SPK Required Reading

Last revised on 2005 NOV 17 by N. J. Bachman.

Abstract

The SPK system is the component of SPICE concerned with ephemeris data.

Purpose

The purpose of this document is to describe the NAIF Toolkit software provided in the software library CSPICE, (C SPICE library) used for producing and accessing SPICE ephemeris data. In addition this document describes SPK---the common file format for NAIF's S-kernel and ephemeris portion of the P-kernel.

Intended Audience

This document is intended for all users of SPK (ephemeris) kernel files.

References

All references are to NAIF documents. The notation [Dn] refers to NAIF document number.

1. [349] Frames Required Reading

2. [174] CK Required Reading

3. [254] PCK Required Reading

4. [222] Spacecraft Clock Time Required Reading. ( SCLK )

5. [218] KERNEL Required Reading.

6. [219] NAIF IDS Required Reading.

7. [163] JPL Internal Memorandum on Modified Difference Array polynomials; F. Krogh

8. [164] Precession Matrix Based on IAU (1976) System of Astronomical Constants; E. M. Standish; Astronomy and Astrophysics 73, 282-284 (1979)

9. [165] Orientation of the JPL Ephemerides, DE200/LE200, to the Dynamical Equinox of J2000; E. M. Standish; Astronomy and Astrophysics 114, 297-302 (1982)

10. [166] The JPL Asteroid and Comet Database (as Implemented by NAIF); a collection of papers and memos; assembled by I. Underwood; 11 Dec 1989

11. [167] Double Precision Array Files (DAF) - Required Reading; latest version

12. [212] COMMNT User's Guide

DAF Run-Time Binary File Format Translation

Starting with the N0052 release of the SPICE Toolkit (January, 2002) certain supported platforms are able to read DAF-based binary files (SPK, CK and binary PCK) that were written using a different, or 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 for details.

Detection of Non-native Text Files

Starting with the N0057 release of the SPICE Toolkit (March, 2004) the SPICE data loading mechanism detects and prohibits loading text kernel files containing lines terminated with EOF character(s) non-native to the platform on which the Toolkit was compiled. If a non-native EOL terminator is detected in the first 132 characters of a text kernel, the execution is stopped and an error message is displayed. This feature does not work with files that are smaller that 132 bytes or have the first line longer that 132 characters.

If you're in a hurry

We'll discuss things in more detail in a moment but in case you are just looking for the right name of the function to perform some ephemeris task, here is a categorization of the most frequently used SPK and related functions in CSPICE. Input arguments are given in lower case and enclosed in ``angle brackets.'' Output arguments are given in plain lower case.

High Level Functions

Loading/Unloading an SPK file

   furnsh_c ( <file> )
   unload_c ( <file> )

   spkezr_c ( <object>,   <et>,  <frame>, <corr>,
              <observer>, state, <             )

   spkpos_c ( <object>,   <et>,  <frame>, <corr>,
              <observer>, postn, <             )

   spkez_c  ( <obj_id>,  <et>,  <frame>,  <corr>,
              <obj_id>,  state, <              )
 
   spkgeo_c ( <obj_id>,  <et>,  <frame>,
              <obj_id>,  state, <     )

   spkezp_c ( <obj_id>,  <et>,  <frame>,  <corr>,
              <obj_id>,  postn, <              )
 
   spkgps_c ( <obj_id>,  <et>,  <frame>,
              <obj_id>,  postn, <     )

   ltime_c ( <etobs>, <obs_id>, <dir>, <targ_id>, &ettarg, &elapsd )

   furnsh_c ( <binary_pck> )
   unload_c ( <binary_pck> )

   furnsh_c ( <text_kernel> )

   furnsh_c ( <c-kernel> )
   unload_c ( <c-kernel> )

Foundation Functions

The functions listed in this section are the real ``work horses'' of the SPK and related systems. Not all of the functions in this section are described in this document. In those cases, the appropriate SPICE document is cited.

Selecting files and segments

   spksfs_c ( <target>, <et>, &handle, descr, ident, &found )

   spkpvn_c ( <handle>, <descr>, <et>, ref, state, ¢er )

   stelab_c ( pobj, vobs, appobj )

   bodn2c_c ( <name>,    &idcode, &found )
   bodc2n_c ( <idcode>,  name,    &found )

   frmnam_c ( <idcode>, name    )
   namfrm_c ( <name>,   &idcode )

   frmchg_c ( <from_idcode>, <to_idcode>, <et>, mat6x6 )

   frinfo_c ( <idcode>, ¢er, &class, &clssid, &found )

Utility Programs

Examining SPK files

   brief
   commnt
   spacit

   spacit
   tobin
   toxfr

Introduction

To help fully understand the science data returned from a spacecraft's instruments it is necessary to know, at any given epoch, the positions and possibly the velocities of the spacecraft and all the target bodies of interest. The purpose of the SPK---which stands for S(pacecraft) and P(lanet) Kernel---file is to allow ephemerides for any collection of solar system bodies to be combined under a common file format, and accessed by a common set of functions.

Historically, ephemerides for spacecraft have been organized differently from those for planets and satellites. They are usually generated through different processes and using different representations. However, there is no essential reason for keeping them separate. A spacecraft, planet, satellite, comet, or asteroid has a position and velocity relative to some center of mass and reference frame. Consequently all of these objects can be represented in an SPK file.

Consider the Galileo mission. Some of the objects of special interest to the Galileo mission are:

   Galileo Spacecraft
   Galileo Probe
   Earth
   Moon
   Earth Moon Barycenter
   Venus
   Sun
   Solar System Barycenter (S.S.B.)
   Asteroid Ida
   Ida's Satellite Dactyl
   Asteroid Gaspra
   Comet Shoemaker-Levy
   Jupiter System Barycenter (J.B.)
   Jupiter
   Io
   Ganymede
   Europa
   Callysto
   Goldstone Tracking Station.

                          +Gll
                         /             probe
                        /               |    o Comet
                Gaspra /             Gll+   /  Shoemaker Levy
         Gll +--o     /                  \ /
                |    /   Venus    Jupiter o--probe
                |   /      o--+           |
    Gll +       |  /      /   Gll         |  Io
        |       | /      /                |  o-----+Gll
        |       |/      /             J.B.| /
   Ida  o-------o------o------------------o ----o------+Gll
       /         Sun   S.S.B.            / \    Europa
      o                 \      Ganymede /   \
   Dactyl                \             o     \
                          \            |      o Callisto
    Earth-Moon Barycenter  o----o      +      |
                           |   Moon    Gll    |
                           |                  + Gll
                           o Earth
                          / \
                         /   \
                        /     + Gll
                       o
                    Goldstone

(Although we can store the entire ephemeris history illustrated above in a single SPK file, for the sake of data management a project is likely to use several SPK files. However, even in this case, all of the SPK files can be used simultaneously.)

The SPK format is supported by a collection of functions that are part of the CSPICE library---the major component of the NAIF Toolkit. This family of SPK functions provides the following capabilities:

1. Insert ephemeris data from some source into an SPK file.

2. Make the ephemeris data in one or more SPK files available to a user's program.

3. Return the apparent, true, or geometric state (position and velocity) of one ephemeris object as seen from another in some convenient reference frame.

SPK Files

SPK files are binary files. The format of these binary files is based upon a more abstract file architecture called Double precision Array File (DAF). Several other SPICE kernels are also based on the DAF architecture. If you are only going to be a consumer of SPK files or if you will be using a SPICE utility program for creating SPK files, you can safely ignore aspects of the DAF system that are not covered by this document. On the other hand, if you plan to write software for creating SPK files you will probably need to familiarize yourself with the DAF software contained in CSPICE. The DAF architecture and supporting software is discussed in [169]. The particular aspects of the DAF architecture that are relevant to the SPK format are discussed later in this document (see below---SPK Format).

Moving SPK files between computers

A binary file suitable for use on one computer, may not be suitable for use on another computer. For example, SPK files created on a Sun Sparc-10 are not suitable for use on a PC running SPICE software compiled with the Borland Bcc32i C++/C compiler. As a result you can't always perform a ``binary copy'' of an SPK file from one machine to another. NAIF provides two utility programs---TOXFR and SPACIT for converting SPICE binary kernels to a ``transfer format'' that is suitable for text copying from one computer to another. Once the transfer format file has been copied, the NAIF utilities TOBIN and SPACIT are available for converting the transfer format file to the binary format suitable for the new machine.

The utilities TOXFR and TOBIN are ``command line'' programs. To convert a binary kernel to transfer format you simply type TOXFR followed by the name of the binary kernel at your terminal prompt.

   prompt> toxfr spk_file

   prompt> tobin transfer_file

Note that transfer format files are suitable only for moving data from one machine to another. They cannot be ``loaded'' into a SPICE based program to retrieve ephemeris data. Only binary format files can be used for retrieving ephemeris data with SPICE software.

Porting files between SPICELIB and CSPICE

In most environments where SPICELIB is supported, CSPICE can use the same binary kernels as does SPICELIB. Environments where this local compatibility exists are:

   Sun, Solaris; Sun Fortran; Sun C or Gnu gcc
   Silicon Graphics, IRIX OS; Silicon Graphics Fortran; Gnu gcc
   HP Series 700 computers, HP-UX 9000/750; FORTRAN/9000; HP C
   VAX/VMS; VAX FORTRAN; VAX C
   PC, DOS/Win95/NT; MS Powerstation Fortran; Borland Bcc32i C++/C
   NeXT, Mach; Absoft Fortran; Gnu gcc
   Macintosh Clasic and OS X

Examining SPK files

Since SPK files are binary files, you can't just open them with your favorite text editor to determine which ephemeris objects are represented in the file. Instead you need to use one of the NAIF utility programs that allow you to summarize the ephemeris contents of an SPK file. The first of these is SPACIT which was introduced above. The second is the command line utility BRIEF.

BRIEF gives a quick summary of the contents of the file and supports a wide set of summary options. SPACIT on the other hand, provides summaries that are more detailed and reflect closely the actual internal structure of the file. Unless you need the more detailed summary, you'll probably find BRIEF to be a better tool for examining the contents of an SPK file.

Meta Data in the SPK file

SPICE kernels may contain ``meta'' data that describe the contents, intended use, accuracy, etc. of the kernel. This meta data is called the ``comments'' portion of the kernel. Many SPK files contain comments that can help you decide upon the suitability of the kernel for your application. Two SPICE utilities are available for examining the comments of a binary kernel---COMMNT and SPACIT.

We've already introduced SPACIT. COMMNT is similar to SPACIT in that it too is an interactive program. However, COMMNT also allows you to modify the comments of an SPK file. Using COMMNT you can delete the comments of an SPK file, extract the comments to a text file, or append the text from some text file to the comments already present in the kernel.

If you create SPK files, we strongly recommend that you add comments to the kernel that describe who created it, expected usage of the kernel, and the expected accuracy of the position/velocity information contained in the kernel. A comment template is provided in the appendix ``COMMENTS''.

Warning: If you add comments to an SPK (or other binary kernel) using COMMNT, you must wait for the program to complete the task before exiting the program. Failure to wait for COMMNT to finish its work will result in irreparable corruption of the binary kernel. (See the COMMNT User's Guide [212] for details on the use of COMMNT).

Terminology

Throughout this document we shall be using terms such as reference frame, state, ephemeris time, etc. We include a brief review of these terms below.

Reference Frame

A reference frame is a Cartesian coordinate system with three axes---x, y and z. The axes are mutually orthogonal. The center of the frame is the origin of the Cartesian reference system. For the reference frames in SPICE, the positions of the axes are typically defined by some observable object. For example, in the J2000 reference frame, the x-axis is defined to lie in the intersection of two planes: the plane of the Earth's equator and the plane of the Earth's orbit. The z-axis is perpendicular to the Earth's equator. The y-axis completes a right-handed system. The center of the frame is typically taken to be the solar system barycenter. (Note we are not attempting to rigorously define the J2000 frame here. We are only illustrating how reference frames are defined. Many more details are required for a rigorous definition of the J2000 frame. These details are given in the SPICE document ``Frames'' [349].)

State

A state is an array of six double precision numbers. The first three numbers give the x, y, and z coordinates respectively for the position of some object relative to another object in some Cartesian reference frame. The next three numbers give the velocity ( dx/dt, dy/dt and dz/dt respectively) of the object with respect to the same reference frame.

Inertial Frame

An inertial frame, is one in which Newton's laws of motion apply. A frame whose axes are not moving with respect to the observed positions of distant galaxies and quasars approximates an inertial frame.

