The purpose of this document is to describe both the format and contents of
the ``Planetary Constants'' kernel files (PCKs) used within the SPICELIB
system, and to describe the NAIF Toolkit software that reads and makes direct
use of these kernel files.
This document is recommended reading for all users of PCK files.
All references are to NAIF documents. The notation [Dn] refers to NAIF
document numbers.
The "P" in ``SPICE'' has two sub-components: PCK kernels, which contain
planetary attitude and body shape information, and SPK kernels, which contain
planetary ephemerides. The PCK kernel includes orientation and shape
information pertaining to extended solar system bodies such as the Sun, the
planets, the natural satellites of the planets, comets, and asteroids.
The functionality of the PCK kernel is supplied by data files called ``PCK kernel files'' and by SPICELIB subroutines that can read and interpret the data in these files. Historically, there was only one kind of PCK kernel file, the PCK text kernel file (called the "P\_constants kernel.") This kind of PCK kernel file contains constants which allow calculation of solar system body orientation and shape. These ASCII files can be easily reviewed and modified. Now, in addition to these text PCK kernels, another format, the binary PCK kernel, has been developed. These files allow higher accuracy calculations of body orientation. They contain shorter-term, but more precise information in binary format where large amounts of data can be stored and accessed quickly. The only bodies for which this higher accuracy type of data is available are the moon, the Earth and the asteroid Eros.
The purpose of the PCK kernels and associated software is to provide SPICE users with a convenient mechanism for supplying planetary physical constants to application programs. SPICELIB's PCK software is able to read files conforming to these formats and return to a calling application program both the data contained in such files and a small number of commonly used numeric quantities derived from the kernel data.
This document specifies both the SPICELIB PCK formats and the interfaces of the SPICELIB subroutines that read or return data from PCKs. Examples of PCK file contents and code examples demonstrating use of the SPICELIB PCK subroutines are included.
This section covers some preliminary information required for understanding
the subsequent discussion of the contents of PCK files and SPICELIB's PCK
software.
Within the NAIF Toolkit software, a system of integer codes is used to
conveniently represent both celestial bodies and spacecraft. This system is
described in detail in ``NAIF IDS Required Reading'' [218].
In this document, the following features of the code system will be relied on:
Some constants that frequently appear in PCK files are associated with a
particular epoch and with a particular reference frame. For example, PCK
files released by NAIF typically contain constants that define the axes of
various body-fixed planetocentric coordinate systems, given relative to a
specified inertial reference frame, as a function of time. In this sort of
definition, the independent variable---time---is measured relative to a
specified reference epoch.
Typical choices of reference frames associated with PCK constants would be J2000 or B1950. Typical choices of reference epochs would be the J2000 epoch (JED 24515145.0) or the J1950 epoch (JED 2433282.5).
Within SPICELIB, reference frames are usually indicated by short character strings, such as 'J2000'. However, SPICELIB also has a system of integer codes that are used by some routines to name reference frames. This coding system is described in detail in [219]. An example of the correspondence of codes and names is show below:
Code Name Description
----- -------- -------------------------------------------
1 J2000 Earth mean equator, dynamical equinox of J2000
2 B1950 Earth mean equator, dynamical equinox of B1950
In PCK files, these integer codes are used to name reference frames
associated with constants.
The body-fixed ``Planetocentric'' coordinate system referred to in this
document is defined for solar system bodies as follows:
There are two general forms for PCK files, text and binary files. Text files
are ASCII and can be created and modified with an editor. Therefore, they are
easily changed and read. Binary files are created via SPICELIB programs and
have a particular format and architecture. They cannot be examined or changed
with an editor. These files require SPICELIB software for their manipulation.
Binary files can contain more data and are faster to use. In the PCK case,
the binary files contain higher precision data than the text files.
Text PCK files express data as ``assignments''; in text PCKs, values are
associated with name strings using a ``keyword = value'' format. These name
strings, together with their associated values, are called ``kernel
variables.'' The SPICELIB routines that access text PCK data at run time use
these associations established by loaded text PCK files to reference desired
data values; these routines look up data ``by name.'' Therefore, programmers
writing applications that use text PCKs must coordinate use of kernel
variable names between their software and the text PCK files used by their
software.
The binary PCK file format is built upon the SPICELIB system's DAF (Double
precision Array File) architecture. Readers who are not familiar with this
architecture are referred to [167] which describes the common aspects of all
DAF formats, as well as a collection of SPICELIB subroutines that support the
DAF architecture. Those users who only intend to read binary PCK files need
not read [167].
This section describes how PCK files and software are used in application
programs.
