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
         Reference Ellipsoid Orientation Offsets
         Text PCK Kernel Variable Names
         Restrictions on the Availability of Orientation Models in Text PCK Kernels
         Models for the Sun, Planets, and some Minor Bodies in Text PCK Kernels
         Models for Satellites in Text PCK Kernels
         Shape models in Text PCK Kernels
         Summary of PCK Variables used in Text PCK Kernels by Icy
      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 their derivatives)
         Type 20: Chebyshev (Only angular derivatives)
      Creating Binary PCKs

   PCK Software
      Getting PCK Data into Your Program
         Loading Text PCK Kernels
         Loading Binary PCK Kernels
         Unloading Binary PCK Kernels
      Access Routines
         High-Level PCK Data Access
         Low-Level PCK Data Access

   Appendix A --- Summary of PCK Routines

   Appendix B --- Epoch and Frame Specifications in Text PCK Kernels

   Appendix C --- Revision History
         2021 DEC 24 by N.J. Bachman
         2013 JAN 22 by E. D. Wright, C. H. Acton
         2010 JUN 03 by B. V. Semenov.
         Original version K.R. Gehringer, K. S. Zukor




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PCK Required Reading





Last revised on 2021 DEC 24 by N.J. Bachman



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Abstract




The Planetary Constants Kernel (PCK) subsystem provides cartographic and physical constants data for Solar System bodies. Icy software uses these data when determining observation geometry dependent on the size, shape, and orientation of planets, natural satellites, comets, and asteroids.



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Intended Audience



This document is recommended reading for all users of PCK files.



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References



    4. SPK Required Reading (spk.req).

    7. Double Precision Array Files Required Reading (daf.req).

    8. ``Planetary Geodetic Control Using Satellite Imaging,'' Journal of Geophysical Research, Vol. 84, No. B3, March 10, 1979, by Thomas C. Duxbury.

    9. ``Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: 2000.''

    10. ``Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements: 2006.''

    11. ``Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2009.''



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Introduction




The functionality of the PCK subsystem is supplied by data files called ``PCK files'' (or PCKs) and by Icy subroutines that can read and interpret the data in these files.

Historically, only one type of PCK existed, the text PCK (called the "P constants kernel.") These ASCII files can be easily viewed and modified via text editor. The current SPICE system also supports a non-ascii binary PCK. These files contain more precise body orientation information in binary format (no size and shape data). This format permits large amounts of data to be stored and quickly accessed. As of the date of this document, 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. Icy 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.



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Body Codes



NAIF software uses a system of integer codes to conveniently represent celestial bodies, locations such as barycenters, Lagrange points, and spacecraft. The NAIF IDS Required Reading document, naif_ids.req, 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; e.g. the code for Jupiter's barycenter is 5. The code for the Sun is 10. SPICE maintains Pluto as the 9th planet.

    -- The code for the nth planet's barycenter is n

    -- The code for the nth planet's mass center is n99; e.g, the code for the Earth (Earth barycenter is 3) 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 (moon 1 of body 399) is 301, and the code for Ganymede (moon 3 of body 599) is 503.



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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.

Within Icy, reference frames are identified by short character strings such as 'J2000'. The names of the body-fixed reference frames are usually constructed by adding the prefix ``IAU_'' to the name of the body, for example ``IAU_MARS'' for Mars. The exception from this rule are body-fixed reference frames associated with high-precision orientation provided in binary PCK files. For more details see FRAMES Required Reading, frames.req.

However, Icy also has a system of integer codes used by some routines to specify reference frames. This coding system is also described in detail in frames.req.



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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.



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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 Icy subroutine cspice_furnsh and supplying the name of the PCK file to load as the input argument or by loading a meta kernel that lists the PCK. All data in a text PCK file is read into memory when the file is loaded by an application program at run-time. Load binary PCKs in the same way. The program can access all loaded data during the program run, unless 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, using loaded PCK data, is accomplished via calls to Icy 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 loaded PCK data.

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 Icy to maintain associations of text kernel variable names and values is called the ``kernel pool.'' Data loaded into memory via cspice_furnsh is referred to as ``being present in the kernel pool.'' There is no analog to the kernel pool for binary PCK files.



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Orientation Models used by PCK Software




The orientation models used by Icy 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 a coordinate system by W radians about the ith coordinate axis (or rotates vectors by -W radians about the same axis), using the right hand rule. (This notation is explained in detail in rotation.req).

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 Icy software are ephemeris days for prime meridian motion and ephemeris centuries for motion of the pole.



