PCK Required Reading

Index Page PCK Required Reading
## Table of Contents
       PCK Required Reading
          Abstract
             Intended Audience
             References
          Introduction
             Body Codes
             Epochs and Reference Frames
             Planetocentric Coordinates
          Using the PCK System: Overview
          Orientation Models used by PCK Software
       The Two Formats of PCK files
             Detection of Non-native Text Files
             DAF Run-Time Binary File Format Translation
          NAIF Text Kernel Format
          Text PCK Contents
             Text PCK Kernel Variable Names
             Restrictions on the Form of Orientation Models in Text PCK Kernels
             Models for the Sun, Planets, and Asteroids in Text PCK Kernels
             Models for Satellites in Text PCK Kernels
             Epoch and Frame Specifications in Text PCK Kernels
             Shape models in Text PCK Kernels
             Summary of PCK Variables used in Text PCK Kernels by CSPICE
          Creating and Modifying Text PCKs
          Binary PCK Kernel Format
             Segments--The Fundamental PCK Building Blocks
             The Comment Area
             Binary PCK Data Types
             Supported Data Types
             Type 2: Chebyshev (Angles only)
             Type 3: Chebyshev (Angles and derivatives)
          Creating Binary PCKs
       PCK Software
          Getting PCK Data into Your Program
             Loading Text PCK Kernels
             Loading Binary PCK Kernels
             Unloading Binary PCK Kernels
          Binary PCK Coverage Summary Routines
          Access Routines
             High-Level PCK Data Access
             Low-Level PCK Data Access
          Examples
             Transforming a body-fixed state to the inertial J2000 frame
          Creating a binary PCK file, type 03.
          Summary of Calling Sequences
       Appendix A: Sample Text PCK file
Top # PCK Required Reading Last revised on 2009 APR 15 by B. V. Semenov. Top ## Abstract The Planetary Constants Kernel (PCK) subsystem provides cartographic and physical constants data for Solar System bodies. CSPICE software uses these data when determining observation geometry dependent on the size, shape, and orientation of planets, natural satellites, comets, and asteroids. Top ### Intended Audience This document is recommended reading for all users of PCK files. Top ### References All references are to NAIF documents. The notation [Dn] refers to NAIF document numbers. `1.` [218] KERNEL Required Reading (kernel.req). `2.` [219] NAIF IDS Required Reading (naif_ids.req). `3.` [168] SPK Required Reading (spk.req). `4.` [225] TIME Required Reading (time.req). `5.` [214] ROTATIONS Required Reading (rotation.req). `6.` [167] Double Precision Array Files (DAF) Required Reading (daf.req). `7.` [195] ``Planetary Geodetic Control Using Satellite Imaging,'' Journal of Geophysical Research, Vol. 84, No. B3, March 10, 1979, by Thomas C. Duxbury. `8.` ``Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: 2000.'' Top ## Introduction The functionality of the PCK subsystem is supplied by data files called ``PCK files'' (or PCKs) and by CSPICE subroutines that can read and interpret the data in these files. Historically, only one type of PCK existed, the text PCK file (called the "P_constants kernel.") These ASCII files can be easily viewed and modified via text editor. The current SPICE system also supports a binary PCK. These files contain more precise body orientation information in binary format, this format permits large amounts of data to be stored and quickly accessed. Binary PCK files exists only for the moon, earth, and the asteroid Eros. The purpose of the PCK and associated software is to provide SPICE users a convenient mechanism for supplying planetary physical constants to application programs. CSPICE software reads files conforming to these formats and returns both the data contained in such files and a few commonly used numeric quantities derived from the kernel data. Top ### Body Codes NAIF software uses a system of integer codes to conveniently represent both celestial bodies and spacecraft. The document ``NAIF IDS Required Reading'', naif_ids.req, [219] describes this system in detail. In this document, the following features of the code system will be relied on: `--` The code for the barycenter of the nth planetary system is n. The count starts at 1, which stands for Mercury. (The code for the Sun is 10.) `--` The code for the nth planet's barycenter is n; e.g., the code for Jupiter's barycenter is 5. `--` The code for the nth planet's mass center is n99; e.g, the code for the Earth is 399. `--` Natural satellites have ID codes of the form
                  PNN, where

                         P  is  1, ..., 9
                     and NN is 01, ... 98
`` or
                  PXNNN, where

                         P   is    1, ...,  9,
                         X   is    0  or    5,
                     and NNN is  001, ... 999

                  Codes with X = 5 are provisional.
`` For example, the code for the Earth's moon is 301, and the code for the Ganymede is 503. Top ### Epochs and Reference Frames Some constants that frequently appear in PCK files are associated with a particular epoch and with a particular reference frame. For example, PCK files released by NAIF typically contain constants that define the axes of various body-fixed planetocentric coordinate systems, given relative to a specified inertial reference frame, as a function of time. In this sort of definition, the independent variable, time, is measured relative to a specified reference epoch. Typical choices of reference frames associated with PCK constants would be J2000 or B1950. Typical choices of reference epochs would be the J2000 epoch (JED 24515145.0) or the J1950 epoch (JED 2433282.5). Within CSPICE, reference frames are usually indicated by short character strings, such as 'J2000'. However, CSPICE also has a system of integer codes used by some routines to name reference frames. This coding system is described in detail in [219]. An example of the correspondence of codes and names is shown below:
       Code    Name       Description
       -----   --------   -------------------------------------------
         1     J2000      Earth mean equator, dynamical equinox of J2000
         2     B1950      Earth mean equator, dynamical equinox of B1950
Top ### Planetocentric Coordinates The body-fixed ``Planetocentric'' coordinate system referred to in this document is defined for solar system bodies as follows: `--` The x-axis of the Planetocentric coordinate system for a specified body lies both in the body's equatorial plane and in the plane containing the body's prime meridian. `--` The z-axis is parallel to the body's mean axis of rotation and points North of the invariable plane of the solar system (regardless of the body's spin direction). The north pole is the pole of rotation. `--` The y-axis is defined as the cross product of the z and x axes, in that order. Thus, the frame is right-handed. The above definition implies that the axes of a planetocentric system are time-varying. Thus a complete specification of the axes requires identification of an epoch as well as the body. Top ## Using the PCK System: Overview This section describes how PCK files and software are used in application programs. The use of PCK data in an application program requires three steps: `1.` Selecting the appropriate PCK file(s) for the problem. `2.` Reading the PCK data into the program. `3.` Using the data within the program. Step 1 is not necessarily trivial since there may be no single set of ``best values'' for physical constants of interest; the ``best'' values - if such exist - depend on the problem. The user's judgment, supported by comments and usage notes in the PCK file, is required for this step. Step 2 is referred to as ``loading'' a PCK file. Text PCK files are loaded by calling the CSPICE subroutine furnsh_c and supplying the name of the PCK file to load as the input argument. All of the data in a text PCK file is read into memory when the file is loaded by an application program at run-time. Binary PCK files are also loaded by calling the CSPICE subroutine furnsh_c. This data will be accessible throughout the rest of the program run, unless it is deliberately overwritten or unloaded. Multiple text and multiple binary PCKs can be used simultaneously. The data available from binary PCKs take precedence over that from text PCKs. If data for a requested planetary constant and time period is covered by a loaded binary PCK file, the subsystem returns and uses the binary data. If multiple binary PCK files are loaded, the most recently loaded file takes precedence, down to the binary file loaded earliest. The subsystem defaults to text PCK data when no binary PCK data is available. If the user loaded multiple text PCKs, and those PCKs contained variable assignments using the same variable name, the later loads overwrite the assignments defined by earlier loads. Step 3, accessing loaded PCK data, is accomplished via calls to CSPICE routines. At the lowest level, these access routines allow the calling program to retrieve specified data that has been read from one or more PCK files. Higher-level access routines can return quantities derived from PCK data that has been loaded; the most commonly used such quantity is a matrix that transforms state vectors between inertial and body-fixed planetocentric coordinates. The CSPICE subroutine sxform_c can calculate this transformation. The subroutine bodvrd_c retrieves information on body orientation and body shape. For text PCK files, the PCK software can be thought of as ``buffering'' all data loaded from PCK files: the data from these files is retained in memory. Therefore, repeated calls to the PCK access routines do not incur the inefficiency of re-reading data from files. For binary PCK file, like the case of the SPK and CK readers, only a portion of the most recently used information is buffered. The data structure used by CSPICE to maintain associations of text kernel variable names and values is called the ``kernel pool.'' Data loaded into memory via furnsh_c is referred to as ``being present in the kernel pool.'' There is no analog to the kernel pool for binary PCK files. Top ## Orientation Models used by PCK Software The orientation models used by CSPICE PCK access routines all express the direction of the pole and location of the prime meridian of a body with respect to an inertial reference frame, as a function of time. This information defines the coordinate axes of the ``Body Equator and Prime Meridian'' system. The orientation models use three Euler angles to describe the pole and prime meridian location: the first two angles, in order, are the right ascension and declination (henceforth RA and DEC) of the north pole of a body as a function of time. The third angle is the prime meridian location (represented by `W'), which is expressed as a rotation about the north pole, also a function of time. The coordinate transformation defined by the Euler angles is represented by the matrix product
       [ W ]    [ Pi/2 - Dec ]    [ Pi/2 + RA ]
            3                 1                3
where
       [ W ]
            i
denotes the matrix that rotates vectors by -W about the ith coordinate axis, using the right hand rule. (This notation is explained in detail in [214]). In PCK files, the time arguments of functions that define orientation always refer to Barycentric Dynamical Time (TDB), measured in centuries or days past a specified epoch such as J2000, which is Julian ephemeris date 2451545.0. The time units expected by the CSPICE software are ephemeris days for prime meridian motion and ephemeris centuries for motion of the pole. Top # The Two Formats of PCK files There are two general forms for PCK files, text and binary files. Text files are ASCII and can be created and modified with an editor. Therefore, they are easily changed and read. Binary files are created via CSPICE programs and have a particular format and architecture. They cannot be examined or changed with an editor. These files require CSPICE software for their manipulation. Binary files can contain more data and are faster to use. In the PCK case, the binary files contain higher precision data than the text files. Top ### Detection of Non-native Text Files The various platforms supported by CSPICE use different end-of-line (EOL) indicators in text files:
       Environment                  Native End-Of-Line
                                    Indicator
       ___________                  _____________________