Using PCK data in an application program requires three steps:
Step 2 is referred to as ``loading'' a PCK file. Text PCK files are loaded by calling the SPICELIB subroutine LDPOOL and supplying the name of the PCK file to load as the input argument. All of the data in a text PCK file is read into memory when the file is loaded by an application program at run-time. Binary PCK files are loaded by calling the SPICELIB subroutine PCKLOF. This data will be accessible throughout the rest of the program run, unless it is deliberately overwritten or unloaded. Multiple text and multiple binary PCK kernels can be used simultaneously.
Binary PCK files take precedence over text PCK files. If data for a requested planetary constant and time period is covered by a loaded binary PCK file, the binary data will be returned and used. If multiple binary PCK files are loaded, the most recently loaded file takes precedence, down to the binary file loaded earliest. Only if no binary PCK data is available will the text PCK file be used.
Step 3, accessing loaded PCK data, is accomplished via calls to SPICELIB routines. At the lowest level, these access routines allow the calling program to retrieve specified data that has been read from one or more PCK files. Higher-level access routines can return quantities derived from PCK data that has been loaded; the most commonly used such quantity is a matrix that transforms vectors from inertial to body-fixed planetocentric coordinates. The SPICELIB subroutine TIPBOD calculates this transformation. The subroutine BODVAR retrieves information on body orientation and body shape by calling RTPOOL to fetch it from the text PCK kernels loaded into the kernel pool.
For text PCK files, the PCK software can be thought of as ``buffering'' all of the data in the PCK files that have been loaded: all of the data from these files is retained in memory. Therefore, repeated calls to the PCK access routines do not incur the inefficiency of re-reading data from files. For binary PCK file, like the case of the SPK and CK readers, only a portion of the most recently used information is buffered.
The data structure used by SPICELIB to maintain associations of text kernel variable names and values is called the ``kernel pool.'' Data loaded into memory via LDPOOL is referred to as ``being present in the kernel pool.'' There is no analog to the kernel pool for binary PCK files.
A NAIF Toolkit utility program (SPACIT) is used to convert binary PCK files
to NAIF transfer files for porting to another type of computer; on the new
host the SPACIT utility is used to convert the NAIF transfer file to the
native binary format. Text format PCK files may be moved between computers
using normal file transfer methods such as ftp (text mode), COPY or e-mail.
The orientation models used by SPICELIB PCK access routines all express the
direction of the pole and location of the prime meridian of a body with
respect to an inertial reference frame, as a function of time. This
information defines the coordinate axes of the ``Body Equator and Prime
Meridian'' system.
The orientation models use three Euler angles to describe the pole and prime meridian location: the first two angles, in order, are the right ascension and declination (henceforth ra and DEC) of the north pole of a body as a function of time. The third angle is the prime meridian location (represented by `W'), which is expressed as a rotation about the north pole, also a function of time. The coordinate transformation defined by the Euler angles is represented by the matrix product
[ W ] [ Pi/2 - Dec ] [ Pi/2 + RA ]
3 1 3
where
[ omega ]
i
denotes the matrix that rotates vectors by --omega about the ith coordinate
axis, using the right hand rule. (This notation is explained in detail in
[214]).
In PCK files, the time arguments of functions that define orientation always refer to Barycentric Dynamical Time (TDB), measured in centuries or days past a specified epoch such as J2000, which is Julian ephemeris date 2451545.0. The time units expected by the SPICELIB software are ephemeris days for prime meridian motion and ephemeris centuries for motion of the pole.
Text PCK files conform to a flexible format called ``NAIF text kernel''
format. (A number of SPICELIB kernels other than text PCKs use this NAIF text
kernel format is described in detail in [218]. For the reader's convenience,
an overview of the format is provided here.
NAIF text kernels are, first of all, ASCII files. As such, they are human readable and can be easily modified by text editors. In addition, NAIF text kernels can be readily ported between computer systems, even when the systems in question have different file systems and file formats.
The NAIF text kernel format provides for representation of data in a ``keyword = value'' syntax. The format also provides for the inclusion of free-form comment blocks.
There are two kinds of data that can be placed in NAIF text kernel files: double precision numbers and UTC time strings.
According to the text kernel format, a text kernel nominally consists of a series of sets of contiguous lines (or ``blocks'') of comments, alternating with blocks of data. Comment blocks are started with the string (called a ``control sequence'')
\begintextalone on a line, as shown here. Comment blocks are ended by the control sequence
\begindataalone on a line. In a text kernel file, the lines preceding the first
\begindatacontrol sequence are considered to constitute a comment block; the
\begintext control sequence is optional for this commentblock.