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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 Icy programs and have a particular format and architecture. They cannot be examined or changed with an editor. These files require Icy software for their manipulation. Binary PCKs can contain more data and are faster to use. In the PCK case, the binary files contain higher precision data than the text files. Binary PCKs contain only orientation data, while text PCKs usually include orientation, size, and shape data, and may include other physical data associated with a body.



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Detection of Non-native Text Files



The various platforms supported by Icy use different end-of-line (EOL) indicators in text files:

   Environment                  Native End-Of-Line
                                Indicator
   ___________                  _____________________
   PC DOS/Windows               <CR><LF>
   Mac OS X, Linux, Unix        <LF>


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DAF Run-Time Binary File Format Translation



As of the Icy N0052 release (January, 2002), 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.



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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 Icy 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, starting in the leftmost column, 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 = VALUE
or

   NAME = ( VALUE1, VALUE2, ... )
where "NAME" is a string no longer than 32 characters, and one or more values appear on the right hand. A specific example is shown below:

   BODY399_RADII     = (  6378.140  6378.140  6356.75  )
The "VALUES" may be integer, double precision or string values.

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 data values can be expressed as integers or reals without causing the PCK software to fail. Either an "E" or "D" can be used to set off an exponent. 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 Icy 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 kernel.req 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.



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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 SPICE 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, and masses or values of GM are examples of data appropriate for inclusion in PCKs.

Icy includes a set of routines (cspice_gipool, cspice_gdpool, cspice_gipool) for general access to text PCK defined data. Another set (cspice_bodvrd, cspice_bodvcd, cspice_sxform, cspice_pxform) 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 Icy 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 Icy 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 (Earth ID = 399) 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. )


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Reference Ellipsoid Orientation Offsets



If you examine a PCK file produced by NAIF, you'll see an additional symbol grouped with the ones listed above; it is

   BODY399_LONG_AXIS
The Icy procedure cspice_bodeul returns the value of the kernel variable

   BODY<id code>_LONG_AXIS
as an output argument, but Icy does not make use of this value.

This value represents the offset between the longest axis of the triaxial ellipsoid used to model the shape of a body and the prime meridian of the body. Historically, IAU orientation models have had only zero offsets.

Icy high-level geometry software that makes use of reference ellipsoids assumes that ellipsoid axes are aligned with those of the corresponding PCK reference frame. When this is not the case, a new TK reference frame can be defined that provides the correct reference ellipsoid orientation relative to the PCK frame. See the Frames Required Reading document frames.req for more information on TK frames.

Defining a TK frame for reference ellipsoid orientation relative to the corresponding PCK frame is an effective way of representing such offsets. It enables user applications to pass the TK frame name to Icy APIs, so that those APIs will perform computations using the desired ellipsoid orientation.



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Text PCK Kernel Variable Names



Text PCK variables recognized by Icy 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
The following sections specify the specific item names recognized by PCK access routines.



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Restrictions on the Availability of Orientation Models in Text PCK Kernels



Orientation models usable by Icy'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.



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Models for the Sun, Planets, and some Minor Bodies in Text PCK Kernels



For the Sun, planets, and minor bodies, 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 as expressed in the J2000 frame, and let W be the prime meridian location, measured in the counterclockwise direction, from the direction defined by the cross product of the Z direction in the J2000 frame (the Earth's ``mean'' North pole at the J2000 epoch) 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  +  ------  + [optional trig polynomials]
                                 2
                                T
 
                                    2
                              DEC2*t
   DEC =  DEC0 + DEC1*t/T  +  ------- + [optional trig polynomials]
                                 2
                                T
 
                                  2
                              W2*t
   W   =  W0   + W1*t/d    +  -----   + [optional trig polynomials]
                                 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
Expressions for RA, Dec, and W for planets rarely include the trigonometric polynomial terms shown above. If they are used, these terms follow the form described below which is used for natural satellites.



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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 sometimes called ``phase angles.'' However, within Icy internal documentation, these quantities often are called ``nutation precession angles.'' That terminology is used here.

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.

Icy 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, by default, are defined by linear polynomial functions of time. It is possible to use polynomials of degree up to 3 to represent nutation precession angles for a specified planetary system. This is done by adding to a text PCK file the kernel variable assignment

   BODY<id code>_MAX_PHASE_DEGREE = <degree>
where ``id'' is the code of the planetary system barycenter. For example, quadratic nutation precession angle expressions can be used for the Mars system if a text PCK contains the assignment

   BODY4_MAX_PHASE_DEGREE = 2
For any planetary system, all nutation precession angles must have the same number of coefficients.