       PC DOS/Windows                <CR><LF>
       Unix                          <LF>
       Linux                         <LF>
       Alpha  Digital Unix           <LF>
       Mac OS X                      <LF>
       Macintosh Classic (OS9)       <CR>
As of CSPICE N0059, the CSPICE text kernel loaders, furnsh_c and ldpool_c, can read and parse non-native text files. The FORTRAN SPICELIB does not include this capability. Please be aware the CSPICE text file reader, rdtext_c, does not possess the capability to read non-native text files. Top ### DAF Run-Time Binary File Format Translation As of the CSPICE N0052 release (January, 2002), certain supported platforms are able to read DAF-based binary files (SPK, CK and binary PCK) written in a non-native, binary representation. This access is read-only; any operations requiring writing to the file (adding information to the comment area, or appending additional ephemeris data, for example) require prior conversion of the file to the native binary file format. See the Convert User's Guide, convert.ug, for details. Top ## NAIF Text Kernel Format Text PCK files express data as ``assignments''; in text PCKs, values are associated with name strings using a ``keyword = value'' format. These name strings, together with their associated values, are called ``kernel variables.'' The CSPICE routines that access text PCK data at run time use these associations established by loaded text PCK files to reference desired data values; these routines look up data ``by name.'' Therefore, programmers writing applications that use text PCKs must coordinate use of kernel variable names between their software and the text PCK files used by their software. Text PCK files conform to a flexible format called ``NAIF text kernel'' format. The SPICE file identification word provided by itself on the first line of the text PCK file is ``KPL/PCK''. Both the NAIF text kernel format and SPICE file identification word are described in detail in the Kernel Required Reading document, kernel.req. For the reader's convenience, an overview of the NAIF text kernel format is provided here. NAIF text kernels are, first of all, ASCII files. As such, they are human readable and can be easily modified by text editors. In addition, NAIF text kernels can be readily ported between computer systems, even when the systems in question have different file systems and file formats. The NAIF text kernel format provides for representation of data in a ``keyword = value'' syntax. The format also provides for the inclusion of free-form comment blocks. There are two kinds of data that can be placed in NAIF text kernel files: double precision numbers and UTC time strings. According to the text kernel format, a text kernel nominally consists of a series of sets of contiguous lines (or ``blocks'') of comments, alternating with blocks of data. Comment blocks are started with the string (called a ``control sequence'')
       \begintext
alone on a line, as shown here. Comment blocks are ended by the control sequence
       \begindata
alone on a line. In a text kernel file, the lines preceding the first
       \begindata
control sequence are considered to constitute a comment block; the
       \begintext
control sequence is optional for this comment block. Comment blocks can contain arbitrary text, except for non-printing characters or lines that can be interpreted as control sequences. On the other hand, data must be organized according to a very specific format: all of the data in a text kernel must appear in the form of an ``assignment'' such as
       NAME = ( VALUE1, VALUE2, ... )
where name is a string no longer than 32 characters, and the values on the right hand side are double precision numbers. A specific example is shown below:
       BODY399_RADII     = (  6378.140  6378.140  6356.75  )
Some variations on the form shown here are allowed: commas between data values are optional, the right hand side of the assignment can be continued over multiple lines, and the numbers can be expressed as integers or reals without causing the PCK software to fail. Assignments of scalars do not require the value on the right hand side to be enclosed in parentheses, but that notation is frequently used as a visual cue. Blank lines within or between assignments are ignored by the CSPICE software that reads text kernels. In addition to numbers, UTC strings can be assigned to variables. The ``@'' character is used to identify the strings as time strings. The strings are stored internally as double precision numbers representing ``UTC seconds past J2000.'' An example is the assignment:
       SCLK_KERNEL_ID            = ( @01-MAY-1991/16:25 )
See [218] for a complete discussion of the allowed form of assignments. The effect of an assignment in a text PCK file is to associate values with a name. The name is referred to as a ``kernel variable.'' When a text PCK file is loaded by an application, the associations of names and values established by the PCK are maintained: the values associated with a given name can be retrieved at any time. Top ## Text PCK Contents Other than the limitations imposed by the PCK file formats, no absolute restrictions exist on the names or values of the variables used in PCK files. However, the CSPICE kernel concept calls for the contents of PCK files to be limited to physical and cartographic constants describing extended solar system bodies: radii of bodies, constants defining orientation models, masses or values of GM are examples of data appropriate for inclusion in PCKs. CSPICE includes a set of routines (gipool_c, gdpool_c, gipool_c) for general access to text PCK defined data. Another set (bodvrd_c, bodvcd_c, sxform_c, pxform_c) recognizes and uses particular PCK data to return body constants or the matrices to transform position or state vectors between reference frames. In this document, the formulas defining time-varying coordinate transformation matrices and Euler angles are referred to as ``orientation models'' since they define the orientation of an extended body with respect to specific inertial frames. Because PCK access routines that deal with orientation models are used extensively in CSPICE and applications that use the Toolkit, the kernel variables that these routines rely on will be discussed in detail. Those functions defining the Euler angles are characterized by a set of parameters. The specific values of the parameters are values assigned to kernel variables in PCK files. The functions themselves are implemented by code within CSPICE routines. The general form of the functions is that used in the IAU/IAG 2000 report. Values shown in this document reflect the 2000 report. For the latest PCK values, check with NAIF. In a text PCK file, the variables (Euler angles)
       RA,  DEC,  W
for the Earth are represented by the names
       BODY399_POLE_RA
       BODY399_POLE_DEC
       BODY399_POLE_PM
The equations above are expressed in a text PCK file by the kernel variable assignments (Values taken from IAU/IAG 2000 report.)
       BODY399_POLE_RA        = (    0.      -0.641         0. )
       BODY399_POLE_DEC       = (  +90.      -0.557         0. )
       BODY399_PM             = (  190.16  +360.9856235     0. )
Note that the string ``PM'' is used in place of ``W'' for the kernel variable associated with the prime meridian. If you examine a PCK file produced by NAIF, you'll see an additional symbol grouped with the ones listed here; it is
       BODY399_LONG_AXIS
This term is currently zero for all bodies except Mars. It represents the offset between the longest axis of the triaxial ellipsoid used to model a body and the prime meridian of the body. Top ### Text PCK Kernel Variable Names Text PCK variables recognized by CSPICE PCK access routines have names that follow a simple pattern: variables related to a body whose NAIF integer code is nnn have names of the form
       BODYnnn_<item name>
where
       <item name>
is a short string that identifies the type of quantity the kernel variable represents. For example, the variable containing quadratic polynomial coefficients for the right ascension of the Earth's north pole is
       BODY399_POLE_RA
Note the number ``399'' appearing in the kernel variable names; this is the NAIF integer code for the Earth. The following sections specify the specific item names recognized by PCK access routines. Top ### Restrictions on the Form of Orientation Models in Text PCK Kernels Orientation models usable by CSPICE's text PCK access routines are not available for all solar system bodies. For example, Saturn's moon Hyperion is ``tumbling'' and does not admit a description of its motion by the sort of models used in text PCKs. To date, no PCK files containing models for the rotation of comets have been produced or collected by NAIF. Models for the rotation of comets, as well as for the rotation of asteroids and the natural satellites of planets, can be accommodated by the PCK system only if the models have the form described in the section ``Models for the Sun, Planets, and Asteroids'' or in ``Models for Satellites'' or if binary PCK data is available. Top ### Models for the Sun, Planets, and Asteroids in Text PCK Kernels For the Sun, planets, and asteroids, the expressions used in text PCK files for the north pole direction and prime meridian location are always quadratic polynomials, where the independent variable is time. Some coefficients may be zero. Let RA and DEC represent the right ascension and declination of a body's north pole, and let W be the prime meridian location, measured in the counterclockwise direction, from the cross product of the Earth's ``mean'' North pole at the J2000 epoch (as used in defining the J2000 frame) and BODY's North pole at et, to BODY's prime meridian at et. The variables RA, DEC, and W constitute sufficient information to compute the transformation from a specified inertial frame to body-fixed, planetocentric coordinates for the body to which they apply, at a specified time. The angles RA, DEC, and W are defined as follows:
                                       2
                                  RA2*t
       RA  =  RA0  +  RA1*t/T  +  ------
                                     2
                                    T