Comment blocks can contain arbitrary text, except for non-printing characters or lines that can be interpreted as control sequences. On the other hand, data must be organized according to a very specific format: all of the data in a text kernel must appear in the form of an ``assignment'' such as
NAME = ( VALUE1, VALUE2, ... )where name is a string no longer than 32 characters, and the values on the right hand side are double precision numbers. A specific example is shown below:
BODY399_RADII = ( 6378.140 6378.140 6356.75 )Some variations on the form shown here are allowed: commas between data values are optional, the right hand side of the assignment can be continued over multiple lines, and the numbers can be expressed as integers or reals without causing the PCK software to fail. Assignments of scalars do not require the value on the right hand side to be enclosed in parentheses, but that notation is frequently used as a visual cue. Blank lines within or between assignments are ignored by the SPICELIB software that reads text kernels.
In addition to numbers, UTC strings can be assigned to variables. The ``@'' character is used to identify the strings as time strings. The strings are stored internally as double precision numbers representing ``UTC seconds past J2000.'' An example is the assignment:
SCLK_KERNEL_ID = ( @01-MAY-1991/16:25 )See [218] for a complete discussion of the allowed form of assignments.
The effect of an assignment in a text PCK file is to associate values with a name. The name is referred to as a ``kernel variable.'' When a text PCK file is loaded by an application, the associations of names and values established by the PCK are maintained: the values associated with a given name can be retrieved at any time.
Other than the limitations imposed by the PCK kernel formats, there are no
absolute restrictions on the names or values of the variables used in PCK
files. However, the SPICELIB kernel concept calls for the contents of PCK
files to be limited to physical and cartographic constants describing
extended solar system bodies: radii of bodies, constants defining orientation
models, masses or values of GM are examples of data appropriate for inclusion
in PCKs.
SPICELIB provides a text PCK access routine (RTPOOL) that can return the values of any variable defined in a text PCK file. There are also more specialized PCK access routines (BODEUL, BODMAT, TIPBOD, TISBOD, BODVAR) that can recognize and make use of a specific set of of kernel variables. These access routines return Euler angles and coordinate and state transformation matrices that are used to convert position and state vectors from inertial to body-fixed, planetocentric coordinates. In this document, the formulas defining time-varying coordinate transformation matrices and Euler angles are referred to as ``orientation models'' since they define the orientation of an extended body with respect to specific inertial frames.
Because PCK access routines that deal with orientation models are used extensively in SPICELIB and applications that use the Toolkit, the kernel variables that these routines rely on will be discussed in detail.
The functions that define the Euler angles are characterized by a set of parameters. The specific values of the parameters are values assigned to kernel variables in PCK files. The functions themselves are implemented by code within SPICELIB routines. The general form of the functions is that used in the latest IAU/IAG/COSPAR report. Values shown in this document reflect the 1991 report, [306]. For the latest PCK values, check with NAIF.
In a text PCK file, the variables (Euler angles)
RA, DEC, Wfor the Earth are represented by the names
BODY399_POLE_RA BODY399_POLE_DEC BODY399_POLE_PMThe equations above are expressed in a text PCK file by the kernel variable assignments (Values taken from [306].)
BODY399_POLE_RA = ( 0. -0.641 0. ) BODY399_POLE_DEC = ( +90. -0.557 0. ) BODY399_PM = ( 190.16 +360.9856235 0. )Note that the string ``PM'' is used in place of ``W'' for the kernel variable associated with the prime meridian.
If you examine a PCK file produced by NAIF, you'll see an additional symbol grouped with the ones listed here; it is
BODY399_LONG_AXISThis term is currently zero for all bodies except Mars. It represents the offset between the longest axis of the triaxial ellipsoid used to model a body and the prime meridian of the body.
Text PCK kernel variables recognized by SPICELIB PCK access routines have
names that follow a simple pattern: variables related to a body whose NAIF
integer code is nnn have names of the form
BODYnnn_<item name>where
<item name>is a short string that identifies the type of quantity the kernel variable represents. For example, the variable containing quadratic polynomial coefficients for the right ascension of the Earth's north pole is
BODY399_POLE_RANote the number ``399'' appearing in the kernel variable names; this is the NAIF integer code for the Earth.
The specific item names that are recognized by PCK access routines are specified in the following sections.
Orientation models that are usable by SPICE's text PCK access routines are
not available for all solar system bodies. For example, Saturn's moon
Hyperion is ``tumbling'' and does not admit a description of its motion by
the sort of models used in text PCK kernels.
To date, no PCK files containing models for the rotation of comets have been produced or collected by NAIF. Models for the rotation of comets, as well as for the rotation of asteroids and the natural satellites of planets, can be accommodated by the PCK system only if the models have the form described in the section ``Models for the Sun, Planets, and Asteroids'' or in ``Models for Satellites'' or if binary PCK data is available.
For the Sun, planets, and asteroids, the expressions used in text PCK files
for the north pole direction and prime meridian location are always quadratic
polynomials, where the independent variable is time. Some coefficients may be
zero.