Units of the polynomial coefficients of the nutation precession angles are, in order of increasing degree,

                 degrees            degrees
   degrees,   --------------,   ---------------,  ...
              Julian century                  2
                                Julian century
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.



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Shape models in Text PCK Kernels



Icy contains a number of geometry routines that make use of triaxial ellipsoidal models of extended solar system bodies. Although Icy 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 Icy geometry routines.

In text PCK files produced by NAIF, the radius values for body nnn are assigned to the variable as:

   BODYnnn_RADII = ( a, b, c )
where ``a,'' ``b,'' and ``c'' are the radius values for each axis.

Three radius values are always assigned for each instance of this variable. The data are ordered as in the IAU/IAG report: the equatorial radii are listed with the largest axis, normally called the ``a'' axis, appearing first; the polar radius, normally called the ``c'' axis, is last.

Spheroids and spheres are obtained when two or all three radii are equal.



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Summary of PCK Variables used in Text PCK Kernels by Icy



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> )


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Creating and Modifying Text PCKs




The text PCK file 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 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 Icy software, should start with the prefix

   BODYnnn_
where nnn is the NAIF integer code of the body corresponding to the variable.

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 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, if DEG is the maximum nutation precession angle polynomial degree for that system, there should be DEG+1 times 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 all nutation precession angle polynomials for a given planetary system must have the same degree.



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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 Icy 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.



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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 frame class ID of the PCK reference frame for which the segment provides orientation data. See the Frames Required Reading document frames.req for further information on frame class IDs.

    Some older SPICE documentation refers to this ID code as as a ``body'' ID code.

    2. The NAIF integer code for the inertial reference frame.

    3. The integer code for the representation (type of PCK data). Currently types 2, 3, and 20 are 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.



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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.

Icy 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.



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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.



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Supported Data Types



Three representations, or data types, are currently supported by the binary PCK routines in Icy. They are:

    1. Type 2, Chebyshev polynomials (Euler angles only).

    2. Type 3, Chebyshev polynomials (Euler angles and their derivatives) for intervals of possibly varying lengths.

    3. Type 20, Chebyshev polynomials (Derivatives of Euler angles).



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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 (RA) and declination (DEC) of a body's north pole, and the prime meridian rotation (W). The rates of the angles are obtained by differentiation.

The segments contain an arbitrary number of logical records with each record describing a set of Chebyshev coefficients valid across an interval of fixed length.

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 component has the same number of coefficients, and all records are the same size (RSIZE), so the degree of each polynomial is

    polynomial degree = ( RSIZE - 2 ) / 3 - 1
The structure of each record:

   ---------------------------------------------------------------
   |  The midpoint of the approximation interval in TDB seconds  |
   ---------------------------------------------------------------
   |  The radius of the approximation interval in TDB seconds    |
   ---------------------------------------------------------------
   |  (polynomial degree + 1) coefficients for RA                |
   ---------------------------------------------------------------
   |  (polynomial degree + 1) coefficients for DEC               |
   ---------------------------------------------------------------
   |  (polynomial degree + 1) coefficients for W                 |
   ---------------------------------------------------------------
TDB seconds is time in ephemeris seconds past J2000, often called ET in the SPICE system.

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 ).



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Type 3: Chebyshev (Angles and their derivatives)



A type 03 PCK segment consists of coefficient sets for fixed order Chebyshev polynomials over consecutive time intervals, where the time intervals need not all be of the same length. The Chebyshev polynomials represent the orientation of a body specified relative to an inertial frame by the angles RA, DEC, W and body fixed angular rates for each axis of the body fixed coordinate system defined by RA, DEC, and W. The angles and the angular rates of the axes are given in degrees and degrees/sec.

Each segment contains an arbitrary number of logical records. 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      |
           +---------------+
The structure of each record:

   ---------------------------------------------------------------
   |  The midpoint of the approximation interval in TDB seconds  |
   ---------------------------------------------------------------
   |  The radius of the approximation interval in TDB seconds    |
   ---------------------------------------------------------------
   |  (polynomial degree + 1) coefficients for RA                |
   ---------------------------------------------------------------
   |  (polynomial degree + 1) coefficients for DEC               |
   ---------------------------------------------------------------
   |  (polynomial degree + 1) coefficients for W                 |
   ---------------------------------------------------------------
   |  (polynomial degree + 1) coefficients for the body          |
   |  fixed X-axis rate                                          |
   ---------------------------------------------------------------
   |  (polynomial degree + 1) coefficients for the body          |
   |  fixed Y-axis rate                                          |
   ---------------------------------------------------------------
   |  (polynomial degree + 1) coefficients for the body          |
   |  fixed Z-axis rate                                          |
   ---------------------------------------------------------------
TDB seconds is time in ephemeris seconds past J2000, called ET in the SPICE system.