                                        2
                                  DEC2*t
       DEC =  DEC0 + DEC1*t/T  +  -------
                                     2
                                    T

                                      2
                                  W2*t
       W   =  W0   + W1*t/d    +  -----
                                     2
                                    d
where
       d = seconds/day
       T = seconds/Julian century
       t = ephemeris time, expressed as seconds past the reference epoch
           for this body or planetary system
Below is an example showing actual values of the parameters used to define the latest IAU model for orientation of the Earth. Here, the motions of both the pole and the prime meridian are given by linear polynomials; the quadratic terms are all zero. The values shown here are taken from the IAU/IAG 2000 report. In that document, the names
       alpha
            0
and
       delta
            0
are used in place of the names RA and DEC used here.
       alpha   =   0.00 - 0.641 T
            0

       delta   =  90.0  - 0.557 T
            0

       W       =  190.16 + 360.9856235 d

       T represents centuries past J2000 (TDB),

       d represents days past J2000 (TDB).
Top ### Models for Satellites in Text PCK Kernels Orientation models for natural satellites of planets are a little more complicated; in addition to polynomial terms, the RA, DEC, and W expressions include trigonometric terms. The arguments of the trigonometric terms are linear polynomials. These arguments are usually called ``phase angles.'' However, within CSPICE internal documentation, these quantities are called ``nutation precession angles''; for consistency with the CSPICE software, we'll use this terminology in the following discussion. Expressions for the right ascension and declination of the north pole and the location of the prime meridian for any satellite of a given planet are as follows:
                                    2      ____
                               RA2*t       \
       RA  = RA0  + RA1*t/T  + ------   +  /     a  sin theta
                                  2        ----   i          i
                                 T           i

                                     2     ____
                               DEC2*t      \
       DEC = DEC0 + DEC1*t/T + -------  +  /    d  cos theta
                                   2       ----  i          i
                                  T          i

                                   2       ____
                               W2*t        \
       W   = W0   + W1*t/d   + -----    +  /     w  sin theta
                                  2        ----   i          i
                                 d           i
where
       d = seconds/day
       T = seconds/Julian century
       t = ephemeris time, expressed as seconds past a reference epoch
RA0, RA1, DEC0, DEC1, W0, and W1 are constants specific to each satellite. The nutation precession angles
       theta
            i
are specific to each planet. The coefficients
       a ,  d ,  and w
        i    i        i
are specific to each satellite. As an example, the nutation precession angles for Earth given by [252] are shown below. That document uses the variable names E1---E5 in place of
       theta  --- theta
            1          5
in the equations above.
       E1 = 125.045 -  0.052992 d
       E2 = 250.090 -  0.105984 d
       E3 = 260.008 + 13.012001 d
       E4 = 176.625 + 13.340716 d
       E5 = 357.529 +  0.985600 d

       Here d represents days past J2000 (TDB)
Because the NAIF Toolkit software expects the time units for the angles to be centuries (as in the IAU models for most bodies---the Earth is an exception), the linear coefficients are scaled by 36525.0 for use in the kernel variable assignments:
       BODY3_NUT_PREC_ANGLES  = (  125.045    -1935.5328
                                   250.090    -3871.0656
                                   260.008   475263.3
                                   176.625   487269.6519
                                   357.529    35999.04     )
In this assignment, the constant and linear polynomial coefficients for each nutation precession angle are listed together: the numbers 125.045 and -1935.5328 are the constant and linear terms for the angle ``E1,'' and so on. Note the body number 3 in the kernel variable name above; this number designates the Earth-Moon barycenter. The PCK access routines expect nutation precession angles to be associated with the barycenters of planetary systems. Here are the expressions for the right ascension and declination of the moon, also taken from [252]:
       alpha   =  270.000 +  0.003 T -  3.878 sin(E1)  -  0.120 sin(E2)
            0
                              +  0.070 sin(E3)  -  0.017 sin(E4)

       delta   =  66.541  + 0.013 T  +  1.543 cos(E1)  +  0.024 cos(E2)
            0
                           -  0.028 cos(E3)  +  0.007 cos(E4)

       W       =  38.317   + 13.1763582 d    +  3.558 sin(E1)

                           +  0.121 sin(E2)

                           -  0.064 sin(E3)

                           +  0.016 sin(E4)

                           +  0.025 sin(E5)

       Here d represents days past J2000 (TDB),
       and T represents Julian centuries past J2000 (TDB).
       E1--E5 are the nutation precession angles.
The polynomial terms are assigned to symbols by the statements
       BODY301_POLE_RA        = (  270.000    0.003        0. )
       BODY301_POLE_DEC       = (  +66.541    0.013        0. )
       BODY301_PM             = (   38.317  +13.1763582    0. )
The coefficients of the trigonometric terms are assigned to symbols by the statements
       BODY301_NUT_PREC_RA  = (  -3.878  -0.120  +0.070  -0.017   0.    )
       BODY301_NUT_PREC_DEC = (  +1.543  +0.024  -0.028  +0.007   0.    )
       BODY301_NUT_PREC_PM  = (  +3.558  +0.121  -0.064  +0.016  +0.025 )
Note that for the RA and PM (prime meridian) assignments, the ith term is the coefficient of sin(Ei) in the expression used in the IAU model, while for the DEC assignment, the ith term is the coefficient of cos(Ei) in the expression used in the IAU model. CSPICE software for text PCKs expects the models for satellite orientation to follow the form of the model shown here: the polynomial terms in the RA, DEC, and W expressions are expected to be quadratic, the trigonometric terms for RA and W (satellite prime meridian) are expected to be sums of sines of nutation precession angles, and the trigonometric terms for DEC are expected to be sums of cosines of nutation precession angles. The nutation precession angles themselves are defined by linear polynomial functions of time. Note that the number of values defining the nutation precession angles for a planetary system must be consistent with the number of trigonometric terms used in the expressions for the RA, DEC and W angles for the satellites of that system. See ``Creating and Modifying Text PCKs Kernels'' for details. Top ### Epoch and Frame Specifications in Text PCK Kernels The constants used in PCK files to define an orientation model for a specified body are assumed by default to define a time-dependent rotation R(t) that converts vectors from J2000 coordinates to body-fixed, planetocentric coordinates at the epoch t seconds past J2000, TDB (JED 2451545.0). We say that the constants are ``referenced to the J2000 epoch and J2000 frame.'' However, these default values for the epoch and frame of the constants may be overridden: it is possible to use constants referenced to the B1950 frame and to the J1950 epoch, for example. The default constants and frame for a body are overridden by setting the values of the kernel variables
       BODY<id code>_CONSTANTS_REF_FRAME
and
       BODY<id code>_CONSTANTS_JED_EPOCH
Here
       <id code>
is: `--` for planets and their satellites: the NAIF integer code of the corresponding planetary system's barycenter. `--` for other bodies: the NAIF integer code of the body itself. The values of the frame specifier variable
       BODY<id code>_CONSTANTS_REF_FRAME
are the codes returned by the CSPICE routine IRFNUM. Some of the commonly used codes and the corresponding frames are:
       Code        Frame
       ----        -----
         1         J2000