Non-Inertial Frame

A non-inertial frame is a frame that rotates with respect to the celestial background. For example a frame whose axes are fixed with respect to the features on the surface of the Earth is a non-inertial frame.

Ephemeris Time (ET)

Ephemeris time, ET, is the independent variable in the equations of motion that describe the positions and velocities of objects in the solar system. In CSPICE we treat ET as a synonym for Barycentric Dynamical Time. As far as has been experimentally determined, an atomic clock placed at the solar system barycenter, would provide a faithful measure of ET.

Seconds Past 2000

In the SPK system times are specified as a count of seconds past a particular epoch---the epoch of the J2000 reference frame. This reference epoch is within a second or two of the UTC epoch: 12:01:02.184 Jan 1, 2000 UTC. (See the document TIME.REQ for a more thorough discussion of the J2000 epoch). Epochs prior to this epoch are represented as negative numbers. The ``units'' of ET are designated in several different ways: seconds past 2000, seconds past J2000, seconds past the Julian year 2000, seconds past the epoch of the J2000 frame. All of these phrases mean the same thing and are used interchangeably throughout this document.

SPK segment

The trajectories of objects in SPK files are represented in pieces called segments. A segment represents some arc of the full trajectory of an object. Each segment contains information that specifies the trajectory of a particular object relative to a particular center of motion in a fixed reference frame over some particular interval of time. From the point of view of the SPK system segments are the atomic portions of a trajectory.

The SPK Family of Functions

CSPICE contains a family of functions that are designed specifically for use with SPK files. The name of each function begins with the letters `spk', followed by a two- or three-character mnemonic. For example, the function that returns the state of one body with respect to another is named spkezr_c, pronounced `S-P-K-easier'. A complete list of mnemonics, translations, and calling sequences can be found at the end of this document.

Each function is prefaced by a complete CSPICE header, which describes inputs, outputs, restrictions, and exceptions, discusses the context in which the function can be used, and shows typical examples of its use. Any discussion of the functions in this document is intended as an introduction: the final documentation for any function is its header.

Whenever an SPK function appears in an example, the translation of the mnemonic part of its name will appear to the right of the reference, in braces. We also continue with the convention of distinguishing between input and output arguments by enclosing input arguments in angle brackets. For example,

   spkezr_c ( <targ>,  <et>,  <frame>,
              <aberr>, <obs>,
              state,   <            );  { Easier state }

SPK readers are available to perform the following functions.

1. Determine the apparent, true, or geometric state of a body with respect to another body relative to a user specified reference frame.

2. Determine the apparent, true, or geometric state of a body with respect to an observer with having a user-supplied state.

3. Determine the geometric state of a body with respect to the solar system barycenter.

4. Determine the geometric state of a target body with respect to its center of motion for a particular segment.

5. Determine, from a list of SPK files supplied by the calling program, the files and segments needed to fulfill a request for the state of a particular body.

Computing States

spkezr_c is the most powerful of the SPK readers. It determines the apparent, true, or geometric state of one body (the target) as seen by a second body (the observer) relative to a user specified reference frame.

   spkezr_c ( <targ>,  <et>,  <frame>,
              <aberr>, <obs>,
              state,   <            );  { Easier state }

The target body, observing body and frame are identified by strings that contain the names of these items. For example, to determine the state of Triton as seen from the Voyager-2 spacecraft relative to the J2000 reference frame

   spkezr_c ( "triton",    et,    "j2000", aberr,
              "voyager-2", state,  <           ); { Easier state }

   et = ( 2447751.8293d0 - j2000() ) * spd_c();
 
   spkezr_c ( "triton",    et,    "j2000", <aberr>,
              "voyager-2", state, <              ); { Easier state }

The ephemeris data in an SPK file may be referenced to a number of different reference frames. States returned by spkezr_c do not have to be referenced to any of these ``native'' frames. The user can specify that states are to be returned in any of the frames recognized by the frame subsystem. For example, to determine the state of Triton as seen from Voyager-2, referenced to the J2000 ecliptic reference frame,

   spkezr_c ( "triton", et,          "eclipj2000",
              aberr,    "voyager-2", state,
              <                                 ); { Easier state }

Apparent states are corrected for planetary aberration, which is the composite of the apparent angular displacement produced by motion of the observer (stellar aberration) and the actual motion of the target body (correction for light-time). True states are corrected for light-time only. Geometric states are uncorrected.

Instead of using the potentially confusing terms `true' and `geometric' to specify the type of state to be returned, spkezr_c requires the specific corrections to be named. To compute apparent states, specify correction for both light-time and stellar aberration: `LT+S'. To compute true states, specify correction for light-time only: `LT'. To compute geometric states, specify no correction: `NONE'.

In all cases, the one-way light-time from the target to the observer is returned along with the state.

The Computation of Light Time

The light time corrected states returned by the SPK system are simply the 6-vector difference

   TARGET_SSB ( ET - LT )   - OBSERVER_SSB ( ET )

         | TARGET_SSB ( ET - LT )   - OBSERVER_SSB ( ET ) |
   LT =  --------------------------------------------------
                        Speed of Light

   | STATE |

(Note that the velocity portion of the state returned is simply the difference in the velocity components of

            TARGET_SSB ( ET - LT ) and OBSERVER_SSB ( ET )

This is NOT the derivative of the light time corrected position because this does not take into account the time derivative of LT.)

   LT_0 = 0
 
 
 
           | TARGET_SSB ( ET - LT_(i-1) ) - OBSERVER_SSB ( ET ) |
   LT_i =  ------------------------------------------------------
                              Speed of Light
 
 
   (for i = 1, 2, 3 ... )

                              i+1
   | LT - LT_i | < LT * ( V/C )

For nearly all objects in the solar system V is less than 60 km/sec. The value of C is 300000 km/sec. Thus the one iteration solution for LT has a potential relative error of not more than 4*10D-8. This is a potential light time error of approximately 2*10D-5 seconds per astronomical unit of distance separating the observer and target. Thus as long as the observer and target are separated by less than 50 Astronomical Units the error in the light time returned using option 'LT' is less than 1 millisecond.

For this reason, we use LT_1 to approximate LT when you request a light time corrected state by setting the aberration correction argument in spkezr_c to `LT' or `LT+S'.

You can make spkezr_c perform a better approximation to LT by requesting that it compute a ``converged Newtonian'' value for LT. To do this set the aberration correction to `CN' or `CN+S'. spkezr_c will then return LT_3 as the approximation for light time. The maximum error in LT_3 is less than a nanosecond for any observer/target pair in the solar system.

However, you should note that this is a purely Newtonian approximation to the light time. To model the actual light time between target and observer one must take into account effects due to General relativity. These may be as high as a few hundredths of a millisecond for some objects.

The functions in the SPK family do not attempt to perform either general or special relativistic corrections in computing the various aberration corrections. For many applications relativistic corrections are not worth the expense of added computation cycles. If, however, your application requires these additional corrections we suggest you consult the astronomical almanac (page B36) for a discussion of how to carry out these corrections.

Light Time Corrected Non-Inertial States

When we observe a distant object, we don't see it as it is at the moment of observation. We see it as it was when the photons we have sensed were emitted by or reflected from the object. Thus when we look at Mars through a telescope, we see it not as it is now, but rather as it was one ``light-time'' ago. This is true not only for the position of Mars, but for its orientation as well.

Suppose that a large balloon has been launched into the Martian atmosphere and we want to determine the Mars bodyfixed state of the balloon as seen from Earth at the epoch ET. We need to determine both the light time corrected position of the balloon, and the light time corrected orientation of Mars. To do this we compute two light times. The light time to the center of the Mars bodyfixed frame (i.e. the center of Mars) and the light time to the balloon. Call the light time to the center of the Mars frame LT_F and call the light time to the balloon LT_T. The light time corrected state of the balloon relative to the Mars bodyfixed frame is the location of the balloon at ET - LT_T in the bodyfixed frame of Mars as oriented at ET - LT_F.

spkezr_c carries out all of these computations automatically. In this case the computation would be computed by a function call similar to this:

   spkezr_c ( "mars_balloon",  <et>,  "iau_mars", "lt",
              "earth",         state, <              );

1. When no corrections are requested from spkezr_c (ABCORR = 'NONE'), the state of the target is determined at the request time ET and is represented in the specified reference frame as it is oriented at time ET.

2. When light time corrections are requested from spkezr_c (ABCORR = 'LT'), two light times are determined: LT_F the light time to the center of the specified reference frame, and LT_T the light time to the target. The state of the target is given as it was at ET - LT_T in the frame as it was oriented at ET - LT_F.

3. When light time and stellar aberrations are requested from spkezr_c (ABCORR = 'LT+S'), both LT_F and LT_T are again computed. The state of the target at ET - LT_T is corrected for stellar aberration and represented in the reference frame as it was oriented at ET - LT_F.

An example

Here we illustrate how you could use spkezr_c together with other CSPICE functions to determine if at a particular epoch ET the Mars Global Surveyor spacecraft is occulted by Mars.

We will need the lengths of the axes of the triaxial ellipsoid that is used to model the surface of Mars. Either of the CSPICE functions bodvcd_c or bodvrd_c will retrieve this information from a loaded PCK file. bodvrd_c uses the name of the body, while bodvcd_c uses the NAIF ID code for Mars (499) to retrieve the lengths of the axes. We may call bodvcd_c as shown:

   bodvcd_c ( 499, "RADII", 3, &nvals, axes );
 
   a = axes[0];
   b = axes[1];
   c = axes[2];

   spkezr_c ( "mars",  et,     "iau_mars", "lt+s",
              "earth", marsst, <                );
 
   spkezr_c ( "mgs",   et,     "iau_mars", "lt+s",
              "earth", mgsst,  <                ); {Easier State}

   vminus_c ( marsst, estate );

   surfpt_c ( estate, mgsst, a, b, c, point, &found );

   if ( found )
      {
      betwn = (  vdist_c ( estate, point ) < vnorm_c ( mgsst )  );
      }
   else
      {
      betwn = SPICEFALSE;
      }
 
 
   if ( betwn )
      {
      printf ( "mgs is behind mars\n" );
      }
   else
      {
      printf ( "mgs is not behind mars\n" );
      }

Integer ID Codes Used in SPK

Low level SPK software uses integer codes to identify ephemeris objects, reference frames and data representation, etc. At low levels of the SPICE system only integer codes are used to communicate information about objects. To some extent, these codes are a historical artifact in the design of the SPICE system. Nevertheless, these integer codes provide economies in the development of SPICE software.

High-level SPICE software uses names (character strings) to refer to the various SPICE objects and translates between names and integer codes. Thus to some extent you can disregard the integer codes used by the SPICE internals. However, occasionally, due to the introduction of new ephemeris objects, the name translation software will be unable to find a name associated with an ID code. To retrieve states for such an object you will need to use the integer code for the object in question. If you are using spkezr_c, you can supply this integer code as a quoted string. For example the following two function calls will both return the state of TRITON as seen from Voyager-2. (The NAIF integer code for TRITON is 801; the NAIF integer code for Voyager 2 is -32).

   spkezr_c ( "triton", et,          "eclipJ2000",
              aberr,    "voyager-2", state,
              <                                 ); { Easier state }
 
 
   spkezr_c ( "801",    et,          "eclipJ2000",
               aberr,   "-32",       state,
               <                                ); { Easier state }

spkez_c and spkgeo_c

spkezr_c relies upon two lower level functions that may be useful under certain circumstances.

The function spkez_c performs the same functions as spkezr_c. The only difference is the means by which objects are specified. spkez_c requires that the target and observing bodies be specified using the NAIF integer ID codes for those bodies.

   spkez_c ( <targ_id>, <et>, <frame>, <corr>, <obj_id>,
             state,     < );                          { SPK Easy }

spkez_c is useful in those situations when you ID codes for objects stored as integers. There is also a modest efficiency gain when using integer ID codes instead of character strings to specify targets and observers.