Let RA and DEC represent the right ascension and declination of a body's north pole, and let W be the prime meridian location, measured in the counterclockwise direction, from the cross product of the Earth's ``mean'' North pole at the J2000 epoch (as used in defining the J2000 frame) and BODY's North pole at et, to BODY's prime meridian at et.
The variables RA, DEC, and W constitute sufficient information to compute the transformation from a specified inertial frame to body-fixed, planetocentric coordinates for the body to which they apply, at a specified time.
The angles RA, DEC, and W are defined as follows:
2
RA2*t
RA = RA0 + RA1*t/T + ------
2
T
2
DEC2*t
DEC = DEC0 + DEC1*t/T + -------
2
T
2
W2*t
W = W0 + W1*t/d + -----
2
d
where
d = seconds/day
T = seconds/Julian century
t = ephemeris time, expressed as seconds past the reference epoch
for this body or planetary system
Below is an example showing actual values of the parameters used to define
the latest IAU model for orientation of the Earth. Here, the motions of both
the pole and the prime meridian are given by linear polynomials; the
quadratic terms are all zero. The values shown here are taken from [306]. In
that document, the names
alpha
0
and
delta
0
are used in place of the names RA and DEC used here.
alpha = 0.00 - 0.641 T
0
delta = 90.0 - 0.557 T
0
W = 190.16 + 360.9856235 d
T represents centuries past J2000 (TDB),
d represents days past J2000 (TDB).
Orientation models for natural satellites of planets are a little more
complicated; in addition to polynomial terms, the RA, DEC, and W expressions
include trigonometric terms. The arguments of the trigonometric terms are
linear polynomials. These arguments are usually called ``phase angles.''
However, within SPICELIB internal documentation, these quantities are called
``nutation precession angles''; for consistency with the SPICELIB software,
we'll use this terminology in the following discussion.
Expressions for the right ascension and declination of the north pole and the location of the prime meridian for any satellite of a given planet are as follows:
2 ____
RA2*t \
RA = RA0 + RA1*t/T + ------ + / a sin theta
2 ---- i i
T i
2 ____
DEC2*t \
DEC = DEC0 + DEC1*t/T + ------- + / d cos theta
2 ---- i i
T i
2 ____
W2*t \
W = W0 + W1*t/d + ----- + / w sin theta
2 ---- i i
d i
where
d = seconds/day T = seconds/Julian century t = ephemeris time, expressed as seconds past a reference epochRA0, RA1, DEC0, DEC1, W0, and W1 are constants specific to each satellite.
The nutation precession angles
theta
i
are specific to each planet. The coefficients
a , d , and w
i i i
are specific to each satellite.
As an example, the nutation precession angles for Earth given by [252] are shown below. That document uses the variable names E1---E5 in place of
theta --- theta
1 5
in the equations above.
E1 = 125.045 - 0.052992 d E2 = 250.090 - 0.105984 d E3 = 260.008 + 13.012001 d E4 = 176.625 + 13.340716 d E5 = 357.529 + 0.985600 d Here d represents days past J2000 (TDB)Because the NAIF Toolkit software expects the time units for the angles to be centuries (as in the IAU models for most bodies---the Earth is an exception), the linear coefficients are scaled by 36525.0 for use in the kernel variable assignments:
BODY3_NUT_PREC_ANGLES = ( 125.045 -1935.5328
250.090 -3871.0656
260.008 475263.3
176.625 487269.6519
357.529 35999.04 )
In this assignment, the constant and linear polynomial coefficients for each
nutation precession angle are listed together: the numbers 125.045 and
-1935.5328 are the constant and linear terms for the angle ``E1,'' and so on.
Note the body number 3 in the kernel variable name above; this number designates the Earth-Moon barycenter. The PCK access routines expect nutation precession angles to be associated with the barycenters of planetary systems.
Here are the expressions for the right ascension and declination of the moon, also taken from [252]:
alpha = 270.000 + 0.003 T - 3.878 sin(E1) - 0.120 sin(E2)
0
+ 0.070 sin(E3) - 0.017 sin(E4)
delta = 66.541 + 0.013 T + 1.543 cos(E1) + 0.024 cos(E2)
0
- 0.028 cos(E3) + 0.007 cos(E4)
W = 38.317 + 13.1763582 d + 3.558 sin(E1)
+ 0.121 sin(E2)
- 0.064 sin(E3)
+ 0.016 sin(E4)
+ 0.025 sin(E5)
Here d represents days past J2000 (TDB),
and T represents Julian centuries past J2000 (TDB).
E1--E5 are the nutation precession angles.