         2         B1950

         3         FK4 (used in CSPICE for `EME50')
For example, to use constants referenced to the FK4 or EME50 frame for the asteroid Gaspra (ID code = 9511010), the PCK file containing the constants should include the assignment
       BODY9511010_CONSTANTS_REF_FRAME   =   (  3  )
The values of the epoch specifier variable
       BODY<id code>_CONSTANTS_JED_EPOCH
are Julian ephemeris dates. To use constants for Gaspra referenced to the J1950 epoch, the PCK file containing the constants should include the assignment
       BODY9511010_CONSTANTS_JED_EPOCH   =   (  2433282.5D0 )
The creator of a PCK file can set the frame and epoch of the constants on a body-by-body basis, except in the case of planets and their (natural) satellites, where a single choice of frame and epoch must be used for each planetary system. For example, to use constants referenced to the B1950 frame and J1950 epoch for the Earth and Moon, you would make the assignments
       BODY3_CONSTANTS_REF_FRAME   =   (  2           )
       BODY3_CONSTANTS_JED_EPOCH   =   (  2433282.5D0 )
The ID code `3' designates the Earth-Moon barycenter. Note: the assignment
       BODY399_CONSTANTS_REF_FRAME   =   (  2           )
       BODY399_CONSTANTS_JED_EPOCH   =   (  2433282.5D0 )
would be ignored by the PCK reader routines; you cannot assign a frame or epoch using the ID code of a planet or satellite. Using constants referenced to frames or epochs other than J2000 does not affect the definitions of the inputs or outputs of any of the PCK access routines. These routines make the necessary transformations internally to take into account the reference frame and epoch of the orientation constants in the kernel pool. Thus the PCK access routine sxform_c, which has the argument list
       sxform_c ( from, to, et, rotate )
returns the transformation matrix mapping state vectors frame ```from''' into frame ```to''' for ephemeris time expressed as ```et''' seconds past the J2000 epoch (JED 2451545.0), regardless of the epoch or frame of the orientation constants used to compute ```rotate'.'' Top ### Shape models in Text PCK Kernels CSPICE contains a number of geometry routines that make use of triaxial ellipsoidal models of extended solar system bodies. Although CSPICE currently contains no routines that directly use the specific PCK variables that define these models, text PCK files typically contain radii of solar system bodies, since these values can be looked up by low-level text PCK access routines and subsequently used by CSPICE geometry routines. In text PCK files produced by NAIF, the radius values for body nnn are assigned to the variable
       BODYnnn_RADII
Three radius values are always assigned for each instance of this variable. The data are ordered as in the IAU/IAG 2000 report: the equatorial radii are listed with the largest axis, often called the ``a'' axis, appearing first; the polar radius is last. Spheroids and spheres are obtained when two or all three radii are equal. Example: Radii of the Earth.
       BODY399_RADII     = (     6378.140    6378.140     6356.75   )
Top ### Summary of PCK Variables used in Text PCK Kernels by CSPICE In order to compute transformations for the Sun, a planet, or an asteroid (say body number ppp), the PCK access routines require that one or more PCK files containing values for the following variables be loaded:
       BODYppp_POLE_RA
       BODYppp_POLE_DEC
       BODYppp_PM
For a satellite (say body number sss), one or more PCK files containing values for the following variables must be loaded:
       BODYsss_POLE_RA
       BODYsss_POLE_DEC
       BODYsss_PM
       BODYsss_NUT_PREC_RA
       BODYsss_NUT_PREC_DEC
       BODYsss_NUT_PREC_PM
       BODYbbb_NUT_PREC_ANGLES
where the code bbb embedded in the last name above is that of the barycenter of the planetary system to which the satellite belongs. The triaxial ellipsoidal model for body nnn is expressed by the assignment
       BODYnnn_RADII = ( <larger equatorial radius>,
                         <smaller  equatorial radius>,
                         <polar radius> )
Top ## Creating and Modifying Text PCKs The PCK file text format allows NAIF Toolkit users to easily modify existing text PCKs and to create their own files containing values of their choosing. Any text editor capable of working with ASCII files can be used to edit text PCK files. Although the text PCK format makes it easy to modify text PCK files, NAIF recommends that application programmers avoid software designs that call for special-purpose, user-created text PCK files. The opportunities for confusion and errors increase with the number of available versions of a text PCK file (or any data file). NAIF recommends that you take the following precautions when modifying a text PCK file: `--` Change the name of the updated file. `--` Document the changes by adding appropriate comments to the file. Each text PCK file should contain sufficient information to allow a human reader to find out who was responsible for creating the current version of the file and what the source was for each data value in the file. If the file is an update, the reason for the update and a summary of the differences from the previous version should be included. `--` Test the file using software that makes use of any values that you've added or modified. The reasons why a NAIF Toolkit user might wish to modify an existing text PCK are: `--` Removing unneeded data or comments to speed up loading and simplify the file. Removal of data is much more important than removal of comments, as far as speeding up kernel loading is concerned. `--` Adding data values for new bodies. `--` Updating existing data values or substituting preferred data values. New kernel variables added to text PCK files should follow the naming conventions described in the ``Kernel Variable Names'' section. All text PCK variable names, whether or not they are recognized by CSPICE software, should start with the prefix
       BODYnnn_
where nnn is the NAIF integer code of the body the variable applies to. Kernel variables having names recognized by users' application software are a potential problem area: if the names used in the application don't match those in the text PCK file, the application will fail to obtain the data as intended. The most frequent cause of this type of failure is misspelling of variable names, but programmers who considering changing the names of PCK variables already in use should also keep this problem in mind. Modifying orientation models for satellites requires attention to the consistency between the number of nutation precession angles and the number of coefficients of trigonometric functions having the nutation precession angles as arguments. For any planetary system, there should be twice as many values for the nutation precession angles as the maximum number of trigonometric terms in the expressions for prime meridian location or right ascension or declination of the pole of any satellite in the system. This is because the nutation precession angles are defined by linear polynomials; each polynomial has two defining coefficients. For example, the 1991 IAU model for the Earth-Moon system uses the following values to determine the Moon's orientation:
       BODY3_NUT_PREC_ANGLES  = (  125.045    -1935.5328
                                   250.090    -3871.0656
                                   260.008   475263.3
                                   176.625   487269.6519
                                   357.529    35999.04     )

       BODY301_POLE_RA        = (  270.000    0.003        0. )
       BODY301_POLE_DEC       = (  +66.541    0.013        0. )
       BODY301_PM             = (   38.317  +13.1763582    0. )