The function spkgeo_c returns only geometric (uncorrected) states. The following two function calls are equivalent.

   spkez_c  ( <targ_id>,  <et>,   <frame>, "none",
              <obj_id>,   state,  <             ); {SPK Easy}
 
   spkgeo_c ( <targ_id>,  <et>,   <frame>, <obj_id>,
              state,      <                     ); {SPK Geometric }

Loading Files

Note that spkezr_c, spkez_c and spkgeo_c do not require the name of an SPK file as input. These functions rely on the lower level routine in the SPK subsystem to maintain a database of ephemeris files. Your application program indicates which files are to be used by passing their names to function furnsh_c -- ``generic loader'' that can be used to load SPICE kernel files of any type.

   for ( i = 0;  i < N;  i++ )
   {
      furnsh_c ( ephem[I] );        { Load kernel file }
   }

            Jupiter_Barycenter --- Europa
            /                       \
           /                         \
          /                          Spacecraft
         /
        /
       /
      /
   SSB
      \
       \
        \
        EMB --- Earth

Each state is computed from a distinct segment. The segments may reside in a single SPK file, or may be contained in as many as five separate files. For example, the segments needed to compute the Earth-spacecraft state shown above might come from the following set of files:

   furnsh_c ( "barycenters.bsp"    );  { Load kernel file }
   furnsh_c ( "planet-centers.bsp" );  { Load kernel file }
   furnsh_c ( "satellites.bsp"     );  { Load kernel file }
   furnsh_c ( "spacecraft.bsp"     );  { Load kernel file }

   furnsh_c ( "earth.bsp"      );      { Load kernel file }
   furnsh_c ( "jupiter.bsp"    );      { Load kernel file }
   furnsh_c ( "spacecraft.bsp" );      { Load kernel file }

Data Precedence

An SPK file may contain any number of segments. A single 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.

Unloading Files

The number of SPK files that may be loaded at any one time is limited but very large -- up to 1000 total for all loaded SPK, CK, and binary PCK files combined. Although unlikely, in some cases your application program may need to unload some SPK files to make room for others or to remove a particular SPK from the set of loaded data. An SPK file may be unloaded by supplying its name to function unload_c -- ``generic unloader'' that can be used to unload SPICE kernel of any type. The sequence of statements shown below,

   furnsh_c ( "file.a" );     { Load kernel file }
   furnsh_c ( "file.b" );     { Load kernel file }
   furnsh_c ( "file.c" );     { Load kernel file }
   unload_c ( "file.b" );     { Unload kernel file }
   furnsh_c ( "file.d" );     { Load kernel file }
   unload_c ( "file.c" );     { Unload kernel file }

   furnsh_c ( "file.a" );     { Load kernel file }
   furnsh_c ( "file.d" );     { Load kernel file }

Loading Auxiliary Files

Prior to the inclusion of non-inertial frames in the SPK system, the states of objects computed by the SPK system required only that you load the correct SPK files and call the correct functions. The inertial frame transformations needed for converting from one inertial frame to another are ``hard wired'' into the SPICE system. The transformations are part of the object code of the CSPICE library---no additional data need be supplied to compute these transformations. This approach to carrying out inertial frame transformations was chosen because the transformations are compactly represented and do not change as the result of further observations. They are essentially definitions.

On the other hand, the orientation of non-inertial frames with respect to other frames are almost always the result of observation. They are improved and extended as further observations are made. For some of these frames (such as spacecraft fixed frames) vary large data sets are needed to express the orientation of the frame with respect to other frames. Frame transformations that are a function of time and require megabytes of data are not suitable for encapsulation in C or FORTRAN source code. As a result, in the SPICE system, the computation of non-inertial frame transformations depends upon data stored in other SPICE kernels. If you request states relative to a non-inertial frame or use ephemerides that are represented relative to non-inertial frames you must load additional SPICE kernels. The method by which an auxiliary kernel is loaded depends upon the type of the kernel.

There are currently four classes of reference frames that are supported by the SPICE system. We give a brief overview of these frames here. For a more thorough discussion of the various types of frames see the recommended reading file ``FRAMES.REQ.''

Inertial frames

Inertial frames are built into the SPICE system. You don't need to do anything to make their definitions available to your program. Inertial frames have NAIF ID codes whose values are in the range from 1 to 10000.

PCK frames are bodyfixed frames. The orientation of a PCK frame is always expressed relative to an inertial frame. The relationship between a PCK frame and its associated inertial frame is provided by a PCK kernel. PCK frames have ID codes between 10000 and 100000. There are two types of PCK kernels---binary and text. Binary PCK kernels are loaded (and unloaded) in a fashion analogous to the loading and unloading of SPK files. To load a binary PCK file

            furnsh_c ( <file> );

To unload a binary PCK file

            unload_c ( <file> );

text based PCK files are loaded via the function furnsh_c.

            furnsh_c ( <file> )

CK frames are frames that are defined relative to a spacecraft structure. The orientation of the structure is provided through a binary SPICE kernel called a C-kernel. The ID codes for C-kernel frames are negative and usually less than -999. A C-kernel frame may be defined relative to any other kind of frame. (Most existing C-kernels are defined relative to inertial frames.)

C-kernels are loaded and unloaded using the same loader functions as used to load and unload SPK kernels. To load a C-kernel

            furnsh_c ( <file> );

To unload a C-kernel

            unload_c ( <file> );

The times used to represent C-kernels are spacecraft clock times---not ET. The relationship between ET and spacecraft clock times is stored in a SPICE text kernel called a spacecraft clock kernel---usually abbreviated as SCLK (ess-clock) kernel. To retrieve states relative to a CK frame you need to make the relationship between ET and the spacecraft clock available to your program by loading the appropriate SCLK kernel. SCLK kernels are loaded via the function furnsh_c.

            furnsh_c ( <sclk_file_name> );

TK frames (short for Text Kernel frames) are frames that are defined via a SPICE text kernel. These frames can be transformed to another reference frame via a constant rotation matrix. Typical examples are topocentric frames and instrument frames. TK frames are loaded via the function furnsh_c.

            furnsh_c ( <TK_frame_file> );

As is evident from the above discussion, the use of non-inertial frames requires more data management on the part of the user of the SPICE system. However, this data management problem is not a new problem. In previous versions of the SPICE system the same kernels would have been required. Moreover, in previous versions of the SPICE system, you would have been required to perform all non-inertial transformations in your own code. With the inclusion of non-inertial frames in the SPK system, we have relieved you of some of the tasks associated with non-inertial frames.

SPK File Structure

An SPK file is made up of one or more data ``segments'' and a ``comment'' area. These components are described below.

Segments--The Fundamental SPK Building Blocks

An SPK file contains one or more ``segments.'' Each segment contains ephemeris data sufficient to compute the geometric state (position and velocity) of one solar system body (the `target') with respect to another (the `center') at any epoch throughout some finite interval of time.

Either body may be a spacecraft, a planet or planet barycenter, a satellite, a comet, an asteroid, a tracking station, a roving vehicle, or an arbitrary point for which an ephemeris has been calculated. Each body in the solar system is associated with a unique integer code. A list of names and codes for the planets, major satellites, spacecraft, asteroids and comets can be found in the document NAIF_IDS.REQ

The states computed from the ephemeris data in a segment must be referenced to a single, recognized reference frame.

The data in each segment are stored as an array of double precision numbers. The summary for the array, called a `descriptor', has two double precision components:

1. The initial epoch of the interval for which ephemeris data are contained in the segment, given in ephemeris seconds past Julian year 2000.

2. The final epoch of the interval for which ephemeris data are contained in the segment, given in ephemeris seconds past Julian year 2000.

1. The NAIF integer code for the target.

2. The NAIF integer code for the center.

3. The NAIF integer code for the reference frame.

4. The integer code for the representation (type of ephemeris data).

5. The initial address of the array.

6. The final address of the array.

The Comment Area

Preceding the `segments', the Comment Area provides space in the SPK file for storing textual information besides what is written in the array names. Ideally, each SPK 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 SPK file could be included in the Comment Area.

The utility programs COMMNT and SPACIT may be used to examine and manipulate the comments in an SPK file. In addition to these utilities, CSPICE provides a family of functions for handling this Comment Area. The name of each function in this family begins with the letters `SPC' which stand for `SPk and Ck' because this feature is common to both types of files. The SPC software provides the ability to add, extract, read, and delete comments and convert commented files from binary format to SPICE transfer format and back to binary again.

The SPC functions and their functions are described in detail in the SPC Required Reading.

SPK Data Types

The fourth integer component of the descriptor---the code for the representation, or `data type'---is the key to the SPK 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---when a state vector is to be computed---that the type of data used to represent the ephemeris becomes important.

Because this step is isolated within a single low-level reader, spkpvn_c, new data types can be added to the SPK format without affecting application programs that use the higher level readers. spkpvn_c is designed so that the changes required to implement a new data type are minimal.

There are no real limits on the possible representations that can be used for ephemeris data. Users with access to data suitable for creating an ephemeris may choose to invent their own representations, adapting spkpvn_c accordingly. (We recommend that you consult with NAIF prior to implementing an new data type.)

The data types currently supported by CSPICE software are listed under ``Supported Data Types'' later in this document.

Lower-level Readers

When computing states, spkezr_c should be sufficient to handle the needs of most users. However, it is possible to exercise more direct control over the way states are computed. In this section we discuss means by which the user of the SPK system can take more direct control over the computation of states.

As noted above, spkezr_c is identical to spkez_c except that it uses the names of objects as inputs instead of integer ID codes. Indeed, spkezr_c ``looks up'' the ID codes associated with the named objects, and then calls spkez_c using these ID codes.

spkez_c computes apparent and true states using two readers of slightly less power---spkssb_c and spkapp_c.

spkssb_c returns the state of a body with respect to the solar system barycenter. spkez_c uses it to compute the state of the observer relative to an inertial reference frame.

The second, spkapp_c, returns the state of a target body as seen from an observer. Where spkez_c requires the integer code for an observer, spkapp_c requires the actual state of the observer with respect to the solar system barycenter relative to an inertial reference frame. A single call to spkez_c,

   spkez_c ( 801, et, "j2000", "lt+s", -32, starg, < )  { Easy
                                                            state }

   spkssb_c ( -32,
              et,
              "j2000",
              stobs    );        { Solar system barycenter }
 
   spkapp_c (  801,
               et,
              "j2000",
               stobs,
              "lt+s",
               starg,
               <       );        { Apparent state }

One possible advantage of using spkapp_c directly is the ability to place an observer somewhere other than at the center of a body (for example, at a specified location on the surface of the Earth).

When computing uncorrected, that is, geometric states, spkez_c does not need to compute the state of the target and observer relative to the solar system barycenter, but only relative to the first common center of motion of those two bodies. spkez_c calls spkgeo_c to compute geometric states.

Using spkgeo_c instead of the combination spkssb_c and spkapp_c as above prevents possible round-off error, may reduce the number of file reads, and may require less data. For example, if SPK ephemeris data for a spacecraft relative to a planet has been loaded, but the ephemeris data for that planet relative to the solar system barycenter is not available, spkgeo_c can still compute the state of the spacecraft relative to the planet, whereas the combination spkssb_c and spkapp_c would be unsuccessful at computing that state.

Primitive States

At the lowest level, it is possible to compute states without combining them at all. Given the handle and descriptor for a particular segment, function spkpvn_c returns a state from that segment directly.

   spkpvn_c ( <handle>,
              <descr>,
              <et>,
              ref,
              state,
              center   );  { Position, velocity, native frame }

The user is also responsible for using DAF functions to determine the particular file and segment from which each state is to be computed.

Note that to use the state returned by spkpvn_c in any frame other than the ``native frame'' of the segment, you must convert the state to the frame of interest. A second low level function spkpv_c can be used to perform the state transformations for you. The calling sequence for spkpv_c is identical to that for spkpvn_c. However, in the case of spkpv_c the reference frame is an input instead of an output argument.

   spkpv_c ( <handle>,
             <descr>,
             <et>,
             <ref>,
             state,
             center   );  { Position, velocity }

If files have been loaded by previous calls to furnsh_c, it is possible to use the same segments that would normally be used by spkezr_c, spkez_c, spkssb_c, spkapp_c, and spkgeo_c. Function spksfs_c selects, from the database of loaded files, the file handle and segment descriptor for the segment best suited to the request. If two segments from different files are suitable, spksfs_c selects the one from the file that was loaded later. If two segments from the same file are suitable, spksfs_c selects the one that is stored later in the file. The call

   spksfs_c ( <801>,
              <et>,
              &handle,
              descr,
              segnam,
              &found );     { Select file and segment }

Examples of Using SPK Readers

Example 1: Computing Latitude and Longitude

The next several sections present sample programs to show how the SPK readers can be used to compute state vectors, and how those vectors can be used to compute derived quantities.

All functions used in the examples are from CSPICE. The convention of expanding SPK function names will be dropped for these examples.