The polynomial terms are assigned to symbols by the statements
BODY301_POLE_RA = ( 270.000 0.003 0. ) BODY301_POLE_DEC = ( +66.541 0.013 0. ) BODY301_PM = ( 38.317 +13.1763582 0. )The coefficients of the trigonometric terms are assigned to symbols by the statements
BODY301_NUT_PREC_RA = ( -3.878 -0.120 +0.070 -0.017 0. ) BODY301_NUT_PREC_DEC = ( +1.543 +0.024 -0.028 +0.007 0. ) BODY301_NUT_PREC_PM = ( +3.558 +0.121 -0.064 +0.016 +0.025 )Note that for the RA and PM (prime meridian) assignments, the ith term is the coefficient of sin(Ei) in the expression used in the IAU model, while for the DEC assignment, the ith term is the coefficient of cos(Ei) in the expression used in the IAU model.
SPICELIB software for text PCK kernels expects the models for satellite orientation to follow the form of the model shown here: the polynomial terms in the RA, DEC, and W expressions are expected to be quadratic, the trigonometric terms for RA and W (satellite prime meridian) are expected to be sums of sines of nutation precession angles, and the trigonometric terms for DEC are expected to be sums of cosines of nutation precession angles. The nutation precession angles themselves are defined by linear polynomial functions of time.
Note that the number of values defining the nutation precession angles for a planetary system must be be consistent with the number of trigonometric terms used in the expressions for the RA, DEC and W angles for the satellites of that system. See ``Creating and Modifying Text PCKs Kernels'' for details.
The constants used in PCK files to define an orientation model for a
specified body are assumed by default to define a time-dependent rotation
R(t) that converts vectors from J2000 coordinates to body-fixed,
planetocentric coordinates at the epoch t seconds past J2000, TDB (JED
2451545.0). We say that the constants are ``referenced to the J2000 epoch and
J2000 frame.'' However, these default values for the epoch and frame of the
constants may be overridden: it is possible to use constants that are
referenced to the B1950 frame and to the J1950 epoch, for example.
The default constants and frame for a body are overridden by setting the values of the kernel variables
BODY<id code>_CONSTANTS_REF_FRAMEand
BODY<id code>_CONSTANTS_JED_EPOCHHere
<id code>is:
BODY<id code>_CONSTANTS_REF_FRAMEare the codes returned by the SPICELIB routine IRFNUM. Some of the commonly used codes and the corresponding frames are:
Code Frame
---- -----
1 J2000
2 B1950
3 FK4 (used in CSPICE for `EME50')
For example, to use constants referenced to the FK4 or EME50 frame for the
asteroid Gaspra (ID code = 9511010), the PCK file containing the constants
should include the assignment
BODY9511010_CONSTANTS_REF_FRAME = ( 3 )The values of the epoch specifier variable
BODY<id code>_CONSTANTS_JED_EPOCHare Julian ephemeris dates. To use constants for Gaspra that are referenced to the J1950 epoch, the PCK file containing the constants should include the assignment
BODY9511010_CONSTANTS_JED_EPOCH = ( 2433282.5D0 )The creator of a PCK file can set the frame and epoch of the constants on a body-by-body basis, except in the case of planets and their (natural) satellites, where a single choice of frame and epoch must be used for each planetary system. For example, to use constants referenced to the B1950 frame and J1950 epoch for the Earth and Moon, you would make the assignments
BODY3_CONSTANTS_REF_FRAME = ( 2 ) BODY3_CONSTANTS_JED_EPOCH = ( 2433282.5D0 )The ID code `3' designates the Earth-Moon barycenter.
Note: the assignment
BODY399_CONSTANTS_REF_FRAME = ( 2 ) BODY399_CONSTANTS_JED_EPOCH = ( 2433282.5D0 )would be ignored by the PCK reader routines; you cannot assign a frame or epoch using the ID code of a planet or satellite.
Using constants that are referenced to frames or epochs other than J2000 does not affect the definitions of the inputs or outputs of any of the PCK access routines. These routines make the necessary transformations internally to take into account the reference frame and epoch of the orientation constants in the kernel pool. Thus the PCK access routine BODMAT, which has the argument list
BODMAT ( BODY, ET, TIPM )returns the J2000-to-body-fixed transformation matrix for ephemeris time expressed as ``ET'' seconds past the J2000 epoch (JED 2451545.0), regardless of the epoch or frame of the orientation constants used to compute TIPM.
SPICELIB contains a number of geometry routines that make use of triaxial
ellipsoidal models of extended solar system bodies. Although SPICELIB
currently contains no routines that directly use the specific PCK variables
that define these models, text PCK files typically contain radii of solar
system bodies, since these values can be looked up by low-level text PCK
access routines and subsequently used by SPICELIB geometry routines.
In text PCK files produced by NAIF, the radius values for body nnn are assigned to the variable
BODYnnn_RADIIThree radius values are always assigned for each instance of this variable. The data are ordered as in [306]: the equatorial radii are listed with the largest axis, often called the ``a'' axis, appearing first; the polar radius is last. Spheroids and spheres are obtained when two or all three radii are equal.
Example: Radii of the Earth.