The type 3 data type is seldom used.



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Type 20: Chebyshev (Only angular derivatives)



PCK data type 20 contains Chebyshev polynomial coefficients for a specified set of Euler angle rates of a body-fixed, body-centered reference frame as a function of time. Euler angles representing the orientation of the frame are obtained by integrating the rates using a specified integration constant.

This data type is provided to accurately represent ``EPM'' orientation data developed by the Institute of Applied Astronomy (IAA), Russian Academy of Sciences (RAS).

Each type 20 segment contains an arbitrary number of logical records. Each record contains a set of Chebyshev coefficients valid throughout an interval of fixed length. Each record also contains an Euler angle set applicable at the midpoint of its coverage interval.

The records within a segment are ordered by increasing initial epoch. All records contain the same number of coefficients.

A segment of this type is structured as follows:

           +---------------+
           | Record 1      |
           +---------------+
           | Record 2      |
           +---------------+
             .
             .
             .
           +---------------+
           | Record N      |
           +---------------+
           | ASCALE        |
           +---------------+
           | TSCALE        |
           +---------------+
           | INITJD        |
           +---------------+
           | INITFR        |
           +---------------+
           | INTLEN        |
           +---------------+
           | RSIZE         |
           +---------------+
           | N             |
           +---------------+
A seven-number `directory' at the end of the segment contains the information needed to determine the location of the record and perform an evaluation of the record corresponding to a particular epoch.

    1. ASCALE is the angular scale used for both orientation and angular rates; ASCALE has units of radians. For example, if the angular units are degrees, then ASCALE is the number of radians in one degree.

    2. TSCALE is the time scale used for angular rates; TSCALE has units of TDB seconds. For example, if the time units of the rate data are TDB Julian days, then TSCALE is 86400.

    3. INITJD is the integer part of the TDB Julian date of the initial epoch of the first record. INITJD has units of Julian days. INITJD may be less than, equal to, or greater than the initial epoch.

    4. INITFR is the fractional part of the TDB Julian date of the initial epoch of the first record. INITFR has units of Julian days. INITFR has magnitude strictly less than 1 day. The sum INITJD + INITFR equals the TDB Julian date of the initial epoch of the first record.

    5. INTLEN is the length of the interval covered by each record, in TDB Julian days.

    6. RSIZE is the total size of (number of array elements in) each record. The same number of coefficients is always used for each component, and all records are the same size. RSIZE is 3 + 3*(DEGP+1), where DEGP is the common degree of the Chebyshev expansions for each Euler angle rate component.

    7. N is the number of records contained in the segment.

Each component has the same number of coefficients, and all records are the same size (RSIZE), so the degree of each polynomial is (solve RSIZE for DEGP)

   polynomial degree = ( RSIZE/3 - 2 )
Define the angles as:

   angle  * ASCALE = ( RA   + pi/2 )
        1
 
   angle  * ASCALE = ( pi/2 - DEC )
        2
 
   angle  * ASCALE = ( W )
        3
The structure of each record:

   ---------------------------------------------------------------
   |  (polynomial degree + 1) coefficients for the rate of       |
   |  angle 1                                                    |
   ---------------------------------------------------------------
   |  value of angle 1 at interval midpoint                      |
   ---------------------------------------------------------------
   |  (polynomial degree + 1) coefficients for the rate of       |
   |  angle 2                                                    |
   ---------------------------------------------------------------
   |  value of angle 2 at interval midpoint                      |
   ---------------------------------------------------------------
   |  (polynomial degree + 1) coefficients for the rate of       |
   |  angle 3                                                    |
   ---------------------------------------------------------------
   |  value of angle 3 at interval midpoint                      |
   ---------------------------------------------------------------
The rate coefficients have units of ASCALE radians/TSCALE seconds: multiplying a Chebyshev expansion's value by ASCALE/TSCALE converts angular rates to units of radians/s.

Euler angles at a record's midpoint epoch are given in units of ASCALE radians: multiplying the angles by ASCALE converts the angles to units of radians.