The first example program computes the planetocentric latitude and longitude of the sub-observer point on a target body for any combination of observer, target, and epoch. (Note that planetocentric coordinates differ from planetographic and cartographic coordinates in that they are always right-handed, regardless of the rotation of the body. Also note that for this example we define the sub-observer point to be the point on the ``surface'' of the target that lies on the ray from the center of the target to the observer. )

   /*
   PROGRAM LATLON
   */
 
      /*
      Standard includes
      */
      #include <stdio.h>
      #include <string.h>
      #include <stdlib.h>
 
      /*
      CSPICE prototypes and definitions.
      */
      #include "SpiceUsr.h"
 
 
      int main()
   {
 
      /*
      Constants
      */
      #define                 BDNMLN   37
      #define                 FRNMLN   33
      #define                 TIMLEN   51
 
      /*
      Variables
      */
      SpiceChar               time  [ TIMLEN ];
      SpiceChar               obs   [ BDNMLN ];
      SpiceChar               targ  [ BDNMLN ];
      SpiceChar               frame [ FRNMLN ];
 
      SpiceDouble             et;
      SpiceDouble             lat;
      SpiceDouble             lon;
      SpiceDouble             lt;
      SpiceDouble             radius;
      SpiceDouble             state  [6];
 
      /*
      Load constants into the kernel pool. Two files are
      needed. The first ("time.ker") contains the dates
      of leap seconds and values for constants needed to
      compute the difference between UTC and ET at any
      epoch. The second ("pck.ker") contains IAU values
      needed to compute transformations from inertial
      (J2000) coordinates to body-fixed (pole and prime
      meridian) coordinates for the major bodies of the
      solar system. (These files, or their equivalents,
      are normally distributed along with CSPICE.)
      */
      furnsh_c ( "time.ker"  );
      furnsh_c ( "pck.ker"   );
 
      /*
      Several ephemeris files are used. Most contain data for
      a single planetary system ("jupiter.ker", "saturn.ker",
      and so on). Some contain data for spacecraft ("vgr1.ker",
      "mgn.ker").
      */
      furnsh_c ( "mercury.bsp" );
      furnsh_c ( "venus.bsp"   );
      furnsh_c ( "earth.bsp"   );
      furnsh_c ( "mars.bsp"    );
      furnsh_c ( "jupiter.bsp" );
      furnsh_c ( "saturn.bsp"  );
      furnsh_c ( "uranus.bsp"  );
      furnsh_c ( "neptune.bsp" );
      furnsh_c ( "pluto.bsp"   );
      furnsh_c ( "vgr1.bsp"    );
      furnsh_c ( "vgr2.bsp"    );
      furnsh_c ( "mgn.bsp"     );
      furnsh_c ( "gll.bsp"     );
 
 
      /*
      Inputs are entered interactively. The user enters three
      items: the name for the observer , the name
      for the target, and the UTC epoch at which the
      sub-observer point is to be computed (a free-format string).
 
      The epoch must be converted to ephemeris time (ET).
      */
      while ( SPICETRUE )
      {
         prompt_c ( "Observer? ", BDNMLN, obs  );
         prompt_c ( "Target?   ", BDNMLN, targ );
         prompt_c ( "Epoch?    ", TIMLEN, time );
 
         str2et_c ( time,  &et            );
         sprintf  ( frame, "IAU_%s", targ );
 
         /*
         Compute the true state (corrected for light-time)
         of the target as seen from the observer at the
         specified epoch in the target fixed reference frame.
         */
         spkezr_c ( targ, et, frame, "lt", obs, state, < );
 
         /*
         We need  the vector FROM the target TO the observer
         to compute latitude and longitude. So reverse it.
         */
         vminus_c ( state, state );
 
         /*
         Convert from rectangular coordinates to latitude and
         longitude, then from radians to degrees for output.
         */
         reclat_c ( state, &radius, &lon, &lat );
 
         printf ( "\n"
                  "Sub-observer latitude (deg): %f\n"
                  "             longitude     : %f\n"
                  "\n"
                  "Range to target (km)       : %f\n"
                  "Light-time (sec)           : %f\n"
                  "\n",
 
                  lat * dpr_c(),
                  lon * dpr_c(),
                  radius,
                  lt                                );
 
         /*
         Get the next set of inputs.
         */
      }
 
      return ( 0 );
   }

Example 2: Occultation or Transit

The second example determines epochs if one target body (spacecraft, planet, or satellite) is occulted by or in transit across another target body as seen from an observer at a user specified epoch. It is similar in both form and generality to the first example.

   /*
   PROGRAM OCCTRN
   */
      /*
      Standard includes
      */
      #include <stdio.h>
      #include <string.h>
      #include <stdlib.h>
      #include <math.h>
 
 
      /*
      CSPICE prototypes and definitions.
      */
      #include "SpiceUsr.h"
 
 
      int main()
   {
 
      /*
      Constants
      */
      #define                 NSPKS     2
      #define                 NTARG     2
      #define                 BDNMLN   37
      #define                 FRNMLN   33
      #define                 TIMLEN   51
 
      /*
      Variables
      */
      SpiceBoolean            found;
 
      SpiceChar               time   [ TIMLEN ];
      SpiceChar               obs    [ BDNMLN ];
      SpiceChar               targ   [NTARG][ BDNMLN ];
 
      SpiceDouble             avg;
      SpiceDouble             d      [NTARG];
      SpiceDouble             et;
      SpiceDouble             lt;
      SpiceDouble             r      [NTARG];
      SpiceDouble             radii  [3];
      SpiceDouble             s      [NTARG][6];
      SpiceDouble             sep;
 
      SpiceInt                dim;
      SpiceInt                i;
      SpiceInt                j;
      SpiceInt                k;
      SpiceInt                t      [NTARG];
 
 
      /*
      Load constants into the kernel pool. Two files are
      needed. The first ("time.ker") contains the dates
      of leap seconds and values for constants needed to
      compute the difference between UTC and ET at any
      epoch. The second ("radii.ker") contains values
      for the tri-axial ellipsoids used to model the major
      major bodies of the solar system.
      */
      furnsh_c ( "time.ker"  );
      furnsh_c ( "radii.ker" );
 
      /*
      Several ephemeris files are needed. Most contain data for
      a single planetary system ("jupiter.ker", "saturn.ker",
      and so on). Some contain data for spacecraft ("vgr1.ker",
      "mgn.ker").
      */
      furnsh_c ( "mercury.bsp" );
      furnsh_c ( "venus.bsp"   );
      furnsh_c ( "earth.bsp"   );
      furnsh_c ( "mars.bsp"    );
      furnsh_c ( "jupiter.bsp" );
      furnsh_c ( "saturn.bsp"  );
      furnsh_c ( "uranus.bsp"  );
      furnsh_c ( "neptune.bsp" );
      furnsh_c ( "pluto.bsp"   );
      furnsh_c ( "vgr1.bsp"    );
      furnsh_c ( "vgr2.bsp"    );
      furnsh_c ( "mgn.bsp"     );
      furnsh_c ( "gll.bsp"     );
 
      /*
      Inputs are entered interactively. The user enters four
      items: the code for the observer (an integer), the codes
      for two target bodies (integers), and the epoch at which
      check for occultation or transit is to be computed
      (a free-format string).
 
      The epoch must be converted to ephemeris time (ET).
      */
      while ( SPICETRUE )
      {
         prompt_c ( "Observer? ", BDNMLN, obs     );
         prompt_c ( "Target 1? ", BDNMLN, targ[0] );
         prompt_c ( "Target 2? ", BDNMLN, targ[1] );
         prompt_c ( "Epoch?    ", TIMLEN, time    );
 
         str2et_c ( time, &et );
 
         /*
         Get the ID codes associated with the targets
         */
         bodn2c_c ( targ[0], &t[0], &found );
         bodn2c_c ( targ[1], &t[1], &found );
 
         /*
         Get the apparent states of the target objects as seen from
         the observer. Also get the apparent radius of each object
         from the kernel pool. (Use zero radius for any spacecraft;
         use average radius for anything else.)
 
            t[i]         is the ID code of the i'th target, i = 0, 1.
            s[i][0..5]   is the apparent state of the i'th target.
            d[i]         is the apparent distance to the i'th target.
            r[i]         is the apparent radius of the i'th target.
 
         Function vnorm_c returns the Euclidean norm (magnitude) of
         a three-vector.
 
         Function sumad_c returns the sum of the elements in a
         double precision array.
         */
         for ( i = 0;  i < 2;  i++ )
         {
            spkezr_c ( targ[i],  et,    "J2000",  "LT+S",
                       obs,      s[i],  <              );
 
            d[i] = vnorm_c( s[i] );
 
 
            if ( t[i] < 0 )
            {
               r[i] = 0.;
            }
            else
            {
               bodvcd_c ( t[i], "RADII", 3, &dim, radii );
               avg  = sumad_c ( radii, 3 ) / 3.0;
               r[i] = asin  ( avg / d[i] );
            }
         }
 
         /*
         Determine the separation between the two bodies. If the
         separation between the centers is greater than the sum of
         the apparent radii, then the target bodies are clear of
         each other.
 
         Function vsep_c returns the angle of separation between
         two three-vectors.
         */
         sep = vsep_c ( s[0], s[1] )  -  ( r[0] + r[1] );
 
         if ( sep > 0. )
         {
            printf ( "\nClear.\n" );
 
            /*
            Otherwise, the smaller body is either occulted or
            in transit.  We compare ranges to decide which.
            */
         }
         else
         {
            /*
            Let index j indicate the target of smaller radius; let k
            indicate the larger target.
            */
            ( r[0] < r[1] )  ?  (j = 0)   :   (j = 1);
 
            k = 1-j;
 
 
            if ( d[j] < d[k] )
            {
               printf ( "\n%s is in transit across %s\n",
                         targ[j],
                         targ[k]                         );
            }
            else
            {
               printf ( "\n%s is occulted by %s\n",
                         targ[j],
                         targ[k]                         );
            }
 
         }
 
         /*
         Get the next set of inputs.
         */
      }
 
      return ( 0 );
   }

Supported Data Types

The following representations, or data types, are currently supported by the SPK functions in CSPICE.

1. Modified Difference Arrays.

Created by the JPL Orbit Determination Program (ODP), these are used primarily for spacecraft ephemerides.

2. Chebyshev polynomials (position only).

These are sets of coefficients for the x, y, and z components of the body position. The velocity of the body is obtained by differentiation. This data type is normally used for planet barycenters, and for satellites whose orbits are integrated.

3. Chebyshev polynomials (position and velocity).

These are sets of coefficients for the x, y, and z components of the body position, and for the corresponding components of the velocity. This data type is normally used for satellites whose orbits are computed directly from theories.

4. Reserved for future use (TRW elements for TDRS and Spacetelescope).

5. Discrete states (two body propagation).

This data type contains discrete state vectors. A state is obtained for a specified epoch by propagating the state vectors to that epoch according to the laws of two body motion and then taking a weighted average of the resulting states. Normally, this data type is used for comets and asteroids, whose ephemerides are integrated from an initial state or set of osculating elements.

6. Reserved for future use (Analytic Model for Phobos and Deimos).

7. Reserved for future use (Precessing Classical Elements---used by STScI).

8. Equally spaced discrete states (Lagrange interpolation)

This data type contains discrete state vectors whose time tags are separated by a constant step size. A state is obtained for a specified epoch by finding a set of states `centered' at that epoch and using Lagrange interpolation on each component of the states.

9. Unequally spaced discrete states (Lagrange interpolation)

This data type contains discrete state vectors whose time tags may be unequally spaced. A state is obtained for a specified epoch by finding a set of states `centered' at that epoch and using Lagrange interpolation on each component of the states.

10. Space Command Two-line Elements (Short Period Orbits)

This data type contains Space Command two-line element representations for objects in Earth orbit (formally called NORAD two-line elements).

11. Reserved for future use.

12. Hermite Interpolation Uniform Spacing.

13. Hermite Interpolation Non-uniform Spacing.

14. Chebyshev polynomials non-uniform spacing (position and velocity).

This data type contains Chebyshev polynomial coefficients for the position and velocity of an object. Unlike SPK Types 2 and 3, the time intervals to which polynomial coefficient sets apply do not have uniform duration.

15. Precessing conic propagation.

This data type allows for first order precession of the line of apsides and regression of the line of nodes due to the effects of the J2 coefficient in the harmonic expansion of the gravitational potential of an oblate spheroid.

