null terminator. */ #define UTCLEN 26 int main( int argc, char **argv ) { /* Define our variable types. Define the cells to use as windows. The windows can hold 8 data values i.e. four intervals. */ SPICEDOUBLE_CELL ( loswin, MAXSIZ ); SPICEDOUBLE_CELL ( phswin, MAXSIZ ); SPICEDOUBLE_CELL ( sched , MAXSIZ ); SpiceInt i; SpiceInt small; SpiceInt large; SpiceChar utcstr[2][UTCLEN]; /* Define sets 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. */ SpiceChar los [MAXSIZ][UTCLEN] = { "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 exits between the ground station, the body and the Sun. */ SpiceChar phase [MAXSIZ][UTCLEN] = { "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" }; SpiceDouble left; SpiceDouble right; SpiceDouble meas; SpiceDouble avg; SpiceDouble stddev; SpiceDouble los_et [MAXSIZ]; SpiceDouble phs_et [MAXSIZ]; /* Load our meta kernel for the leapseconds data. */ furnsh_c ( "meta.ker" ); /* Windows consist of double precision values, convert the time tags defined in the LOS and PHASE arrays to double precision ET. Store the double values in the loswin and phswin arrays. */ for ( i=0; i < MAXSIZ; ++i ) { str2et_c ( los[i] , &los_et[i] ); str2et_c ( phase[i], &phs_et[i] ); } /* Initialize the cells from the double precision arrays, then validate the cells as windows. Since we use 4 intervals, set the window to accept 8 (MAXSIZ) data values ( 4 * 2 = 8 ). Since we require no more than 8 data values, assign a window size of 8. */ memmove ( (SpiceDouble*)loswin.data, los_et, MAXSIZ * sizeof(SpiceDouble) ); memmove ( (SpiceDouble*)phswin.data, phs_et, MAXSIZ * sizeof(SpiceDouble) ); wnvald_c ( MAXSIZ, MAXSIZ, &loswin ); wnvald_c ( MAXSIZ, MAXSIZ, &phswin ); wnvald_c ( MAXSIZ, MAXSIZ, &sched ); /* 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, place the results in the window 'sched'. */ wnintd_c ( &loswin, &phswin, &sched ); puts ( " " ); printf ( "No. data values in sched : %d\n", (int)card_c(&sched) ); printf ( "Space available for values in sched : %d\n", (int)size_c(&sched) ); /* Output the results. The number of intervals in 'sched' is half the number of data points (the cardinality). Use a call to card_c to retrieve the window's cardinality. */ puts ( " " ); puts ( "Time intervals meeting defined criterion."); for ( i=0; i < card_c(&sched)/2 ; ++i ) { /* Extract from the derived 'sched' the values defining the time intervals, [small, large]. */ wnfetd_c ( &sched, i, &left, &right ); /* Convert the ET values to UTC for human comprehension. */ et2utc_c ( left , "C", 3, UTCLEN, utcstr[0] ); et2utc_c ( right, "C", 3, UTCLEN, utcstr[1] ); /* Output the UTC string and the corresponding index for the interval. */ printf ( " %d %s %s\n", (int)i, utcstr[0], utcstr[1] ); } puts ( " " ); puts ( "Summary of sched window" ); wnsumd_c ( &sched, &meas, &avg, &stddev, &small, &large ); /* Summarize the 'sched' window. */ printf( "o Total measure of sched : %12.5f\n", meas ); printf( "o Average measure of sched : %12.5f\n", avg ); printf( "o Standard deviation of\n " ); printf( " the measures in sched : %12.5f\n", stddev ); /* The values for small and large refer to the indexes of the values in the window ('sched'). The shortest interval is [ SPICE_CELL_ELEM_D( &sched, small), SPICE_CELL_ELEM_D( &sched, small+1) ]; the longest is [ SPICE_CELL_ELEM_D( &sched, large), SPICE_CELL_ELEM_D( &sched, large+1) ]; Output the indexes for the shortest and longest intervals. As C bases an array index on 0, the interval index is half the array index. */ printf ( "o Index of shortest interval: %d\n", (int)small/2 ); printf ( "o Index of longest interval : %d\n", (int)large/2 ); exit (0); }
The output window has the name SCHED (schedule).
Output the amount of data held in SCHED compared to the maximum possible amount.
No. data values in SCHED : 6 Space available for values in SCHED : 8List 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 02:18:01.000Finally, 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 : 25980.00001 o Average measure of SCHED : 8660.00000 o Standard deviation of the measures in SCHED : 5958.55022 o Index of shortest interval: 1 o Index of longest interval : 0
Lesson Goals:
CSPICE provides several routines to perform commonly needed tasks. Among these include calls to convert values between unit expressions, determine the equality of strings, and indicate whether a file exists.
CSPICE also includes a set of functions that return constant values often used in astrodynamics, time calculations, and geometry.
The references used to define or calculate the constants functions are
found in the source code file and/or the API reference. Also reference
the other_functions.ppt tutorial file.