BODY399_RADII = ( 6378.140 6378.140 6356.75 )
In order to compute transformations for the Sun, a planet, or an asteroid
(say body number ppp), the PCK access routines require that one or more PCK
files containing values for the following variables be loaded:
BODYppp_POLE_RA BODYppp_POLE_DEC BODYppp_PMFor a satellite (say body number sss), one or more PCK files containing values for the following variables must be loaded:
BODYsss_POLE_RA BODYsss_POLE_DEC BODYsss_PM BODYsss_NUT_PREC_RA BODYsss_NUT_PREC_DEC BODYsss_NUT_PREC_PM BODYbbb_NUT_PREC_ANGLESwhere the code bbb embedded in the last name above is that of the barycenter of the planetary system to which the satellite belongs.
The triaxial ellipsoidal model for body nnn is expressed by the assignment
BODYnnn_RADII = ( <larger equatorial radius>,
<smaller equatorial radius>,
<polar radius> )
The PCK file text format allows NAIF Toolkit users to easily modify existing
text PCKs and to create their own files containing values of their choosing.
Any text editor capable of working with ASCII files can be used to edit text
PCK files.
Although the text PCK format makes it easy to modify text PCK files, NAIF recommends that application programmers avoid software designs that call for special-purpose, user-created text PCK files. The opportunities for confusion and errors increase with the number of available versions of a text PCK file (or any data file).
NAIF recommends that you take the following precautions when modifying a text PCK file:
BODYnnn_where nnn is the NAIF integer code of the body the variable applies to.
Kernel variables having names recognized by users' application software are a potential problem area: if the names used in the application don't match those in the text PCK file, the application will fail to obtain the data as intended. The most frequent cause of this type of failure is misspelling of variable names, but programmers who are considering changing names of PCK variables that are already in use should also keep this problem in mind.
Modifying orientation models for satellites requires attention to the consistency between the number of nutation precession angles and the number of coefficients of trigonometric functions having the nutation precession angles as arguments. For any planetary system, there should be twice as many values for the nutation precession angles as the maximum number of trigonometric terms in the expressions for prime meridian location or right ascension or declination of the pole of any satellite in the system. This is because the nutation precession angles are defined by linear polynomials; each polynomial has two defining coefficients.
For example, the 1991 IAU model for the Earth-Moon system uses the following values to determine the Moon's orientation:
BODY3_NUT_PREC_ANGLES = ( 125.045 -1935.5328
250.090 -3871.0656
260.008 475263.3
176.625 487269.6519
357.529 35999.04 )
BODY301_POLE_RA = ( 270.000 0.003 0. )
BODY301_POLE_DEC = ( +66.541 0.013 0. )
BODY301_PM = ( 38.317 +13.1763582 0. )
BODY301_NUT_PREC_RA = ( -3.878 -0.120 +0.070 -0.017 0. )
BODY301_NUT_PREC_DEC = ( +1.543 +0.024 -0.028 +0.007 0. )
BODY301_NUT_PREC_PM = ( +3.558 +0.121 -0.064 +0.016 +0.025 )
Note that there are five nutation precession angles, with two coefficients
defining each one. The trigonometric terms in the expressions for the right
ascension, declination, and prime meridian location for the moon require five
nutation precession angles.
If a NAIF Toolkit user were to update this model with a new one that had, for example, only one nutation precession angle, then the variables
BODY301_NUT_PREC_RA BODY301_NUT_PREC_DEC BODY301_NUT_PREC_PMwould each have to be assigned only one value. Failure to make this change would result in an error being signalled at run-time by any SPICELIB PCK access routine that uses these variables.
A binary PCK file contains one or more `segments'. Each segment contains data
sufficient to compute the axes of a body-fixed planetary coordinate system,
relative to a specified inertial reference frame, as a function of time.
The data in each segment are stored as a single array. The summary for the array, called a `descriptor', has two double precision components:
Preceding the `segments', the Comment Area provides space in a binary PCK
file for storing additional textual information besides what is written in
the array names. Ideally, each binary PCK file would contain internal
documentation that describes the origin, recommended use, and any other
pertinent information about the data in that file. For example, the beginning
and ending epochs for the file, the names and NAIF integer codes of the
bodies included, an accuracy estimate, the date the file was produced, and
the names of the source files used in making the binary PCK file could be
included in the Comment Area.
SPICELIB provides a family of subroutines for handling this Comment Area. This software provides the ability to add, extract, read, and delete comments and convert commented files from binary format to transfer format and back to binary again.
The third integer component of the descriptor---the code for the
representation, or `data type'---is the key to the binary PCK format. For
purposes of determining the segment best suited to fulfill a particular
request, all segments are treated equally. It is only when the data in a
segment are to be evaluated that the type of data used to represent the data
becomes important. Because this step is isolated within low-level readers,
new data types can be added to the binary PCK format without affecting
application programs that use the higher level readers.