16. Reserved for future use (Elements for European Space Agency's ISO spacecraft).

17. Equinoctial Elements

This data type represents the motion of an object about another using equinoctial elements. It provides for precession of the line of apsides and regression of the line of nodes. Unlike Type 15, the mean motion, regression of the nodes and precession of the line of apsides are not derived from the gravitational properties of the central body, but are empirical values.

Type 1: Modified Difference Arrays

The first SPK data type contains Modified Difference Arrays (MDA), sometimes called `difference lines'. This data type is normally used for spacecraft whose ephemerides are produced by JPL's principal trajectory integrator---DPTRAJ. Difference lines are extracted from the spacecraft trajectory file (`P-files' and `PV-files') created by DPTRAJ.

Each segment containing Modified Difference Arrays contains an arbitrary number of logical records. Each record contains difference line coefficients valid up to some final epoch, along with the state at that epoch. The contents of the records themselves are described in [163]. The function spke01_ contains the algorithm used to construct a state from a particular record and epoch.

The records within a segment are ordered by increasing final epoch. A segment of this type is structured as follows:

   +-----------------------------------------+
   | Record 1 (difference line coefficients) |
   +-----------------------------------------+
   | Record 2 (difference line coefficients) |
   +-----------------------------------------+
     .
     .
     .
   +-----------------------------------------+
   | Record N (difference line coefficients) |
   +-----------------------------------------+
   | Epoch 1                      |
   +------------------------------+
   | Epoch 2                      |
   +------------------------------+
     .
     .
     .
   +------------------------------+
   | Epoch N                      |
   +------------------------------+
   | Epoch 100                    |   (First directory epoch)
   +------------------------------+
   | Epoch 200                    |   (Second directory epoch)
   +------------------------------+
     .
     .
     .
   +------------------------------+
   | Epoch (N/100)*100            |   (Final directory epoch)
   +------------------------------+
   | N                            |
   +------------------------------+

Records 1 through N contain the difference line coefficients and other constants needed to compute state data. Each one of these records contains 71 double precision numbers.

The list of final epochs for the records is stored immediately after the last record.

Following the list of epochs is a second list, the `directory', containing every 100th epoch from the previous list. If there are N epochs, there will be N/100 directory epochs. If there are fewer than 100 epochs, then the segment will not contain any directory epochs. Directory epochs are used to speed up access to desired records.

The final element in the segment is the number of records contained in the segment, N.

The index of the record corresponding to a particular epoch is the index of the first epoch not less than the target epoch.

Type 2: Chebyshev (position only)

The second SPK data type contains Chebyshev polynomial coefficients for the position of the body as a function of time. Normally, this data type is used for planet barycenters, and for satellites whose ephemerides are integrated. (The velocity of the body is obtained by differentiating the position.)

Each segment contains an arbitrary number of logical records. Each record contains a set of Chebyshev coefficients valid throughout an interval of fixed length. The function spke02_ contains the algorithm used to construct a state from a particular record and epoch.

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      |
   +---------------+
   | INIT          |
   +---------------+
   | INTLEN        |
   +---------------+
   | RSIZE         |
   +---------------+
   | N             |
   +---------------+

1. INIT is the initial epoch of the first record, given in ephemeris seconds past 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.

   +------------------+
   | MID              |
   +------------------+
   | RADIUS           |
   +------------------+
   | X  coefficients  |
   +------------------+
   | Y  coefficients  |
   +------------------+
   | Z  coefficients  |
   +------------------+

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

Type 3: Chebyshev (position and velocity)

The third SPK data type contains Chebyshev polynomial coefficients for the position and velocity of the body as a function of time. Normally, this data type is used for satellites for which the ephemerides are computed from analytical theories.

The structure of the segment is nearly identical to that of the SPK data Type 2 (Chebyshev polynomials for position only). The only difference is that each logical record contains six sets of coefficients instead of three. The function spke03_ contains the algorithm used to construct a state from a particular record and epoch.

Each record is structured as follows:

   +------------------+
   | MID              |
   +------------------+
   | RADIUS           |
   +------------------+
   | X  coefficients  |
   +------------------+
   | Y  coefficients  |
   +------------------+
   | Z  coefficients  |
   +------------------+
   | X' coefficients  |
   +------------------+
   | Y' coefficients  |
   +------------------+
   | Z' coefficients  |
   +------------------+

   ( RSIZE - 2 ) / 6 - 1

Type 5: Discrete states (two body propagation).

The fifth standard SPK data type contains discrete state vectors. A state is obtained from a Type 5 segment for any epoch that is within the bounds of that segment by propagating the discrete states to the specified epoch according to the laws of two body motion. Normally, this data type is used for comets and asteroids, whose ephemerides are integrated from an initial state or set of osculating elements.

Each segment contains of a number of logical records. Each record consists of an epoch (ephemeris seconds past J2000) and the geometric state of the body at that epoch (x, y, z, dx/dt, dy/dt, dz/dt, in kilometers and kilometers per second). Records are ordered with respect to increasing time.

The records that correspond to an epoch for which a state is desired are the ones whose associated epochs bracket that epoch. The state in each record is used as the initial state in a two-body propagation; a weighted average of the propagated states gives the position of the body at the specified epoch. The velocity is given by the derivative of the position. Thus the position and velocity at the specified epoch are given by:

   P  = W(t) * P1(t) + (1-W(t)) * P2(t)
 
   V  = W(t) * V1(t) + (1-W(t)) * V2(t) + W'(t) * ( P1(t) - P2(t) )

The weighting function used is:

   W(t) = 0.5 + 0.5 * cos [ PI * ( t - t1 ) / ( t2 - t1 ) ]

Physically, the epochs and states are stored separately, so that the epochs can be searched as an ordered array. Thus, the initial part of each segment looks like this:

   +--------------------+
   | State 1            |
   +--------------------+
            .
            .
            .
   +--------------------+
   | State N            |
   +--------------------+
   | Epoch 1            |
   +--------------------+
            .
            .
            .
   +--------------------+
   | Epoch N            |
   +--------------------+

This directory contains every 100th epoch in the epoch array. If there are N epochs, there will be N/100 directory epochs. (If there are fewer than 100 epochs, no directory epochs are stored.)

The final items in the segment are GM, the gravitational parameter of the central body (kilometers and seconds), and N, the number of states in the segment. Thus, the complete segment looks like this:

   +--------------------+
   | State 1            |
   +--------------------+
            .
            .
            .
   +--------------------+
   | Epoch 1            |
   +--------------------+
            .
            .
            .
   +--------------------+
   | Epoch N            |
   +--------------------+
   | Epoch 100          |           (First directory epoch)
   +--------------------+
   | Epoch 200          |
   +--------------------+
            .
            .
            .
   +--------------------+
   | Epoch (N/100)*100  |           (Final directory epoch)
   +--------------------+
   | GM                 |
   +--------------------+
   | N                  |
   +--------------------+

Type 8: Lagrange Interpolation --- Equal Time Steps

The eighth SPK data type represents a continuous ephemeris using a discrete set of states and a Lagrange interpolation method. The epochs (also called `time tags') associated with the states must be evenly spaced: there must be some positive constant STEP such that each time tag differs from its predecessor and successor by STEP seconds. For a request epoch not corresponding to the time tag of some state, the data type defines a state by interpolating each component of a set of states whose epochs are `centered' near the request epoch. Details of how these states are selected and interpolated are given below.

The SPK system can also represent an ephemeris using unequally spaced discrete states and Lagrange interpolation; SPK Type 9 does this. SPK Type 9 sacrifices some run-time speed and economy of storage in order to achieve greater flexibility.

The states in a Type 8 segment are geometric: they do not take into account aberration corrections. The six components of each state vector represent the position and velocity (x, y, z, dx/dt, dy/dt, dz/dt, in kilometers and kilometers per second) of the body to which the ephemeris applies, relative to the center specified by the segment's descriptor. The epochs corresponding to the states are barycentric dynamical times (TDB), expressed as seconds past J2000.

Each segment also has a polynomial degree associated with it; this is the degree of the interpolating polynomials to be used in evaluating states based on the data in the segment. The identical degree is used for interpolation of each state component.

Type 8 SPK segments have the structure shown below:

                                       +--------+
                                       |  x(1)  |
                                   /   +--------+
                                  /    |  y(1)  |
                                 /     +--------+
                                /      |  z(1)  |
   +-----------------------+   /       +--------+
   | State 1               |  <        |dx(1)/dt|
   +-----------------------+   \       +--------+
   | State 2               |    \      |dy(1)/dt|
   +-----------------------+     \     +--------+
               .                  \    |dz(1)/dt|
               .                       +--------+
               .
   +-----------------------+
   | State N               |
   +-----------------------+
   | Epoch of state 1 (TDB)|
   +-----------------------+
   | Step size             |
   +-----------------------+
   | Polynomial degree     |
   +-----------------------+
   | Number of states      |
   +-----------------------+

The Type 8 interpolation method works as follows: given an epoch at which a state is requested and a segment having coverage for that epoch, the Type 8 reader finds a group of states whose epochs are `centered' about the epoch. The size of the group is one greater than the polynomial degree associated with the segment. If the group size N is even, then the group will consist of N consecutive states such that the request time is between the epochs of the members of the group having indices, relative to the start of the group, of N/2 and (N/2 + 1), inclusive. When N is odd, the group will contain a central state whose epoch is closest to the request time, and will also contain (N-1)/2 neighboring states on either side of the central one. The Type 8 evaluator will then use Lagrange interpolation on each component of the states to produce a state corresponding to the request time. For the jth state component, the interpolation algorithm is mathematically equivalent to finding the unique polynomial of degree N-1 that interpolates the ordered pairs

   ( epoch(i), state(j,i) ),  i = k ,  k , ... , k
                                   1    2         N

    k ,  k , ... , k
     1    2         N

   epoch(i)

   state(j,i)

There is an exception to the state selection algorithm described above: the request time may be too near the first or last state of the segment to be properly bracketed. In this case, the set of states selected for interpolation still has size N, and includes either the first or last state of the segment.

To facilitate the creation of Type 8 segments, a segment writing function called spkw08_c has been provided. This function takes as input arguments the handle of an SPK 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 function provides a complete description of the input arguments and an example of its usage.

Type 9: Lagrange Interpolation --- Unequal Time Steps

The ninth SPK data type represents a continuous ephemeris using a discrete set of states and a Lagrange interpolation method. The epochs (also called `time tags') associated with the states need not be evenly spaced. For a request epoch not corresponding to the time tag of some state, the data type defines a state by interpolating each component of a set of states whose epochs are `centered' near the request epoch. Details of how these states are selected and interpolated are given below.

The states in a Type 9 segment are geometric: they do not take into account aberration corrections. The six components of each state vector represent the position and velocity (x, y, z, dx/dt, dy/dt, dz/dt, in kilometers and kilometers per second) of the body to which the ephemeris applies, relative to the center specified by the segment's descriptor. The epochs corresponding to the states are barycentric dynamical times (TDB), expressed as seconds past J2000.

Each segment also has a polynomial degree associated with it; this is the degree of the interpolating polynomials to be used in evaluating states based on the data in the segment. The identical degree is used for interpolation of each state component.

Type 9 SPK segments have the structure shown below:

                                       +--------+
                                       |  x(1)  |
                                   /   +--------+
                                  /    |  y(1)  |
                                 /     +--------+
                                /      |  z(1)  |
   +-----------------------+   /       +--------+
   | State 1               |  <        |dx(1)/dt|
   +-----------------------+   \       +--------+
   | State 2               |    \      |dy(1)/dt|
   +-----------------------+     \     +--------+
               .                  \    |dz(1)/dt|
               .                       +--------+
               .
   +-----------------------+
   | State N               |
   +-----------------------+
   | Epoch 1               |
   +-----------------------+
   | Epoch 2               |
   +-----------------------+
               .
               .
               .
   +-----------------------+
   | Epoch N               |
   +-----------------------+
   | Epoch 100             | (First directory)
   +-----------------------+
               .
               .
               .
   +-----------------------+
   | Epoch ((N-1)/100)*100 | (Last directory)
   +-----------------------+
   | Polynomial degree     |
   +-----------------------+
   | Number of states      |
   +-----------------------+
 

The set of time tags is augmented by a series of directory entries; these entries allow the Type 9 reader to search for states more efficiently. The directory entries contain time tags whose indices are multiples of 100. The set of indices of time tags stored in the directories ranges from 100 to

   (  (N-1) / 100  ) * 100

   Q * 100

   Q - 1

The Type 9 interpolation algorithm is virtually identical to the Type 8 algorithm; see the discussion of SPK Type 8 for details. However, the Type 9 algorithm executes more slowly than the Type 8 algorithm, since the Type 9 reader must search through tables of time tags to find appropriates states to interpolate, while the Type 8 reader can locate the correct set of states to interpolate by a direct computation.