The Euler angles represent the orientation of the PCK reference frame relative to its base frame. The angles, which are numbered according to their ordinal position in the logical records, define a transformation matrix R as follows:

   R = [ angle  *A ]  [ angle  *A ]  [ angle  *A ]
              3     3        2     1        1     3
where A is the angular scale ASCALE. Here the notation

      [ THETA ]
               i
denotes a reference frame rotation of THETA radians in the right-hand sense about the ith coordinate axis. See the Rotation Required Reading for further discussion of this notation.



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Creating Binary PCKs




NAIF creates most binary PCKs. Normally, binary PCK files should be obtained from NAIF.

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 Icy. We also strongly recommend that the writer of a PCK file include descriptive comments in the comment area.

The creation of binary form kernels is expected to occur using a Fortran or C based program rather than programmatically. If a user needs a custom routine for binary kernel creation, the SPICELIB and CSPICE Toolkits contain all needed APIs. The Icy Toolkit is based on CSPICE and so includes all CSPICE APIs.

Also note most binary PCK APIs in C lack CSPICE wrappers and so C based code will need to call to f2c'd version of the corresponding SPICELIB routines.








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PCK Software





This section describes the proper use of the Icy PCK software.



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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.



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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 Icy routine cspice_furnsh. The name of the text PCK file to load is supplied as an input to cspice_furnsh, for example:

   cspice_furnsh, 'example_pck.tcp'
File names supplied to cspice_furnsh will generally be system-dependent. It is good programming practice to not use hard-coded file names in calls to cspice_furnsh. Instead, applications should obtain kernel file names by one of the following methods:

    -- Reading the kernel file names from a meta-kernel, 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.



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Loading Binary PCK Kernels



The routine cspice_furnsh maintains a database of loaded binary PCK files. The calling program indicates which files are to be used by passing their names to cspice_furnsh.

   cspice_furnsh, 'example_binary_pck.tcp'
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.



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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 cspice_unload. The call to this subroutine is shown below,

   cspice_unload, 'example_binary_pck.tcp'


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Access Routines




Icy 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.



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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 cspice_pxform. The calling sequence is

   cspice_pxform, from, to,  et,  rotate
In the argument list for cspice_pxform:

`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'.
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 transformation operator returned from cspice_pxform by the equation

   rotate = [ W ]   [ Pi/2 - DEC ]   [ Pi/2 + RA ]
                 3                1               3

   Icy provides a routine analogous to cspice_pxform that returns the
   matrix to transform state vectors between reference frames for a
   particular time. This routine is called cspice_sxform; the calling
   sequence being

   cspice_sxform, from, to, et, rotate
The input arguments ``from'', ``to'', and ``et'' have the same meanings as in the argument list of cspice_pxform. The output argument ``rotate'' is the 6x6 matrix required to transform state vectors from inertial to body-fixed coordinates. Left multiplication of a state vector by ``rotate'' will transform it from the frame specified by ``from'' to the frame specified by ``to'' at time ``et''.



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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 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 cspice_sxform and cspice_pxform. We recommend the user who loads binary PCKs NOT USE these low-level routines!

The lowest-level Icy PCK access routines are cspice_gipool, cspice_gdpool and cspice_gcpool. These are general-purpose routines for retrieving any text kernel data by data type (integer, double precision, and character string, respectively) loaded via cspice_furnsh. The calling sequences for the routines:

   cspice_gcpool, name, start, room,   length, values, found
   cspice_gdpool, name, start, room,           values, found
   cspice_gipool, name, start, room,           values, found
   cspice_stpool, item, nth,   contin, string, size,  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. The index follows the C convention of being 0 based. If `start' is less than 0, it will be treated as 0.
`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 cspice_gipool, cspice_gdpool, and cspice_gcpool set is frequently used by other Icy routines; however, Icy users will usually find it more convenient to use the PCK access routines that return double precision body constants, e.g radius, RA/DEC of the spin axis, the GM value, etc.