       BODY301_NUT_PREC_RA  = (  -3.878  -0.120  +0.070  -0.017   0.    )
       BODY301_NUT_PREC_DEC = (  +1.543  +0.024  -0.028  +0.007   0.    )
       BODY301_NUT_PREC_PM  = (  +3.558  +0.121  -0.064  +0.016  +0.025 )
Note that there are five nutation precession angles, with two coefficients defining each one. The trigonometric terms in the expressions for the right ascension, declination, and prime meridian location for the moon require five nutation precession angles. If a NAIF Toolkit user were to update this model with a new one that had, for example, only one nutation precession angle, then the variables
       BODY301_NUT_PREC_RA
       BODY301_NUT_PREC_DEC
       BODY301_NUT_PREC_PM
would each have to be assigned only one value. Failure to make this change would result in an error being signaled at run-time by any CSPICE PCK access routine that uses these variables. Top ## Binary PCK Kernel Format The binary PCK file format is built upon the SPICE DAF (Double precision Array File) architecture. Readers who are not familiar with this architecture are referred to the DAF Required Reading document, daf.req, which describes the common aspects of all DAF formats, as well as a collection of CSPICE subroutines that support the DAF architecture. The SPICE file identification word occupying the first eight bytes of a properly created binary PCK file is ``DAF/PCK ''. For more information on SPICE identification words refer to the Kernel Required Reading document, kernel.req. Most users will not need to understand the details of the structure of binary PCK files. Top ### Segments--The Fundamental PCK Building Blocks A binary PCK file contains one or more `segments'. Each segment contains data sufficient to compute the axes of a body-fixed planetary coordinate system, relative to a specified inertial reference frame, as a function of time. The data in each segment are stored as a single array. The summary for the array, called a `descriptor', has two double precision components: `1.` The initial epoch of the interval for which data are contained in the segment, in ephemeris seconds past Julian year 2000; `2.` The final epoch of the interval for which data are contained in the segment, in ephemeris seconds past Julian year 2000. The descriptor has five integer components: `1.` The NAIF integer code for the body; `2.` The NAIF integer code for the inertial reference frame; `3.` The integer code for the representation (type of PCK data). Only type 2 is presently supported; `4.` The initial address of the array; `5.` The final address of the array. The name of each array may contain up to 40 characters. This space may be used to store a `pedigree' for the data in the array. The pedigree of a segment should allow a user to determine the conditions under which the data in the segment were generated. Top ### The Comment Area Preceding the `segments', the Comment Area provides space in a binary PCK file for storing additional textual information besides what is written in the array names. Ideally, each binary PCK file would contain internal documentation that describes the origin, recommended use, and any other pertinent information about the data in that file. For example, the beginning and ending epochs for the file, the names and NAIF integer codes of the bodies included, an accuracy estimate, the date the file was produced, and the names of the source files used in making the binary PCK file could be included in the Comment Area. CSPICE provides a family of subroutines for handling this Comment Area. This software provides the ability to add, extract, read, and delete comments and convert commented files from binary format to transfer format and back to binary again. Top ### Binary PCK Data Types The third integer component of the descriptor---the code for the representation, or `data type'---is the key to the binary PCK format. For purposes of determining the segment best suited to fulfill a particular request, all segments are treated equally. It is only when the data in a segment are to be evaluated that the type of data used to represent the data becomes important. Because this step is isolated within low-level readers, new data types can be added to the binary PCK format without affecting application programs that use the higher level readers. Top ### Supported Data Types Two representations, or data types, are currently supported by the binary PCK routines in CSPICE. They are Chebyshev polynomials (Euler angles only), called "Type 2" and Chebyshev polynomials (Euler angles and their derivatives) for intervals of possibly varying lengths, called "Type 3". Top ### Type 2: Chebyshev (Angles only) These are sets of Chebyshev polynomial coefficients for the Euler angles, defining as a function of time the right ascension and declination of a body's north pole, and the prime meridian rotation. The rates of the angles are obtained by differentiation. The segments contains an arbitrary number of logical records with each record describing a set of Chebyshev coefficients valid across an interval of fixed length. The subroutine pcke02_ contains the algorithm used to construct a set of Euler angles from a particular record and epoch. A segment consists of a set of records, ordered by increasing initial epoch, each record containing the same number of coefficients. The segment structure is illustrated below:
               +---------------+
               | Record 1      |
               +---------------+
               | Record 2      |
               +---------------+
                 .
                 .
                 .
               +---------------+
               | Record N      |
               +---------------+
               | INIT          |
               +---------------+
               | INTLEN        |
               +---------------+
               | RSIZE         |
               +---------------+
               | N             |
               +---------------+
A four-number `directory' at the end of the segment contains the information needed to determine the location of the record corresponding to a particular epoch. `1.` INIT is the initial epoch of the first record, given in ephemeris seconds past 2000 Jan 01 12:00:00, also known as J2000. `2.` INTLEN is the length of the interval covered by each record, in seconds. `3.` RSIZE is the total size of (number of array elements in) each record. `4.` N is the number of records contained in the segment. Each record is structured as follows:
               +------------------+
               | MID              |
               +------------------+
               | RADIUS           |
               +------------------+
               | X  coefficients  |
               +------------------+
               | Y  coefficients  |
               +------------------+
               | Z  coefficients  |
               +------------------+
The first two elements in the record, MID and RADIUS, are the midpoint and radius of the time interval covered by coefficients in the record. These are used as parameters to perform transformations between the domain of the record (from MID - RADIUS to MID + RADIUS) and the domain of Chebyshev polynomials (from -1 to 1 ). The same number of coefficients is always used for each component, and all records are the same size (RSIZE), so the degree of each polynomial is ( RSIZE - 2 ) / 3 - 1 Top ### Type 3: Chebyshev (Angles and derivatives) These are sets of Chebyshev polynomial coefficients for the Euler angles, defining right ascension (RA) and declination (DEC) of the body's north pole, and its prime meridian rotation (W) as a function of time, and their derivatives. This data type was created for the attitude of the asteroid Eros. Each segment contains an arbitrary number of logical records. Each record contains a set of Chebyshev coefficients for angles and derivatives valid throughout an interval defined in the record. The lengths of these intervals may vary within a segment. The subroutine pcke03_ contains the algorithm used to construct a set of Euler angles from a particular record and epoch. All records contain the same number of coefficients. A segment of this type is structured as follows:
               +---------------+
               | Record 1      |
               +---------------+
               | Record 2      |
               +---------------+
                 .
                 .
                 .
               +---------------+
               | Record N - 1  |
               +---------------+
               | Record N      |
               +---------------+
where each record has the following format:
       ---------------------------------------------------
       |  Midpoint of the approximation interval in TDB  |
       ---------------------------------------------------
       | Radius of the approximation interval in seconds |
       ---------------------------------------------------
       |        coefficients for the RA position         |
       ---------------------------------------------------
       |        coefficients for the DEC position        |
       ---------------------------------------------------
       |        coefficients for the W position          |
       ---------------------------------------------------
       |        coefficients for the RA velocity         |
       ---------------------------------------------------
       |        coefficients for the DEC velocity        |
       ---------------------------------------------------
       |        coefficients for the W velocity          |
       ---------------------------------------------------
TDB is time in ephemeris seconds past J2000, called et in the CSPICE system. Top ## Creating Binary PCKs Only very knowledgeable users who need to incorporate new planetary/satellite orientation information in binary format should consider writing binary PCK files. Users who write binary PCK files must have a thorough understanding of the information they wish to place in a binary PCK file. They must also master the high level structure of the PCK files, and they must be sure to correctly package the data for the PCK writing subroutines provided in CSPICE. We also strongly recommend that the writer of a PCK file include descriptive comments in the comment area. Normally, binary PCK files should be obtained from NAIF. The user should keep in mind that the PCK segments should be as large as possible to create smaller, faster to load files. The are generally three steps to creating a binary PCK file. `1.` Open the file. `2.` Begin the segment, add data to the segment and close the segment. `3.` Close the file. The subroutine pckopn_ is used to open a new binary PCK file. Below is an example for a call to pckopn_. ```name''' is the name of the file to be opened, ```ifname''' is the internal file name, ```handle''' is the handle of the opened SPK file. We use ```i''' for the number of record to reserve for comments.
             pckopn_( file, ifname, &i, &handle, file_len, ifname_len)

             (file_len is the length of the name string,
              ifname_len is the length of the ifname string )
The method for beginning the segment, adding data to the segment and closing the segment differs with the PCK type. For segments of type 2, there is a segment writing routine called pckw02_ in CSPICE. This routine takes as input arguments the handle of an PCK file that is open for writing, the information needed to construct the segment descriptor, and the data to be stored in the segment. The header of the subroutine provides a complete description of the input arguments and an example of its usage. Here's an example of a call to pckw02_:
             pckw02_ ( &handle   , &body  , frame  , &first, &last, segid,
                       &intlen   , &n     , &polydg,  cdata, &btime,
                       frame_len, segid_len);
For type 3, there are three subroutines used in creating a binary PCK file. They are pck03b_, which begins a type 3 segment, PCK03A, which adds data to segment, and pck03e_, which ends a segment. The type 3 subroutines can be used in a loop, where pck03a_ is called to add data to the segment. Here is a code fragment that begins a type 3 segment, writes data to that segment in a loop, and then closes the segment.
          pck03b_( &handle, segid    , &body, frame, &first, &last,
                   chbdeg , segid_len, frame_len);

          do
             {
             ...
             pck03a_ ( &handle, &n, coeffs, epochs);
             ...
             } while ( <a condition> );