To facilitate the creation of Type 9 segments, a segment writing function called spkw09_c has been provided. This function takes as input arguments the handle of an SPK 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 function provides a complete description of the input arguments and an example of its usage.

Type 10: Space Command Two-Line Elements

The SPK data Type 10 uses the SPICE concept of a generic segment to store a collection of packets each of which models the trajectory of some Earth satellite using Space Command two-line element sets (TLEs) (formerly the North American Air Defense --- NORAD). TLE propagation occurs using the algorithms as described in the Spacetrak 3 report for SGP4 and SDP4. Note: The Spacetrak 3 implementation of SDP4 contained several programming errors. The errors were corrected for CSPICE implementation.

The SPICE generic segment software handles storage, arrangement, and retrieval of the TLEs. We review only the pertinent points about generic segments here.

A generic SPK segment contains several logical data partitions:

1. A partition for constant values to be associated with each data packet in the segment.

2. A partition for the data packets.

3. A partition for epochs.

4. A partition for a packet directory, if the segment contains variable sized packets.

5. A partition for an epoch directory.

6. A reserved partition that is not currently used. This partition is only for the use of the NAIF group at the Jet Propulsion Laboratory (JPL).

7. A partition for the meta data which describes the locations and sizes of other partitions as well as providing some additional descriptive information about the generic segment.

      +============================+
      |         Constants          |
      +============================+
      |          Packet 1          |
      |----------------------------|
      |          Packet 2          |
      |----------------------------|
      |              .             |
      |              .             |
      |              .             |
      |----------------------------|
      |          Packet N          |
      +============================+
      |      Reference Epochs      |
      +============================+
      |      Packet Directory      |
      +============================+
      |       Epoch Directory      |
      +============================+
      |       Reserved  Area       |
      +============================+
      |     Segment Meta Data      |
      +----------------------------+

 
      A single SPK Type 10 segment packet
 
      +-------------------+
    1 |      NDT20        |
      +-------------------+
    2 |      NDD60        |
      +-------------------+
    3 |      BSTAR        |
      +-------------------+
    4 |      INCL         |
      +-------------------+
    5 |      NODE0        |     Two-line element packet
      +-------------------+
    6 |      ECC          |
      +-------------------+
    7 |      OMEGA        |
      +-------------------+
    8 |      MO           |
      +-------------------+
    9 |      NO           |
      +-------------------+
   10 |      EPOCH        |
      +-------------------+
   11 |      NU.OBLIQUITY |
      +-------------------+
   12 |      NU.LONGITUDE |
      +-------------------+
   13 |     dOBLIQUITY/dt |
      +-------------------+
   14 |     dLONGITUDE/dt |
      +-------------------+

      +-------------------------------------------+
   1  |  J2 gravitational harmonic for Earth      |
      +-------------------------------------------+
   2  |  J3 gravitational harmonic for Earth      |
      +-------------------------------------------+
   3  |  J4 gravitational harmonic for Earth      |
      +-------------------------------------------+
      |  Square root of the GM for Earth where GM |
   4  |  is expressed in Earth radii cubed per    |
      |  minutes squared                          |
      +-------------------------------------------+
   5  |  Equatorial radius of the Earth in km     |
      +-------------------------------------------+
   6  |  Low altitude bound for atmospheric       |
      |  model in km                              |
      +-------------------------------------------+
   7  |  High altitude bound for atmospheric      |
      |  model in km                              |
      +-------------------------------------------+
   8  |  Distance units/Earth radius (normally 1) |
      +-------------------------------------------+

The ``epoch directory'' contains every 100th reference epoch. The epoch directory is used to efficiently locate an the reference epoch that should be associated with a two line element packet.

The ``packet directory'' is empty.

Access to the data should be made via the SPK Type 10 reader---spkr10_ or via the SPICELIB generic segment functions. Use the function spkw10_c to write a Type 10 generic segment.

Type 12: Hermite Interpolation --- Equal Time Steps

The twelfth SPK data type represents a continuous ephemeris using a discrete set of states and a sliding window Hermite interpolation method. The epochs, also called "time tags," associated with the states must be evenly spaced: there must be some positive constant STEP such that each time tag differs from its predecessor by STEP seconds. For any request epoch, the data type defines a state by interpolating a set of consecutive states, or "window," centered as closely as possible to the request epoch. Interpolated position values are obtained for each coordinate by fitting a Hermite polynomial to the window's set of position and velocity values for that coordinate; interpolated velocity is obtained by differentiating the interpolating polynomials. Details of the interpolation method are given below.

The SPK system can also represent an ephemeris using unequally spaced discrete states and Hermite interpolation; SPK type 13 does this. SPK type 13 sacrifices some run-time speed and economy of storage in order to achieve greater flexibility.

The states in a type 12 segment are geometric: they do not take into account aberration corrections. The six components of each state vector represent the position and velocity (x, y, z, dx/dt, dy/dt, dz/dt, in kilometers and kilometers per second) of the body to which the ephemeris applies, relative to the center specified by the segment's descriptor. The epochs corresponding to the states are barycentric dynamical times (TDB), expressed as seconds past J2000.

Each segment also has a polynomial degree associated with it; this is the degree of the interpolating polynomials to be used in evaluating states based on the data in the segment. The identical degree is used for interpolation of each state component.

Type 12 SPK segments have the structure shown below:

                                       +--------+
                                       |  x(1)  |
                                   /   +--------+
                                  /    |  y(1)  |
                                 /     +--------+
                                /      |  z(1)  |
   +-----------------------+   /       +--------+
   | State 1               |  <        |dx(1)/dt|
   +-----------------------+   \       +--------+
   | State 2               |    \      |dy(1)/dt|
   +-----------------------+     \     +--------+
               .                  \    |dz(1)/dt|
               .                       +--------+
               .
   +-----------------------+
   | State N               |
   +-----------------------+
   | Epoch of state 1 (TDB)|
   +-----------------------+
   | Step size             |
   +-----------------------+
   | Window size - 1       |
   +-----------------------+
   | Number of states      |
   +-----------------------+

   DEGREE  =  2 * WINDOW_SIZE  -  1

For the jth coordinate, the interpolation algorithm is mathematically equivalent to finding the unique polynomial of degree 2*S-1 that interpolates the ordered pairs

   ( epoch(i), position(j,i) ),  i = k ,  k , ... , k
                                      1    2         S

   ( epoch(i), velocity(j,i) ),  i = k ,  k , ... , k
                                      1    2         S

    k ,  k , ... , k
     1    2         S

   epoch(i)

   position(j,i)
   velocity(j,i)

There is an exception to the state selection algorithm described above: the request time may be too near the first or last state of the segment to be properly bracketed. In this case, the set of states selected for interpolation still has size S, and includes either the first or last state of the segment.

To facilitate the creation of type 12 segments, a segment writing routine called spkw12_c has been provided. This routine takes as input arguments the handle of an SPK 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.

Type 13: Hermite Interpolation --- Unequal Time Steps

The thirteenth SPK data type represents a continuous ephemeris using a discrete set of states and a sliding window Hermite interpolation method. The epochs, also called "time tags," associated with the states need not be evenly spaced. For any request epoch, the data type defines a state by interpolating a set of consecutive states, or "window," centered as closely as possible to the request epoch. Interpolated position values are obtained for each coordinate by fitting a Hermite polynomial to the window's set of position and velocity values for that coordinate; interpolated velocity is obtained by differentiating the interpolating polynomials. Details of the interpolation method are given below.

The states in a type 13 segment are geometric: they do not take into account aberration corrections. The six components of each state vector represent the position and velocity (x, y, z, dx/dt, dy/dt, dz/dt, in kilometers and kilometers per second) of the body to which the ephemeris applies, relative to the center specified by the segment's descriptor. The epochs corresponding to the states are barycentric dynamical times (TDB), expressed as seconds past J2000.

Each segment also has a polynomial degree associated with it; this is the degree of the interpolating polynomials to be used in evaluating states based on the data in the segment. The identical degree is used for interpolation of each state component.

Type 13 SPK segments have the structure shown below:

                                       +--------+
                                       |  x(1)  |
                                   /   +--------+
                                  /    |  y(1)  |
                                 /     +--------+
                                /      |  z(1)  |
   +-----------------------+   /       +--------+
   | State 1               |  <        |dx(1)/dt|
   +-----------------------+   \       +--------+
   | State 2               |    \      |dy(1)/dt|
   +-----------------------+     \     +--------+
               .                  \    |dz(1)/dt|
               .                       +--------+
               .
   +-----------------------+
   | State N               |
   +-----------------------+
   | Epoch 1               |
   +-----------------------+
   | Epoch 2               |
   +-----------------------+
               .
               .
               .
   +-----------------------+
   | Epoch N               |
   +-----------------------+
   | Epoch 100             | (First directory)
   +-----------------------+
               .
               .
               .
   +-----------------------+
   | Epoch ((N-1)/100)*100 | (Last directory)
   +-----------------------+
   | Window size - 1       |
   +-----------------------+
   | Number of states      |
   +-----------------------+
 

   DEGREE  =  2 * WINDOW_SIZE  -  1

   (  (N-1) / 100  ) * 100

   Q * 100

   Q - 1

The type 13 interpolation algorithm is virtually identical to the type 12 algorithm; see the discussion of SPK type 12 for details. However, the type 13 algorithm executes more slowly than the type 12 algorithm, since the type 13 reader must search through tables of time tags to find appropriates states to interpolate, while the type 12 reader can locate the correct set of states to interpolate by a direct computation.

To facilitate the creation of type 13 segments, a segment writing routine called spkw13_c has been provided. This routine takes as input arguments the handle of an SPK 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.

Type 14: Chebyshev Polynomials --- Unequal Time Steps

The SPK data Type 14 uses the SPICE concept of a generic segment to store a collection of packets each of which models the trajectory of some object with respect to another over some interval of time. Each packet contains a set of coefficients for Chebyshev polynomials that approximate the position and velocity of some object. The time intervals corresponding to each packet are non-overlapping. Moreover their union covers the interval of time spanned by the start and end times of the Type 14 segment. Unlike Types 2 and 3 the time spacing between sets of coefficients for a Type 14 segment may be non-uniform.

The storage, arrangement and retrieval of packets is handled by the SPICE generic segment software. That software is documented in the document GENSEG.REQ. (The document GENSEG.REQ is currently in preparation.) We only review the pertinent points about generic segments here.

A generic SPK segment contains several logical data partitions:

1. A partition for constant values to be associated with each data packet in the segment.

2. A partition for the data packets.

3. A partition for epochs.

4. A partition for a packet directory, if the segment contains variable sized packets.

5. A partition for an epoch directory.

6. A reserved partition that is not currently used. This partition is only for the use of the NAIF group at the Jet Propulsion Laboratory (JPL).

7. A partition for the meta data which describes the locations and sizes of other partitions as well as providing some additional descriptive information about the generic segment.

      +============================+
      |         Constants          |
      +============================+
      |          Packet 1          |
      |----------------------------|
      |          Packet 2          |
      |----------------------------|
      |              .             |
      |              .             |
      |              .             |
      |----------------------------|
      |          Packet N          |
      +============================+
      |      Reference Epochs      |
      +============================+
      |      Packet Directory      |
      +============================+
      |       Epoch Directory      |
      +============================+
      |       Reserved  Area       |
      +============================+
      |     Segment Meta Data      |
      +----------------------------+

In the case of Type 14 SPK segments each ``packet'' contains an epoch, EPOCH, an allowed time offset, OFFSET, from the epoch, and 6 sets of Chebyshev polynomial coefficients which are used to evaluate the x,y,z, dx/dt, dy/dt, and dz/dt components of the state for epochs within OFFSET seconds of the EPOCH. Each packet is organized with the following structure:

   ------------------------------------------------
   |  The midpoint of the approximation interval  |
   ------------------------------------------------
   |  The radius of the approximation interval    |
   ------------------------------------------------
   |  CHBDEG+1 coefficients for the X coordinate  |
   ------------------------------------------------
   |  CHBDEG+1 coefficients for the Y coordinate  |
   ------------------------------------------------
   |  CHBDEG+1 coefficients for the Z coordinate  |
   ------------------------------------------------
   |  CHBDEG+1 coefficients for the X velocity    |
   ------------------------------------------------
   |  CHBDEG+1 coefficients for the Y velocity    |
   ------------------------------------------------
   |  CHBDEG+1 coefficients for the Z velocity    |
   ------------------------------------------------

The ``constants'' partition contains a single value, the degree of the Chebyshev representation.