Two representations, or data types, are currently supported by the binary PCK
routines in SPICELIB. They are Chebyshev polynomials (Euler angles only),
called "Type 2" and Chebyshev polynomials (Euler angles and their
derivatives) for intervals of possibly varying lenghts, called "Type 3".
These are sets of Chebyshev polynomial coefficients for the Euler angles,
defining right ascension and declination of the body's north pole, and its
prime meridian rotation as a function of time. The rates of the angles are
obtained by differentiation.
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 subroutine PCKE02 contains the algorithm used to construct a set of Euler angles 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 |
+---------------+
A four-number `directory' at the end of the segment contains the information
needed to determine the location of the record corresponding to a particular
epoch.
+------------------+
| MID |
+------------------+
| RADIUS |
+------------------+
| X coefficients |
+------------------+
| Y coefficients |
+------------------+
| Z coefficients |
+------------------+
The first two elements in the record, MID and RADIUS, are the midpoint and
radius of the time interval covered by coefficients in the record. These are
used as parameters to perform transformations between the domain of the
record (from MID - RADIUS to MID + RADIUS) and the domain of Chebyshev
polynomials (from -1 to 1 ).
The same number of coefficients is always used for each component, and all records are the same size (RSIZE), so the degree of each polynomial is
( RSIZE - 2 ) / 3 - 1
These are sets of Chebyshev polynomial coefficients for the Euler angles,
defining right ascension (RA) and declination (DEC) of the body's north pole,
and its prime meridian rotation (W) as a function of time, and their
derivatives. This data type was created for the attitude of the asteroid
Eros.
Each segment contains an arbitrary number of logical records. Each record contains a set of Chebyshev coefficients for angles and derivatives valid throughout an interval defined in the record. The lengths of these intervals may vary within a segment. The subroutine PCKE03 contains the algorithm used to construct a set of Euler angles from a particular record and epoch. All records contain the same number of coefficients.
A segment of this type is structured as follows:
----------------------------------------------------- | Record 1 | Record 2 | ... | Record N-1 | Record N | -----------------------------------------------------where each record has the following format:
--------------------------------------------------- | Midpoint of the approximation interval in TDB | --------------------------------------------------- | Radius of the approximation interval in seconds | --------------------------------------------------- | coefficients for the RA position | --------------------------------------------------- | coefficients for the DEC position | --------------------------------------------------- | coefficients for the W position | --------------------------------------------------- | coefficients for the RA velocity | --------------------------------------------------- | coefficients for the DEC velocity | --------------------------------------------------- | coefficients for the W velocity | ---------------------------------------------------TDB is time in ephemeris seconds past J2000, called et in the SPICELIB system.
Only very knowledgeable users who need to incorporate new planetary/satellite
orientation information in binary format should consider writing binary PCK
files. Users who write binary PCK files must have a thorough understanding of
the information they wish to place in a binary PCK file. They must also
master the high level structure of the PCK files, and they must be sure to
correctly package the data for the PCK writing subroutines provided in SPICE.
We also strongly recommend that the writer of a PCK file include descriptive
comments in the comment area. Normally, binary PCK files should be obtained
from NAIF.
To create files that are smaller and faster to load, the user should keep in mind that the PCK segments should be as large as possible.
The are generally three steps to creating a binary PCK file.
CALL PCKOPN ( FILE, IFNAME, I, HANDLE )
The method for beginning the segment, adding data to the segment and closing
the segment differs with the PCK type.
For segments of type 2, there is a segment writing routine called PCKW02 in SPICELIB. This routine takes as input arguments the handle of an PCK file that is open for writing, the information needed to construct the segment descriptor, and the data to be stored in the segment. The header of the subroutine provides a complete description of the input arguments and an example of its usage. Here's an example of a call to PCKW02:
CALL PCKW02 ( HANDLE, BODY, FRAME, FIRST,
LAST, SEGID, INTLEN, N,
POLYDG, CDATA, BTIME )
For type 3, there are three subroutines used in creating a binary PCK file.
They are PCK03B, which begins a type 3 segment, PCK03A, which adds data to
segment, and PCK03E, which ends a segment. The type 3 subroutines can be used
in a loop, where PCK03A is called to add data to the segment. Here is a code
fragment which begins a type 3 segment, writes data to that segment in a
loop, and then closes the segment.
CALL PCK03B ( HANDLE, SEGID, BODY, FRAME,
ETSTRT, ETSTOP, CHBDEG )
DO WHILE ( <a condition> )
...
CALL PCK03A ( HANDLE, N, COEFFS, EPOCHS )
...
END DO
CALL PCKO3E ( HANDLE )
When a user is finished writing segments to an PCK file, the file must be
closed with the subroutine PCKCLS.