          pck03e_( &handle);
When a user is finished writing segments to an PCK file, the file must be closed with the subroutine pckcls_.
          pckcls_ ( &handle );
Top # PCK Software This section describes the specifications and proper use of the CSPICE PCK software. Top ## Getting PCK Data into Your Program Because loading PCK files is usually time-consuming, it is good programming practice to have applications load PCK files during program initialization rather than throughout their main processing thread, especially if that processing thread is a loop. It is also wise to avoid designing data processing systems that effectively place PCK loading in a tight loop by requiring repeated runs of programs that expend a significant fraction of their run time on loading PCK files. If a program loads PCK files, it is preferable that it do all of its processing in a single run, or at least in a small number of runs, rather than carry out its processing by being re-run a large number of times: the former design will greatly reduce the ratio of the time the program spends loading PCKs to the time it spends on the rest of its data processing. Top ### Loading Text PCK Kernels As earlier mentioned, in order to use text PCK files in an application, the data in the files must be read into memory. This is accomplished by calling the CSPICE routine furnsh_c. The name of the text PCK file to load is supplied as an input to furnsh_c, for example:
       furnsh_c ( "P_CONSTANTS.KER" );
File names supplied to furnsh_c will generally be system-dependent. It is good programming practice to not use hard-coded file names in calls to furnsh_c. Instead, applications should obtain kernel file names by one of the following methods: `--` Reading the kernel file names from a file containing the names. (This allows users to change the kernel files without re-compiling and re-linking the application.) `--` Prompting the user for the file names at run-time. An application can load any number of text PCK files during a single program run. There are, however, parameterized limits on both the total number of kernel variables that can be stored and on the total number of data values assigned to those variables. Each time a text PCK is loaded, the assignments made in the file are maintained in the PCK software. In particular, if a kernel variable occurs in multiple PCKs loaded in a single run of a program, the value of the variable will be the one assigned in the following priority: last binary PCK file loaded, previously loaded binary PCK files, then last loaded text PCK files followed by previously loaded text PCK files. All binary PCK files take precedence over text PCK files. Within the binary and/or text file groups, the last loaded files takes precedence. Top ### Loading Binary PCK Kernels The routine furnsh_c maintains a database of loaded binary PCK files. The calling program indicates which files are to be used by passing their names to furnsh_c.
          furnsh_c ( "example.pck" );
Once an PCK file has been loaded, it may be accessed by the PCK software. Each set of constants is computed from a distinct segment. A PCK file may contain any number of segments. In fact, the same file may contain overlapping segments: segments containing data for the same body over a common interval. When this happens, the latest segment in a file supersedes any competing segments earlier in the file. Similarly, the latest file loaded supersedes any earlier files. In effect, several loaded files become equivalent to one large file. Binary PCK files take precedence over text PCK files. Top ### Unloading Binary PCK Kernels It is possible, though unlikely, that a program would need to make use of many binary PCK files in the course of a single execution. On the other hand, the number of binary PCK files that may be open at any one time is limited, so such a program might need to unload some PCK files to make room for others. A binary PCK file may be unloaded by supplying its name to subroutine unload_c. The call to this subroutine is shown below,
          unload_c ( filename );     { Unload binary PCK file }
Top ## Binary PCK Coverage Summary Routines The CSPICE includes two functions for obtaining information about the contents of a binary PCK file from within an application. The pckfrm_c function provides an API via which an application can find the set of reference frames for which a specified binary PCK file contains data. The reference frame class ID codes are returned in a SPICE ``set'' data structure (see sets.req). The pckcov_c function provides an API via which an application can find the time periods for which a specified binary PCK file provides data for a reference frame of interest. The coverage information is a set of disjoint time intervals returned in a SPICE ``window'' data structure (see windows.req). Refer to the headers of pckfrm_c and pckcov_c for details on the use of those routines. Top ## Access Routines CSPICE contains two basic categories of PCK access routines: those that return PCK data directly, and those that return quantities derived from PCK data. This section discusses the PCK access routines in the later category: these routines deal with coordinate and state transformations. All of the routines listed here make use of the orientation models discussed in the section titled ``Orientation Models used by PCK Software.'' Note that in order to use these routines, an application must first load a PCK file (or files) containing sufficient data to define all of the required orientation models. If needed data has not been loaded, these routines will signal run-time errors when called. Top ### High-Level PCK Data Access To obtain the matrix that transforms 3-vectors from a specified reference frame to another frame, at a specified ephemeris time, use the routine pxform_c. The calling sequence is
       pxform_c ( from, to,  et,  rotate );
In the argument list for pxform_c: `from' is the name of a reference frame in which a position vector is known. `to' is the name of a reference frame in which it is desired to represent a position vector. `et' is the epoch in ephemeris seconds past the epoch of J2000 (TDB) at which the position transformation matrix `rotate' should be evaluated. `rotate' is the matrix that transforms position vectors from the reference frame `from' to the frame `to' at epoch `et'. For example, let V50 be a vector specified relative to the B1950 inertial reference frame. The call
       pxform_c( "B1950", "IAU_EARTH", &et, rotate );
returns a matrix ```rotate''' such that left-multiplying V50 by ```rotate''' --- accomplished in CSPICE by the call
       mxm_c ( rotate, v50, vbodfx );
will return the vector ```vbodfx''' specified relative to the Earth's (``body-fixed'') planetocentric frame at time ```et'''. Note that many practical applications of pxform_c require that a light-time corrected value of et be supplied as an input. See ``Computing the Sub-Observer Point'' in the ``Examples'' section below. The fundamental quantities defined by PCK orientation models are actually Euler angles, not matrices. These Euler angles, which we call ``RA, DEC, and W,'' are related to the matrix ```rotate''' shown above by the equation
       rotate = [ W ]   [ Pi/2 - DEC ]   [ Pi/2 + RA ]
                   3                1               3
The units of these angles are radians. To directly retrieve these angles, use the call
       bodeul_ ( &body, &et, &ra, &dec, &w, &lambda );
`body' is the NAIF integer code of the body defining the planetocentric coordinate system. `et' is the ephemeris time at which the orientation model given the basis vectors of the planetocentric frame is to be evaluated. `ra' and `dec' represent the right ascension and declination of the North pole of body at et with respect to the J2000 inertial reference frame. `w' is the prime meridian location for ```body''' at ```et''', also measured with respect to the J2000 inertial reference frame. `lambda' is the positive west longitude, measured from the prime meridian of body, of the longest axis of the triaxial ellipsoidal model for body given in a PCK file. Currently, the only body having a non-zero value of LAMBDA is Mars (see [195]). CSPICE software does not currently make use of ```lambda'''. CSPICE provides a routine analogous to pxform_c that returns the matrix to transform state vectors between reference frames. This routine is called sxform_c; the calling sequence being
       sxform_c ( from, to,  et,  xform );
The input arguments ```from''', ```to''', and ```et''' have the same meanings as in the argument list of pxform_c. The output argument ```xform''' is the 6x6 matrix required to transform state vectors from inertial to body-fixed coordinates. Left multiplication of a state vector by ``XFORM'' will transform it from the frame specified by ```from''' to the frame specified by ```to''' at time ```et'''. Top ### Low-Level PCK Data Access WARNING: These low-level access routines for text PCK files only search the text kernel pool for these values. Values found in loaded binary PCK files will NOT be found by these routines. The values retrieved from a binary PCK file take precedence over the values found in the text PCK kernels. Therefore, if binary kernels have been loaded, values returned by these low level routines may not be the same values used by higher level routines like sxform_c and pxform_c. We recommend the user who loads binary PCKs NOT USE these low-level routines! The lowest-level CSPICE PCK access routines are gipool_c, gdpool_c and gcpool_c. These are general-purpose routines for retrieving any text kernel data by data type (integer, double precision, and character string, respectively) loaded via furnsh_c. The calling sequences for the routines:
       gcpool_c ( name, start, room, lenout, &n, vals, &found );
       gdpool_c ( name, start, room, &n, vals, &found );
       gipool_c ( name, start, room, &n, vals, &found );
The meanings of the arguments are follows: `name' is the name of the kernel variable whose values are desired. This is the name used in a PCK file to make an assignment. `start' is the index of the first component of NAME to return. If `start' is less than 1, it will be treated as 1. `room' is the maximum number of components that should be returned for this variable. `lenout' is the allowed length of the output string. This length must be large enough to hold the output string plus the terminator. `n' is the number of data values assigned to the kernel variable. `vals' is the return arrays of sufficient size and correct type to contain the data corresponding to `name'. `found' is a logical flag indicating whether the kernel variable designated by name was actually loaded. The gipool_c, gdpool_c, and gcpool_c set is frequently used by other CSPICE routines; however, CSPICE users will usually find it more convenient to use the PCK access routines bodvrd_c or bodvcd_c, routines that return double precision body constants, e.g radius, RA/DEC of the spin axis, the GM value, etc. In text PCK's produced by NAIF, PCK variables will have names conforming to the naming convention used in CSPICE, that is, the kernel variable names have the form
       BODYnnn_<item name>
bodvrd_c and bodvcd_c retrieve the values of such variables from the kernel pool; bodvrd_c accepts as inputs the body name and a string making up the portion of the item's name following the prefix:
       bodvrd_c ( bodynm, item, maxn, &dim, values );
bodvcd_c functions in the same manner as bodvrd_c except bodvcd_c accepts as inputs the body NAIF ID and the item string, ```item''', as described for bodvrd_c:
       bodvcd_c ( bodyid, item, maxn, &dim, values );
For example, to obtain the radii of the of Earth, a program could use either the call
       bodvrd_c ( "EARTH", "RADII", 3 &dim, values );
or the call
       bodvcd_c ( 399, "RADII", 3 &dim, values );
Both calls return the dimension and values associated with the variable
       BODY399_RADII
namely
       dim     = 3;
       value[0] = 6378.140;
       value[1] = 6378.140;
       value[2] = 6356.755;
It is possible to test whether a kernel variable has been loaded by calling the CSPICE logical function bodfnd_c, as long as the variables in question follow the CSPICE naming convention. The calling sequence is
       found = bodfnd_c ( body, item );
where body is the NAIF integer code of the body, and ```item''' is the string making up the portion of the item's name following the prefix
       BODYnnn_
For example, to test whether values for Jupiter's radii have been loaded, the test
       found = bodfnd_c ( 599, "RADII" )
could be used. The variable ```found''' would be returned as SPICETRUE if a PCK file had been loaded containing an assignment of the variable
       BODY599_RADII
Top ## Examples This section illustrates some typical applications of CSPICE PCK software. Top ### Transforming a body-fixed state to the inertial J2000 frame Occasionally, it may be useful to transform a state vector known in body-fixed coordinates to inertial J2000. To perform the transformation correctly, it is necessary to take into account the time derivative of the inertial-to-body-fixed coordinate transformation. A discussion of the error made by ignoring this derivative term is given in [214]. The following code fragment shows how to use the CSPICE routine sxform_c to transform state vectors between coordinate frames. The 6-vector ```state''' represents the body-fixed state (position and velocity) of an object with respect to the center of the body at time ```et'''. The matrix ```xform''' is declared as a 6x6 double-precision matrix. This program loads both a text and a binary PCK file. The question of from which file is the data retrieved is answered by the coverage of the files. If a particular requested time and body is covered by the loaded binary file, the binary data will be used. If not, the text data will be used. In this example, we present a small program that solves a realistic geometry problem: transform an earth station location given geodetic coordinates to the corresponding state vector in the J2000 reference frame.
       #include "SpiceUsr.h"
       #include <stdlib.h>

       SpiceDouble     lon;
       SpiceDouble     lat;
       SpiceDouble     alt;
       SpiceDouble     f;
       SpiceDouble     equatr;
       SpiceDouble     polar;
       SpiceDouble     et;
       SpiceDouble     abc[3];
       SpiceDouble     pos[3];
       SpiceDouble     jstate[6];
       SpiceDouble     xform[6][6];
       SpiceDouble     state[] = { 0., 0., 0.,
                                   0., 0., 0. };

       SpiceInt        dim;
       SpiceInt        i;

       int main()
          {

          /*

          Suppose you have geodetic coordinates of a station on the
          surface of Earth and that you need the inertial (J2000)
          state of this station.  The following code fragment
          illustrates how to transform the geodetic state of the
          station to a J2000 state.