The reference epochs partition contains an ordered collection of epochs. The i'th reference epoch corresponds to the beginning of the interval for which the i'th packet can be used to determine the state of the object modeled by this segment.

The ``epoch directory'' contains every 100th reference epoch. The epoch directory is used to efficiently locate an the reference epoch that should be associated with an epoch for which a state has been requested.

The ``packet directory'' is empty.

As noted above the exact location of the various partitions must be obtained from the Meta data contained at the end of the segment.

Access to the data should be made via the SPICELIB generic segment functions.

Type 14 segments should be created using the functions spk14b_c, spk14a_c, and spk14e_c. The usage of these functions is discussed in spk14b_c.

Type 15: Precessing Conic Propagation.

The SPK data Type 15 represents a continuous ephemeris using a compact analytic model. The object is modeled as orbiting a central body under the influence of a central mass plus first order secular effects of the J2 term in harmonic expansion of the central body gravitational potential.

Type 15 SPK segments have the structure shown below:

           +--------------------------------+
           | Epoch of Periapsis             |
           +--------------------------------+
           | Trajectory pole_x              |
           +--------------------------------+
           | Trajectory pole_y              |
           +--------------------------------+
           | Trajectory pole_z              |
           +--------------------------------+
           | Periapsis Unit Vector_x        |
           +--------------------------------+
           | Periapsis Unit Vector_y        |
           +--------------------------------+
           | Periapsis Unit Vector_z        |
           +--------------------------------+
           | Semi-Latus Rectum              |
           +--------------------------------+
           | Eccentricity                   |
           +--------------------------------+
           | J2 Processing Flag             |
           +--------------------------------+
           | Central Body Pole_x            |
           +--------------------------------+
           | Central Body Pole_y            |
           +--------------------------------+
           | Central Body Pole_z            |
           +--------------------------------+
           | Central Body GM                |
           +--------------------------------+
           | Central Body J2                |
           +--------------------------------+
           | Central Body Equatorial Radius |
           +--------------------------------+

The effects of the J2 term are not applied if the eccentricity is greater than or equal to 1.

To facilitate the creation of Type 15 segments, a segment writing function called spkw15_c has been provided. This function takes as input arguments the handle of an SPK 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 function provides a complete description of the input arguments and an example of its usage.

Type 17: Equinoctial Elements.

The SPK data Type 17 represents a continuous ephemeris using a compact analytic model. The object is following an elliptic orbit with precessing line of nodes and argument of periapse relative to the equatorial frame of some central body. The orbit is modeled via equinoctial elements.

Type 17 SPK segments have the structure shown below:

             +----------------------------------+
           1 | Epoch of Periapsis               |
             +----------------------------------+
           2 | Semi-Major Axis                  |
             +----------------------------------+
           3 | H term of equinoctial elements   |
             +----------------------------------+
          4  | K term of equinoctial elements   |
             +----------------------------------+
          5  | Mean longitude at epoch          |
             +----------------------------------+
          6  | P term of equinoctial elements   |
             +----------------------------------+
          7  | Q term of equinoctial elements   |
             +----------------------------------+
          8  | rate of longitude of periapse    |
             +----------------------------------+
          9  | mean longitude rate              |
             +----------------------------------+
         10  | longitude of ascending node rate |
             +----------------------------------+
         11  | equatorial pole right ascension  |
             +----------------------------------+
         12  | equatorial pole declination      |
             +----------------------------------+

Type 18: MEX/Rosetta Hermite/Lagrange Interpolation

SPK type 18 has been provided to support accurate duplication within the SPK system of spacecraft ephemerides used by the European Space Agency (ESA) on the Mars Express (MEX) and Rosetta missions. However, the algorithms used by SPK type 18 are very general; type 18's applicability is by no means limited to these missions.

Because of the possibility of evolution of the mathematical representations of ephemerides used by ESA, SPK type 18 is designed to accommodate multiple representations, thereby avoiding a proliferation of SPK data types. SPK type 18 refers to each supported mathematical representation of ephemeris data as a ``subtype.''

Currently SPK type 18 supports two subtypes:

1. Subtype 0:

Separate sliding-window Hermite interpolation of position and velocity. The ephemeris is represented by a series of 12-element ``packets'' and associated time tags. The time tags may be unequally spaced. Each packet contains three Cartesian position components, three velocity components meant to be used for Hermite interpolation of the position, three velocity components (not necessarily equal to the previous three), and three acceleration components meant to be used with the second set of velocity components for Hermite interpolation of the velocity. The position and velocity resulting from this interpolation method are in principle independent. The same interpolation degree is used for each position and velocity component.

2. Subtype 1:

Separate sliding-window Lagrange interpolation of position and velocity. The ephemeris is represented by a series of 6-element ``packets'' and associated time tags. The time tags may be unequally spaced. Each packet contains three Cartesian position components and three velocity components. The position components and velocity components are interpolated separately. The position and velocity resulting from this interpolation method are in principle independent. The same interpolation degree is used for each position and velocity component.

When the request time is near a segment boundary, the window is truncated if necessary on the side closest to the boundary. If a segment contains too few packets to form a window of nominal size, as many packets as are needed and available are used to construct the window. In this case the window size may be odd. In any case the window never includes more than WNDSIZ/2 time tags on either side of the request time, where WNDSIZ is the nominal window size.

The states in a type 18 segment are geometric: they do not take into account aberration corrections. The position and velocity components of each packet represent the position (x, y, z, in kilometers and kilometers per second) of the body to which the ephemeris applies, relative to the center specified by the segment's descriptor. The epochs corresponding to the states are barycentric dynamical times (TDB), expressed as seconds past J2000.

Type 18 SPK segments have the structure shown below:

   +-----------------------+
   | Packet 1              |
   +-----------------------+
   | Packet 2              |
   +-----------------------+
               .
               .
               .
   +-----------------------+
   | Packet N              |
   +-----------------------+
   | Epoch 1               |
   +-----------------------+
   | Epoch 2               |
   +-----------------------+
               .
               .
               .
   +-----------------------+
   | Epoch N               |
   +-----------------------+
   | Epoch 100             | (First directory)
   +-----------------------+
               .
               .
               .
   +-----------------------+
   | Epoch ((N-1)/100)*100 | (Last directory)
   +-----------------------+
   | Subtype code          |
   +-----------------------+
   | Window size           |
   +-----------------------+
   | Number of packets     |
   +-----------------------+
 

   Subtype 0:     DEGREE  =  2 * WINDOW_SIZE  -  1
   Subtype 1:     DEGREE  =      WINDOW_SIZE  -  1

   (  (N-1) / 100  ) * 100

   Q * 100

   Q - 1

To facilitate the creation of type 18 segments, a segment writing routine called spkw18_c has been provided. This routine takes as input arguments the handle of an SPK 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.

Appendix A --- Summary of SP-kernel Functions

Summary of Mnemonics

CSPICE contains a family of functions that are designed specifically for use with SPK files. The name of each function begins with the letters `spk', followed by a two- or three-character mnemonic. For example, the function that returns the state of one body with respect to another is named spkez_c, pronounced `S-P-K-E-Z'.

Many of the lower-level CSPICE functions have SPICELIB counterparts implemented in Fortran as entry points of another function.

The following is a complete list of mnemonics and translations, in alphabetical order.

   Implemented CSPICE wrappers:
 
   furnsh_c           ( Load kernel file                     )
   spk14a_c           ( S/P-kernel, add to a Type 14 segment )
   spk14b_c           ( S/P-kernel, begin  a Type 14 segment )
   spk14e_c           ( S/P-kernel, end    a Type 14 segment )
   spkapo_c           ( S/P-Kernel, "apparent" position only )
   spkapp_c           ( S/P-kernel, Apparent state           )
   spkcls_c           ( S/P-kernel, close after write        )
   spkez_c            ( S/P-kernel, Easy state               )
   spkezp_c           ( S/P Kernel, easy position            )
   spkezr_c           ( S/P-kernel, Easier state             )
   spkgeo_c           ( S/P-kernel, Geometric state          )
   spkgps_c           ( S/P Kernel, geometric position       )
   spklef_c           ( S/P-kernel, Load ephemeris file      )
   spkopa_c           ( S/P-kernel, open for addition        )
   spkopn_c           ( S/P-kernel, open new file            )
   spkpds_c           ( S/P-kernel, pack descriptor          )
   spkpos_c           ( S/P Kernel, position                 )
   spkssb_c           ( S/P-kernel, Solar system barycenter  )
   spksub_c           ( S/P-kernel, Subset a segment         )
   spkuds_c           ( S/P-kernel, unpack descriptor        )
   spkuef_c           ( S/P-kernel, Unload ephemeris file    )
   spkw02_c           ( S/P-kernel, Write segment, Type 02   )
   spkw03_c           ( S/P-kernel, Write segment, Type 03   )
   spkw05_c           ( S/P-kernel, Write segment, Type 05   )
   spkw08_c           ( S/P-kernel, Write segment, Type 08   )
   spkw09_c           ( S/P-kernel, Write segment, Type 09   )
   spkw10_c           ( S/P-kernel, Write segment, Type 10   )
   spkw12_c           ( S/P-kernel, Write segment, Type 12   )
   spkw13_c           ( S/P-kernel, Write segment, Type 13   )
   spkw15_c           ( S/P-kernel, Write segment, Type 15   )
   spkw17_c           ( S/P-kernel, Write segment, Type 17   )
   spkw18_c           ( S/P-kernel, Write segment, Type 18   )
   unload_c           ( Unload kernel file                   )
 
   Unimplemented CSPICE wrappers:
 
   spkpv_c            ( S/P-kernel, Position, velocity       )
   spkpvn_c           ( S/P-kernel, Position, velocity---native)
   spksfs_c           ( S/P-kernel, file and segment         )
 
   Low-level routines converted via f2c:
 
   spke01_            ( S/P-kernel, Evaluate record, Type 01 )
   spke02_            ( S/P-kernel, Evaluate record, Type 02 )
   spke03_            ( S/P-kernel, Evaluate record, Type 03 )
   spke05_            ( S/P-kernel, Evaluate record, Type 05 )
   spke08_            ( S/P-kernel, Evaluate record, Type 08 )
   spke09_            ( S/P-kernel, Evaluate record, Type 09 )
   spke10_            ( S/P-kernel, Evaluate record, Type 10 )
   spke12_            ( S/P-kernel, Evaluate record, Type 12 )
   spke13_            ( S/P-kernel, Evaluate record, Type 13 )
   spke14_            ( S/P-kernel, Evaluate record, Type 14 )
   spke15_            ( S/P-kernel, Evaluate record, Type 15 )
   spke17_            ( S/P-kernel, Evaluate record, Type 17 )
   spke18_            ( S/P-kernel, Evaluate record, Type 18 )
   spkr01_            ( S/P-kernel, Read record, Type 01     )
   spkr02_            ( S/P-kernel, Read record, Type 02     )
   spkr03_            ( S/P-kernel, Read record, Type 03     )
   spkr05_            ( S/P-kernel, Read record, Type 05     )
   spkr08_            ( S/P-kernel, Read record, Type 08     )
   spkr09_            ( S/P-kernel, Read record, Type 09     )
   spkr10_            ( S/P-kernel, Read record, Type 10     )
   spkr12_            ( S/P-kernel, Read record, Type 12     )
   spkr13_            ( S/P-kernel, Read record, Type 13     )
   spkr14_            ( S/P-kernel, Read record, Type 14     )
   spkr15_            ( S/P-kernel, Read record, Type 15     )
   spkr17_            ( S/P-kernel, Read record, Type 17     )
   spkr18_            ( S/P-kernel, Read record, Type 18     )
   spks01_            ( S/P-kernel, Subset data, Type 01     )
   spks02_            ( S/P-kernel, Subset data, Type 02     )
   spks03_            ( S/P-kernel, Subset data, Type 03     )
   spks05_            ( S/P-kernel, Subset data, Type 05     )
   spks08_            ( S/P-kernel, Subset data, Type 08     )
   spks09_            ( S/P-kernel, Subset data, Type 09     )
   spks10_            ( S/P-kernel, Subset data, Type 10     )
   spks12_            ( S/P-kernel, Subset data, Type 12     )
   spks13_            ( S/P-kernel, Subset data, Type 13     )
   spks14_            ( S/P-kernel, Subset data, Type 14     )
   spks15_            ( S/P-kernel, Subset data, Type 15     )
   spks17_            ( S/P-kernel, Subset data, Type 17     )
   spks18_            ( S/P-kernel, Subset data, Type 18     )

Summary of Calling Sequences

The calling sequences for the SPK functions are summarized below. The functions are grouped by purpose.