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.
#include <stdio.h> #include <stdlib.h> #include <string.h> #include "SpiceUsr.h" #define UTCLEN 32 void tostan ( SpiceChar * alias ); int main( int argc, char **argv ) { /* Define the few variables needed for data input and output. */ SpiceChar funits [UTCLEN]; SpiceChar tunits [UTCLEN]; SpiceChar fromstr[UTCLEN]; SpiceDouble fvalue; SpiceDouble tvalue; /* Define the tkvrsn_c return value. */ ConstSpiceChar * vers; /* Display the Toolkit version string with a tkvrsn_c call. */ vers = tkvrsn_c( "TOOLKIT" ); printf( "\n Convert demo program compiled against " "CSPICE Toolkit %s\n\n ", vers ); /* The user first inputs the name of a unit of measure. Send the name through TOSTAN for de-aliasing. */ prompt_c ( "From Units : ", UTCLEN, funits ); tostan ( funits ); /* Input a double precision value to express in a new unit format. */ prompt_c ( "From Value : ", UTCLEN, fromstr ); prsdp_c ( fromstr, &fvalue ); /* Now the user inputs the name of the output units. Again we send the units name through TOSTAN for de-aliasing. */ prompt_c ( "To Units : ", UTCLEN, tunits ); tostan ( tunits ); convrt_c ( fvalue, funits, tunits, &tvalue ); printf ( "%f %s\n", tvalue, tunits ); exit(0); } void tostan ( SpiceChar * alias ) { /* As a convenience, let's alias a few common terms to their appropriate counterpart. Use eqstr_c to compare strings. The comparison ignores letter case and trailing/leading spaces. */ if ( eqstr_c ( alias, "meter" ) ) { /* First, a 'meter' by any other name is a 'METER' and smells as sweet ... */ strcpy ( alias, "METERS"); } else if ( eqstr_c ( alias, "clicks" ) || eqstr_c ( alias, "kilometers" ) || eqstr_c ( alias, "kilometer" ) ) { /* ... 'clicks' and 'KILOMETERS' and 'KILOMETER' identifies 'KM'.... */ strcpy ( alias, "KM"); } else if ( eqstr_c ( alias, "secs") ) { /* ... 'secs' to 'SECONDS'. */ strcpy ( alias, "SECONDS"); } else if ( eqstr_c ( 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. */ strcpy ( alias, "STATUTE_MILES"); } /* Much better. Now return. If the input matched none of the aliases, this routine did nothing. */ }
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_N0057 >From Units : clicks >From Value : 3 To Units : miles 1.8641135767120 STATUTE_MILESNow we know. Three kilometers equals 1.864 miles.
Pheidippides ran 26.2 miles from the Marathon Plain to Athens. How far in kilometers?
>From Units : miles >From Value : 26.2 To Units : km 42.164812800000 km
Write a program to output CSPICE constants and use those constants to
calculate some rudimentary values.
#include <stdlib.h> #include <stdio.h> #include <strings.h> #include "SpiceUsr.h" int main( int argc, char **argv ) { /* All the functions have the same calling sequence: VALUE = function_name(); some_procedure( function_name() ); printf ( "%19.12f\n", function_name() ); First a simple example using the seconds per day constant... */ printf ("Number of (S)econds (P)er (D)ay : %19.12f\n", spd_c() ); /* ...then show the value of degrees per radian, 180/Pi... */ printf ("Number of (D)egrees (P)er (R)adian : %19.16f\n", dpr_c() ); /* ...and the inverse, radians per degree, Pi/180. It is obvious dpr_c() equals 1.0/rpd_c(), or more simply dpr_c() * rpd_c() equals 1.0. */ printf("Number of (R)adians (P)er (D)egree : %19.16f\n", rpd_c() ); /* What's the value for the astrophysicist's favorite physical constant (in a vacuum)? */ printf ("Speed of light in KM per second : %19.12f\n", clight_c() ); /* How long (in Julian days) from the J2000 epoch to the J2100 epoch? */ printf ("Number of days between epochs J2000 \n" ); printf (" and J2100 : %19.12f\n", j2100_c() - j2000_c() ); /* Redo the calculation returning seconds... */ printf ("Number of seconds between epochs\n" ); printf (" J2000 and J2100 : %19.5f\n", spd_c() * (j2100_c() - j2000_c() ) ); /* ...then tropical years. */ printf ( "Number of tropical years between\n" ); printf ( " epochs J2000 and J2100 : %19.12f\n", ( spd_c() / tyear_c() ) * (j2100_c() - j2000_c() ) ); /* Finally, how can I convert a radian value to degrees. */ printf ("Number of degrees in Pi/2 radians of arc : %19.16f\n", halfpi_c() * dpr_c() ); /* and degrees to radians. */ printf ("Number of radians in 250 degrees of arc : %19.16f\n", 250. * rpd_c() ); exit(0); }
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