In text PCKs produced by NAIF, PCK variables will have names conforming to the naming convention used in Icy, that is, the kernel variable names have the form

   BODYnnn_<item name>
cspice_bodvrd and cspice_bodvcd retrieve the values of such variables from the kernel pool; cspice_bodvrd accepts as inputs the body name and a string making up the portion of the item's name following the prefix:

   cspice_bodvrd, bodynm, item, maxn, values
cspice_bodvcd functions in the same manner as cspice_bodvrd except cspice_bodvcd accepts as inputs the body NAIF ID and the string, ``item'', as described for cspice_bodvrd:

   cspice_bodvcd, bodyid, item, maxn, values



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Appendix A --- Summary of PCK Routines





   cspice_bodvcd ( Return d.p. values from the kernel pool )
   cspice_bodvrd ( Return d.p. values from the kernel pool )
   cspice_furnsh ( Furnish the environment with SPICE kernels )
   cspice_gcpool ( Get character data from the kernel pool )
   cspice_gdpool ( Get d.p. values from the kernel pool )
   cspice_gipool ( Get integers from the kernel pool )
   cspice_pckcov ( PCK, coverage )
   cspice_pckfrm ( PCK, get reference frame class ID set )
   cspice_pxform ( Position Transformation Matrix )
   cspice_sxform ( State Transformation Matrix )
   cspice_unload ( Unload a kernel )


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Appendix B --- 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 epoch and inertial base frame for a body are overridden by setting the values of either of the kernel variables

   BODY<id code>_CONSTANTS_REF_FRAME
   BODY<id code>_CONSTS_REF_FRAME
and

   BODY<id code>_CONSTANTS_JED_EPOCH
   BODY<id code>_CONSTS_JED_EPOCH
The shorter forms of the kernel variable names enable use of 11-character ID codes, which can represent any 32-bit signed integer, while keeping the names within the 32-character limit imposed by Icy.

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 variables

   BODY<id code>_CONSTANTS_REF_FRAME
   BODY<id code>_CONSTS_REF_FRAME
are the frames IDs for the inertial reference frames coded into the Frames subsystem. Refer to the Frames Required Reading document, frames.req, for a list of the inertial reference frames and the corresponding frame IDs.

For example, to use constants referenced to the FK4 frame (frame ID 3) for the asteroid Gaspra (ID code = 9511010), the PCK file containing the constants should include one of the assignments

   BODY9511010_CONSTANTS_REF_FRAME   =   3
   BODY9511010_CONSTS_REF_FRAME      =   3
The values of the epoch specifier variables

   BODY<id code>_CONSTANTS_JED_EPOCH
   BODY<id code>_CONSTS_JED_EPOCH
are Julian ephemeris dates. To use constants for Gaspra referenced to the J1950 epoch, the PCK file containing the constants should include one of the assignments

   BODY9511010_CONSTANTS_JED_EPOCH   =   2433282.5
   BODY9511010_CONSTS_JED_EPOCH      =   2433282.5
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 (frame ID 2) and J1950 epoch for the Earth and Moon, use the assignments

   BODY3_CONSTANTS_REF_FRAME   =   2
   BODY3_CONSTANTS_JED_EPOCH   =   2433282.5
 
      or
 
   BODY3_CONSTS_REF_FRAME   =   2
   BODY3_CONSTS_JED_EPOCH   =   2433282.5
The ID code `3' designates the Earth-Moon barycenter.

Note: the assignments

   BODY399_CONSTANTS_REF_FRAME   =   2
   BODY399_CONSTANTS_JED_EPOCH   =   2433282.5
 
      or
 
   BODY399_CONSTS_REF_FRAME   =   2
   BODY399_CONSTS_JED_EPOCH   =   2433282.5
would be ignored by the PCK reader routines; you cannot assign a frame or epoch using the ID code of a planet or satellite.



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Appendix C --- Revision History







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2021 DEC 24 by N.J. Bachman



Added documentation of shortened kernel variable names for alternative PCK base frames or JED epochs.

Added documentation of extended nutation precession angle polynomial capability.

Deleted summary of calling sequences.

Updated summary of PCK routines.

Added subsection discussing possible offsets of reference ellipsoid axes from the corresponding PCK frame, and handling this situation via TK frames.

Added description of nutation precession angle coefficient units.

Changed description of segment descriptor ID from ``body ID'' to ``frame class ID.'' Changed names of arguments in calling sequence documentation to match.

Updated description of PCK ID word to say this string must start in the leftmost column.

Removed unnecessary parentheses from kernel variable assignment examples.



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2013 JAN 22 by E. D. Wright, C. H. Acton



Corrections and updates to properly describe PCK binary Type 2 and PCK binary Type 3 data segments. Added information concerning PCK binary type 20 data segments.

Eliminated Examples section.

Corrections to text eliminating typos in the code call examples.

Update to document structure to include Revision History.

The document now includes description of Icy, and Mice PCK APIs.



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2010 JUN 03 by B. V. Semenov.



Previous edits.



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Original version K.R. Gehringer, K. S. Zukor