          Load the SPK, PCK and LSK kernels.

          */
          furnsh_c( "/kernels/gen/lsk/naif0008.tls");
          furnsh_c( "/kernels/gen/pck/pck00008.tpc");
          furnsh_c( "/kernels/gen/spk/de405_2000-2050.bsp");

          /*
          Also load a high precision earth orientation kernel. This
          returns orientation to milli-second accuracy.
          */
          furnsh_c( "/kernels/gen/pck/earth_000101_050509_050215.bpc");

          /*
          Define a geodetic longitude, latitude, altitude
          coordinate set. These coordinates are defined in the
          non-inertial, earth fixed frame "IAU_EARTH".
          */
          lon = 118.25 * rpd_c();
          lat = 34.05  * rpd_c();
          alt = 0.;

          /*
          Define a UTC time of interest. Convert the 'utc' string
          to ephemeris time J2000.
          */
          str2et_c( "March 1, 2005", &et);

          /*
          Retrieve the equatorial and polar axis of the earth.
          */
          bodvrd_c( "EARTH", "RADII", 3, &dim, abc );
          equatr =  abc[0];
          polar  =  abc[2];

          /*
          Calculate the flattening factor for earth.
          */
          f =  ( equatr - polar  ) / equatr;

          /*
          Calculate the Cartesian coordinates on earth
          in the ITRF93 frame for the location at
          'lon', 'lat', 'alt'.
          */
          georec_c( lon, lat, alt, equatr, f, pos );

          /*
          georec_c returned the position vector of the geodetic
          coordinates, but we want the state vector. Since it is a fixed
          location on the earth referenced in the high precision
          "ITRF93" frame, the location has no velocity in that frame.
          We need to extend 'pos' to a 6-vector, the final three elements
          with value 0. Copy 'pos' to the first
          three elements of 'state'.
          */
          state[0] = pos[0];
          state[1] = pos[1];
          state[2] = pos[2];

          /*
          Retrieve the transformation matrix from "ITRF93"
          to "J2000" at epoch 'et'.
          */
          sxform_c( "ITRF93", "J2000", et, xform );

          /*
          Transform the Cartesian state vector from "IAU_EARTH"
          to "J2000."
          */
          mxvg_c( xform, state, 6,6, jstate );

          /*
          Write out the results.
          */
          for( i=0; i<6; i++ )
             {
             printf( " %24.8f\n", jstate[i] );
             }

          /*
          It's always good form to unload kernels after use.
          */
          unload_c( "standard.ker" );

          return 0;
          }
Top ## Creating a binary PCK file, type 03. We assume that we are creating a new file for this example. In addition, we will make use of the fictitious subroutine GENREC to generate a type 03 PCK data record. This is for demonstrative purposes only, and is not intended to be a complete program. The following routines will be used in this example: `--` pckcls_ -- Close a PCK file. `--` pckopn_ -- Open a new PCK file. `--` pck03b_ -- Begin a type 03 PCK segment. `--` pck03a_ -- Add data to a type 03 PCK segment. `--` pck03e_ -- End a type 03 PCK segment. For the complete details of these routines, please see the appropriate source code files. Variable declarations for the example code fragment.
          SpiceChar       *  filename;
          SpiceChar       *  ifname;
          SpiceChar       *  frame;
          SpiceChar       *  segid;

          SpiceDouble        et;
          SpiceDouble        etstrt;
          SpiceDouble        etstop;
          SpiceDouble     *  record;
          SpiceDouble        step;

          SpiceInt           body;
          SpiceInt           chbdeg;
          SpiceInt           handle;
          /*
          THIS IS A CODE FRAGMENT, NOT A PROGRAM!

          Assign the name of the file to be created.
          */

          filename   = "new_pck.bpc";

          /*  Assign an internal filename for the file. */

          ifname     = "THIS IS A NEW PCK filename";

          /* Open the PCK file. */

          pckopn_( filename, ifname, 0L, &handle, strlen(filename),
                                                 strlen(ifname)   );

          /*
          Set the identifier for the segment. This is a character
          string of at most 40 printing ASCII characters. It may
          be blank.
          */

          SEGID = "This is a test."

          /*
          Set the body for the PCK segment. We will use the
          Moon, ID code 301.
          */

          body   = 301;

          /* We will use the J2000 reference frame for the segment. */

          *frame = "J2000";

          /*
          Set the degree of the Chebyshev polynomials used for the
          segment.
          */

          chbdeg = 10;

          /* Begin the PCK segment. */

          pck03b_( &handle, segid, &body, frame, &etstrt, &etstop, chbdeg,
                   strlen(segid), strlen(frame_len) );

          /*
          We have a start time and a stop time available, etstrt
          and etstop, and we want to generate records for
          sub-intervals of the interval (etstrt, etstop). For
          simplicity, we will assume equal width intervals and
          that (etstop-etstrt)/step is a positive integer. The
          times are in et, ephemeris seconds past J2000.
          */

          /* The time step will be one day, 86400 seconds. */

          step = 86400.0;

          /* Set the initial time. */

          et  = etstrt;

          /*
          Loop until we have processed all of the time intervals,
          i.e., when et >= etstop.
          */

          do
             {

             /*
             Get a type 03 PCK record for the interval et,
             et+step (getrec is not a CSPICE routine).
             */

             getrec ( et, et+step, record );

             /* Add the record to the segment. */

             pck03a_ ( &handle, 1L, record, &et );

             /* Increment the time interval. */

             et = et + step;

             } while ( et >= etstop );

          /* End the segment. */

          pck03e_ ( &handle );

          /* Close the PCK file. */

          pckcls_ ( &handle );
Top ## Summary of Calling Sequences Loading files:
       furnsh_c ( filename );   for text and binary PCKs
Unloading binary PCK files:
       unload_c ( filename );   for text or binary PCKs
Getting binary PCK coverage summary:
       pckfrm_c ( filename, ids )
       pckcov_c ( filename, idcode, cover  )
Searching binary PCK files for appropriate information:
       pcksfs_ ( &body, &et, &handle, &descr, ident, &found, ident_len);
Testing for the presence of variables in the text kernel pool:
       bodfnd_c ( body, item );
Obtaining values assigned variables from the text kernel pool:
       bodvrd_c ( bodynm, item, maxn, &dim, values );
       bodvcd_c ( bodyid, item, maxn, &dim, values );

       gcpool_c ( name, start, room, lenout, &n, vals, &found );
       gdpool_c ( name, start, room, &n, vals, &found );
       gipool_c ( name, start, room, &n, vals, &found );
Obtaining Euler angles and their derivatives from a binary PCK file:
       pckeul_ ( &body, &et, &found, ref, eulang, ref_len);
Obtaining position transformation matrices between reference frames:
       pxform_c ( from, to,  et,  rotate );
Obtaining Euler angles defining inertial-to-body-fixed coordinate transformations:
       bodeul_ ( &body, &et, &ra, &dec, &w, &lambda );
Obtaining state transformation matrices between reference frames:
       sxform_c ( from, to, et, rotate )
Opening a binary PCK file for writing:
       pckopn_( file, ifname, &ncomch, &handle, file_len, ifname_len)
Writing type 2 segment to a binary PCK file:
       pckw02_ ( &handle   , &body, frame  , &first, &last , segid,
                 &intlen   , &n   , &polydg,  cdata, &btime,
                 frame_len, segid_len);
Writing type 3 segment to a binary PCK file:
       To begin a type 3 segment:
       pck03b_ ( &handle  , segid, &body, frame, &first, &last, &chbdeg,
                 segid_len, frame_len);

       To add data to a type 3 segment:
       pck03a_( &handle, &nrecs, recrds, epochs);

       To end a type 3 segment:
       pck03e_ ( &handle);
Close a binary PCK file after writing:
       pckcls_ ( &handle );
Reading a type 2 segment from a binary PCK file:
       pckr02_ ( &handle, descr, &et, record);
Evaluating a type 2 segment from a binary PCK file:
       pcke02_ ( &et, record, eulang);
Reading a type 3 segment from a binary PCK file:
       pckr03_  ( &handle, descr, &et, record );
Evaluating a type 3 segment from a binary PCK file:
       pcke03_ ( &et, record, rotmat);
Top # Appendix A: Sample Text PCK file The file shown here is an example of a text PCK file. This file is intended only for use as an example; it should not be used as a source of data.
       P_constants (PcK) SPICE kernel file
       ===================================================================

       Update by: Karen Zukor (NAIF)    1994 March 30

            First draft of a PCK with internal labels included.
            NOTE: some of the label keywords, values, syntax and overall
            organization are likely to change. Do not write any code that
            uses the above labels.