High level routines for loading, unloading files:

   furnsh_c ( fname )
   unload_c ( fname )

   spklef_c ( fname, &handle )
   spkuef_c (         handle )

   spkezr_c ( tname,  et, ref,        aberr, oname, state, < )
   spkpos_c ( tname,  et, ref,        aberr, oname, postn, < )
   spkez_c  ( target, et, ref,        aberr, obs,   state, < )
   spkezp_c ( target, et, ref,        aberr, obs,   postn, < )
   spkapp_c ( target, et, ref, stobs, aberr,        state, < )
   spkapo_c ( target, et, ref, stobs, aberr,        postn, < )
   spkssb_c ( target, et, ref,                      state      )
   spkgeo_c ( target, et, ref,               obs,   state, < )
   spkgps_c ( target, et, ref,               obs,   postn, < )
 
   Unimplemented:
 
   spkpvn_c ( handle, descr, et, &ref, state, ¢er )
   spkpv_c  ( handle, descr, et, ref,  state, ¢er )

   Unimplemented:
 
   spksfs_c ( target, et, &handle, descr, ident, &found )

   spkr01_ ( handle, descr, et, record        )
   spke01_ (                et, record, state )
 
   spkr02_ ( handle, descr, et, record        )
   spke02_ (                et, record, state )
 
   spkr03_ ( handle, descr, et, record        )
   spke03_ (                et, record, state )
 
   spkr05_ ( handle, descr, et, record        )
   spke05_ (                et, record, state )
 
   spkr08_ ( handle, descr, et, record        )
   spke08_ (                et, record, state )
 
   spkr09_ ( handle, descr, et, record        )
   spke09_ (                et, record, state )
 
   spkr10_ ( handle, descr, et, record        )
   spke10_ (                et, record, state )
 
   spkr12_ ( handle, descr, et, record        )
   spke12_ (                et, record, state )
 
   spkr13_ ( handle, descr, et, record        )
   spke13_ (                et, record, state )
 
   spkr14_ ( handle, descr, et, record        )
   spke14_ (                et, record, state )
 
   spkr15_ ( handle, descr, et, record        )
   spke15_ (                et, record, state )
 
   spkr17_ ( handle, descr, et, record        )
   spke17_ (                et, record, state )
 
   spkr18_ ( handle, descr, et, record        )
   spke18_ (                et, record, state )

   spkpds_c ( body,   center, frame,  type,   first, last,  descr )
 
   spkw02_c ( handle, body,   center, frame,  first, last,  segid,
              intlen, n,      polydg, cdata,  btime              )
 
   spkw03_c ( handle, body,   center, frame,  first, last,  segid,
              intlen, n,      polydg, cdata,  btime              )
 
   spkw05_c ( handle, body,   center, frame,  first, last,  segid,
              gm,     n,      states, epochs                     )
 
   spkw08_c ( handle, body,   center, frame,  first, last,  segid,
              degree, n,      states, epoch1, step               )
 
   spkw09_c ( handle, body,   center, frame,  first, last,  segid,
              degree, n,      states, epochs                     )
 
   spkw10_c ( handle, body,   center, frame,  first, last,
              segid,  consts, n,      elems,  epochs      )
 
 
   spkw12_c ( handle, body,   center, frame,  first, last,  segid,
              degree, n,      states, epoch0, step               )
 
   spkw13_c ( handle, body,   center, frame,  first, last,  segid,
              degree, n,      states, epochs                     )
 
   spk14b_c ( handle, segid,  body,   center, frame,
              first,  last,   chbdeg  )
 
   spk14a_c ( handle, ncsets, coeffs, epochs )
 
   spk14e_c ( handle )
 
 
   spkw15_c ( handle, body,   center, frame,  first, last,  segid,
              epoch,  tpole,  peri,   p,      ecc,   j2flg, cpole,
              gm,     j2,     radius                             )
 
   spkw17_c ( handle, body,   center, frame,  first, last,
              segid,  epoch,  eqel,   rapol,  decpol      )
 
   spkw18_c ( handle, subtyp, body,   center, frame,  first, last,
              segid,  degree, n,      packts, epochs              )

   spkuds_c ( descr,  &body, ¢er, frame, &type,
              &first, &last, &begin,  &end         )
 

   spks01_ ( handle, baddr, eaddr, begin, end )
   spks02_ ( handle, baddr, eaddr, begin, end )
   spks03_ ( handle, baddr, eaddr, begin, end )
   spks05_ ( handle, baddr, eaddr, begin, end )
   spks08_ ( handle, baddr, eaddr, begin, end )
   spks09_ ( handle, baddr, eaddr, begin, end )
   spks10_ ( handle, baddr, eaddr, begin, end )
   spks12_ ( handle, baddr, eaddr, begin, end )
   spks13_ ( handle, baddr, eaddr, begin, end )
   spks14_ ( handle, baddr, eaddr, begin, end )
   spks15_ ( handle, baddr, eaddr, begin, end )
   spks17_ ( handle, baddr, eaddr, begin, end )
   spks18_ ( handle, baddr, eaddr, begin, end )
 
   spksub_c ( handle, descr, ident, begin, end, newh )

   spkopn_c ( name, ifname, ncomch, handle )
   spkopa_c ( file, handle                 )
   spkcls_c ( handle                       )

Appendix B --- A Template for SPK Comments

An undocumented ephemeris is in many respects worse than undocumented source code. With source code you can at least read the code and perhaps discern the function of the source code. An ephemeris on the other hand is a binary file. All it contains are numbers. It's very difficult to determine the purpose of an ephemeris simply from the state information it contains. For this reason, any ephemeris created for use by anyone other than yourself needs documentation.

If you create SPK files NAIF strongly recommends that you include descriptive documentation in the comments portion of the SPK file. You can use the utility program COMMNT to insert comments into the file, or you may use the functions in the SPC family to insert the comments when you create the SPK file. (See COMMNT.UG or SPC.REQ for further details.)

This appendix addresses the contents of your comments. What will others (or yourself) want to know about the SPK file weeks, months or years after it has been created? Providing this information can be a challenge. It's difficult to know in advance all the questions someone might ask about an ephemeris you've created. To assist with this task NAIF has devised a ``template'' that you may wish to use as a starting point when creating the comments for an SPK file.

Constraints

The comments you place in an SPK file must be plain ASCII text. Each line of text must consist of 80 or fewer characters. The text must contain only printing characters (ASCII characters 32 through 126).

The Basic Template

Here's one way to create the comments for an SPK file.

Objects in the Ephemeris

List the names and NAIF ID codes for the objects in the file.

Approximate Time Coverage

Provide a summary of the time for which states are available for the objects in the file. If you use UTC times in this summary and the ephemeris extends more than 6 months into the future, you should probably state that the times are approximate. You don't know when leapseconds will occur more than a few months in advance, so you can't know the exact UTC time boundaries for the ephemeris if it extends years into the future.

Status

Provide the ``status'' of the ephemeris. Tell the user why this ephemeris was created and for whom it is intended. For example, if this is the second in a series of ephemerides that will be produced for some object tell which ephemeris this one supersedes. Tell the user when the next ephemeris in the series will be available. Is the ephemeris suitable only for preliminary studies? Is it good for all Earth based observations? Is this an official operational product? Are there situations for which the ephemeris is not suitable?

Pedigree

Provide a production summary for the ephemeris. Tell when the ephemeris was produced (the system time stamp may not port if the file is copied to other systems). Say who produced the ephemeris; what source products were used in the production; what version of the producing program was used in the creation of the ephemeris. If the ephemeris is based on a set of recent observations, say so. In short give the user the pedigree of this ephemeris. This information is mostly for your benefit. If a problem arises with the ephemeris, you will know how the problem was created and have a better chance of fixing the problem.

Usage

Provide information the user will need to effectively use the ephemeris. Tell the user what other SPICE kernels are needed to use this ephemeris. For example, if the ephemeris contains only the state of an asteroid relative to the sun, the user will probably need a planetary ephemeris to effectively use the one you've created. Recommend a planetary ephemeris to use with your SPK file. If the ephemeris contains states of objects relative to non-inertial frames, the user will probably need other kernels so that various state transformations can be performed. Recommend which of these kernels the user should use with your SPK file.

Accuracy

If possible give some estimate as to the accuracy of your SPK file. Use numbers. Words such as ``this is the best available'' do not convey how much you know about the ephemeris.

Special Notes

Provide a description of any special properties of this ephemeris. For example, if some observation seems to be in conflict with this ephemeris you should probably point this out.

References

List any references that may be relevant to the understanding of the ephemeris. For example, if the ephemeris is based upon observations contained in the literature, site the appropriate articles. If there is some technical memorandum or private communication that addresses certain aspects of this ephemeris list it. This will allow you to more easily answer questions about the ephemeris.

Contacts

List your phone number, mail or e-mail address so that users of the ephemeris will be able to get in touch with you to ask questions or offer praise.

Appendix C---Revision History

November 17, 2005

Abstract was added.

Calls/references to the deprecated routine bodvar_c were replaced with calls/referenes to bodvcd_c. bodvrd_c is mentioned as another routine superseding bodvar_c.

C examples showing incorrect calling sequences for prompt_c were corrected.

December 22, 2004

Calls/references to lower level loader/unloader functions -- ldpool_c, spklef_c, and spkuef_c -- were replaced with calls to the current high level generic loader routines -- furnsh_c and unload_c -- throughout the document.

February 2, 2004

In the diagram of the type 1 segment layout, the label on the final directory epoch was corrected. In addition, labeling of directory epochs was made consistent with similar diagrams for other SPK data types.

Performed a spell-check on text.

Edited description of type 10 segments.

September 04, 2002

Updated to reflect addition of SPK type 18.

Added a brief discussion of the DAF run-time binary file format translation capability now present in the SPICE Toolkit.

July 21, 2001

A few typos were corrected.

March 1, 2000

This version describes the Hermite data types 12 and 13.

October 14, 1999

This is the initial release of the CSPICE edition of the SPK "Required Reading" document. The underlying Fortran NAIF Toolkit version is N0050.

The SPICE system has been extended to include CSPICE---a version of the NAIF Toolkit software coded in the ANSI C programming language.

To better accommodate CSPICE users, NAIF translated the Fortran SPK Required Reading document into this "CSPICE edition." This document closely parallels the current Fortran edition but contains C versions of illustrations of source code, including listings of calling sequences and example programs.

The CSPICE library---the C counterpart of SPICELIB---consists of two categories of functions:

-- Low level functions, translated from Fortran to ANSI C via the automatic translation program f2c.

-- Application interface-level functions, hand-coded in ANSI C. These hand-coded functions are called ``wrappers'' since they typically serve to encapsulate C code generated by running f2c on Fortran source code.

   _c

   _

The set of currently available CSPICE SPK wrapper functions:

   spk14a_c
   spk14b_c
   spk14e_c
   spkapo_c
   spkapp_c
   spkcls_c
   spkez_c
   spkezp_c
   spkezr_c
   spkgeo_c
   spkgps_c
   spklef_c
   spkopa_c
   spkopn_c
   spkpds_c
   spkpos_c
   spkssb_c
   spksub_c
   spkuds_c
   spkuef_c
   spkw02_c
   spkw03_c
   spkw05_c
   spkw08_c
   spkw09_c
   spkw10_c
   spkw12_c
   spkw13_c
   spkw15_c
   spkw17_c

   frmchg_c
   frmnam_c
   namfrm_c
   spkpv_c
   spkpvn_c
   spksfs_c
 
   Portions of the DAF family of functions
   The SPC family of functions

This version of the ``SPK Required Reading'' documents for the first time this important expansion of the SPK system.

Also in this version, we document:

1. the ability to request states of objects by name instead of by object ID codes;

2. the addition of SPK data Type 10 which allows the incorporation of NORAD ``two-line'' elements for Earth orbiters into the SPK system;

3. the addition of SPK data Type 14 which supports Chebyshev interpolation over non-uniformly spaced time intervals;

4. the addition of SPK data Type 17 which supports the inclusion of equinoctial elements into the SPK system.