       Organization
       --------------------------------------------------------

            The sections of this file are as follows.

            Introductory Information:

                --   Version description

                --   Disclaimer

                --   Sources

                --   Explanation of the PcK contents

                --   Body numbers and names

            Pck Data:

                --   Orientation constants for the Sun and planets

                --   Orientation constants for satellites

                --   Radii for all bodies

       Version description
       --------------------------------------------------------

            This is a prototype PcK, for use in SPICE training and
            constants evaluation only.

            This file is based on the 1991 IAU report,
            NAIF document [306].

       Disclaimer
       --------------------------------------------------------

            This constants file may not contain the parameter values that
            you prefer. Note that this file may be readily modified by
            you or anyone else. NAIF suggests that you inspect this file
            visually before proceeding with any critical or extended data
            processing.

            NAIF requests that you update the `by line' and date if
            you modify the file.

       Sources
       --------------------------------------------------------

            The sources for the constants listed in this file are:

                1.   ``Report of the IAU/IAG/COSPAR Working Group on
                     Cartographic Coordinates and Rotational Elements of
                     the Planets and Satellites: 1991,'' March 3, 1992.

                2.   ``The Astronomical Almanac,'' 1990.

                3.   ``Planetary Geodetic Control Using Satellite
                     Imaging,'' Journal of Geophysical Research, Vol. 84,
                     No. B3, March 10, 1979, by Thomas C. Duxbury. This
                     paper is cataloged as NAIF document 190.0.

                4.   Letter from Thomas C. Duxbury to Dr. Ephraim
                     Lazeryevich Akim, Keldish Institute of Applied
                     Mathematics, USSR Academy of Sciences, Moscow,
                     USSR. This letter is catalogued as NAIF document
                     number 195.0.

                5.   Mars Observer Planetary Constants and Models,
                     November 1990, Mars Observer Document No. 642-321,
                     JPL Document No. D-3444.

            Most values are from [1], and these are generally taken from
            [1].  All exceptions are commented where they occur in this
            file. The exceptions are:

                --   The second nutation precession angle (M2) for Mars is
                     represented by a quadratic polynomial in the 1991
                     IAU report.   The SPICE subroutine BODEUL can not
                     handle this term (which is extremely small), so we
                     truncate the polynomial to a linear one.

                --   The expression for the prime meridian of Deimos (
                     body 402 ) includes a cosine term, which BODEUL
                     doesn't yet handle. The amplitude of the term is
                     0.19 degrees. We simply ignore this term.

       Body numbers and names
       (Contains only information pertinent to Mars Observer)
       ----------------------------------------------------------

          Barycenters:

               3  Earth barycenter
               4  Mars barycenter

               While not relevant to the P_constants kernel, we note here
               for completeness that 0 is used to represent the solar
               system barycenter.

          Mass centers:

               399 Earth

               401 Phobos
               402 Deimos
               499 Mars

               10  Sun

       Orientation constants for the Sun and planets
       --------------------------------------------------------

       Sun

               \begindata

               BODY10_POLE_RA         = (  286.13       0.          0. )
               BODY10_POLE_DEC        = (   63.87       0.          0. )
               BODY10_PM              = (   84.10     +14.18440     0. )
               BODY10_LONG_AXIS       = (    0.                        )

               \begintext

       Earth

               \begindata

               BODY399_POLE_RA        = (    0.      -0.641         0. )
               BODY399_POLE_DEC       = (  +90.      -0.557         0. )
               BODY399_PM             = (  190.16  +360.9856235     0. )
               BODY399_LONG_AXIS      = (    0.                        )

               \begintext

               The linear terms before and after scaling:

                  -.052992   -->     -1935.5328
                  -.105984   -->     -3871.0656
                -13.012      -->   -475263.3
                 13.340716   -->   +487269.6519
                  -.9856     -->    -35999.04

               \begindata

               BODY3_NUT_PREC_ANGLES  = (  125.045    -1935.5328
                                           250.090    -3871.0656
                                           260.008   475263.3
                                           176.625   487269.6519
                                           357.529    35999.04     )

               \begintext

       Mars

               \begindata

               BODY499_POLE_RA          = (  317.681     -0.108       0. )
               BODY499_POLE_DEC         = (  +52.886     -0.061       0. )
               BODY499_PM               = (  176.868   +350.8919830   0. )

               \begintext

            Source [3] specifies the following value for the lambda_a
            term ( BODY4_LONG_AXIS ) for Mars.

            This term is the POSITIVE WEST LONGITUDE, measured from the
            prime meridian, of the longest axis of the ellipsoid
            representing the `mean planet surface', as the article states.

                  body499_long_axis        = (  110.  )

            Source [4] specifies the lambda_a value

                  body499_long_axis        = (  104.9194  )

            We list these lambda_a values for completeness. [5] gives
            equal values for both equatorial radii, so the lambda_a
            offset does not apply.

            The 1991 IAU report defines M2, the second nutation
            precession angle, by:

                                                       2
               192.93  +  1128.4096700 d  +  8.864 T

            We truncate the M2 series to a linear expression.

            Again, the linear terms are scaled by 36525.0:

                -0.4357640000000000      -->     -15916.28010000000
                  1128.409670000000      -->   41215163.19675000
                -1.8151000000000000E-02  -->       -662.9652750000000

               \begindata
               BODY4_NUT_PREC_ANGLES  = (  169.51     -15916.2801
                                           192.93  +41215163.19675
                                            53.47       -662.965275  )

               \begintext

       Orientation constants for the satellites
       --------------------------------------------------------

       Satellites of Mars

            Phobos:

            The quadratic prime meridian term is scaled by 1/36525**2:

               8.864000000000000   --->   6.6443009930565219E-09

               \begindata

               BODY401_POLE_RA      = (317.68    -0.108     0.           )
               BODY401_POLE_DEC     = (+52.90    -0.061     0.           )
               BODY401_PM           = ( 35.06 +1128.8445850 8.864        )
               BODY401_LONG_AXIS    = (  0.                              )

               BODY401_NUT_PREC_RA  = ( +1.79   0.    0.  )
               BODY401_NUT_PREC_DEC = ( -1.08   0.    0.  )
               BODY401_NUT_PREC_PM  = ( -1.42  -0.78  0.  )

               \begintext

            Deimos:

            There's a new wrinkle in the Deimos prime meridian
            expression, which is:
                                                         2
                  W = 79.41  +  285.1618970 d  -  0.520 T  -  2.58 sin M
                                                                        3

                                                           +  0.19 cos M .
                                                                        3

                                                                  ^
                                                            (new wrinkle)

            At the present time, the constants kernel software (the
            routine bodeul_ in particular) cannot handle the cosine term;
            we omit this term for the time being. The maximum error we
            can make is 0.19 degrees.

            The quadratic prime meridian term is scaled by 1/36525**2:

                -0.5200000000000000  --->   -3.8978300049519307E-10

               \begindata

               BODY402_POLE_RA      = (316.65   -0.108      0.           )
               BODY402_POLE_DEC     = (+53.52   -0.061      0.           )
               BODY402_PM           = ( 79.41 +285.1618970 -3.897830D-10 )
               BODY402_LONG_AXIS    = (  0.                              )

               BODY402_NUT_PREC_RA  = (  0.   0.   +2.98  )
               BODY402_NUT_PREC_DEC = (  0.   0.   -1.78  )
               BODY402_NUT_PREC_PM  = (  0.   0.   -2.58  )

               \begintext

       Radii of bodies
       --------------------------------------------------------

       Sun

            Value for the Sun is from the 1990 Almanac (page K7).

               \begindata

               BODY10_RADII      = (   696000.   696000.   696000.   )

               \begintext

       Earth

            Values for the Earth are unchanged in the 1991 IAU report.

               \begindata

               BODY399_RADII     = (   6378.140   6378.140    6356.75   )

               \begintext

       Mars

            Current values taken from [5]:

               \begindata

               BODY499_RADII       = (   3393.4     3393.4     3375.7   )

               \begintext

       Satellites of Mars

               \begindata

               BODY401_RADII     = (       13.4        11.2        9.2   )
               BODY402_RADII     = (        7.5         6.1        5.2   )