CALL PCKCLS ( HANDLE )
This section describes the specifications and proper use of the SPICELIB PCK
software.
Because loading PCK files is usually time-consuming, it is good programming
practice to have applications load PCK files during program initialization
rather than throughout their main processing thread, especially if that
processing thread is a loop.
It is also wise to avoid designing data processing systems that effectively place PCK loading in a tight loop by requiring repeated runs of programs that expend a significant fraction of their run time on loading PCK files. If a program loads PCK files, it is preferable that it do all of its processing in a single run, or at least in a small number of runs, rather than carry out its processing by being re-run a large number of times: the former design will greatly reduce the ratio of the time the program spends loading PCKs to the time it spends on the rest of its data processing.
As mentioned in the ``System Overview'' section, in order to use text PCK
files in an application, the data in the files must be read into memory. This
is accomplished by calling the SPICELIB routine LDPOOL. The name of the text
PCK file to load is supplied as an input to LDPOOL, for example:
CALL LDPOOL ( 'P_CONSTANTS.KER' )File names supplied to LDPOOL will generally be system-dependent. It is good programming practice to not use hard-coded file names in calls to LDPOOL. Instead, applications should obtain kernel file names by one of the following methods:
Each time a text PCK is loaded, the assignments made in the file are maintained in the PCK software. In particular, if a kernel variable occurs in multiple PCKs that are loaded in a single run of a program, the value of the variable will be the one assigned in the following priority: last binary PCK file loaded, previously loaded binary PCK files, then last loaded text PCK files followed by previously loaded text PCK files. All binary PCK files take precedence over text PCK files. Within the binary and/or text file groups, the last loaded files takes precedence.
The routine PCKLOF maintains a database of loaded binary PCK files. The
calling program indicates which files are to be used by passing their names
to PCKLOF.
CALL PCKLOF ( 'example.pck', HANDLE)
PCKLOF returns a DAF file handle for each file, which may be used to access
the file directly using DAF subroutines. Once an PCK file has been loaded, it
may be accessed by the PCK software. Each set of constants is computed from a
distinct segment.
An PCK file may contain any number of segments. In fact, the same file may contain overlapping segments: segments containing data for the same body over a common interval. When this happens, the latest segment in a file supersedes any competing segments earlier in the file. Similarly, the latest file loaded supersedes any earlier files. In effect, several loaded files become equivalent to one large file. Binary PCK files take precedence over text PCK files.
It is possible, though unlikely, that a program would need to make use of
many binary PCK files in the course of a single execution. On the other hand,
the number of binary PCK files that may be open at any one time is limited,
so such a program might need to unload some PCK files to make room for
others. A binary PCK file may be unloaded by supplying its handle to
subroutine PCKUOF. The call to this subroutine is shown below,
CALL PCKUOF ( HANDLE ) { Unload binary PCK file }
SPICELIB contains two basic categories of PCK access routines: those that
return PCK data directly, and those that return quantities derived from PCK
data. This section discusses the PCK access routines in the later category:
these routines deal with coordinate and state transformations.
All of the routines listed here make use of the orientation models discussed in the section titled ``Orientation Models used by PCK Software.'' Note that in order to use these routines, an application must first load a PCK file (or files) containing sufficient data to define all of the required orientation models. If needed data has not been loaded, these routines will signal run-time errors when called.
To obtain the matrix that transforms vectors from a specified inertial reference frame to body-fixed planetocentric coordinates for a specified body, at a specified ephemeris time, use the routine TIPBOD. The calling sequence is
CALL TIPBOD ( REF, BODY, ET, TIPM )In the argument list for TIPBOD:
CALL TIPBOD ( 'B1950', 399, ET, TIPM )returns a matrix TIPM such that left-multiplying V50 by TIPM--- accomplished in SPICELIB by the call
CALL MXM ( TIPM, V50, VBODFX )will return the vector VBODFX specified relative to the Earth's (``body-fixed'') planetocentric frame at time ET.
Note that many practical applications of TIPBOD require that a light-time corrected value of et be supplied as an input. See ``Computing the Sub-Observer Point'' in the ``Examples'' section below.
The subroutine BODMAT is an older, less general version of TIPBOD that does not accept an input argument specifying an inertial reference frame. Instead, BODMAT assumes that the frame is J2000. The calling sequence is the same as that of TIPBOD, minus the argument ref:
CALL BODMAT ( BODY, ET, TIPM )The fundamental quantities defined by PCK orientation models are actually Euler angles, not matrices. These Euler angles, which we call ``RA, DEC, and W,'' are related to the matrix TIPM shown above by the equation
TIPM = [ W ] [ Pi/2 - DEC ] [ Pi/2 + RA ]
3 1 3
The units of these angles are radians. To retrieve these angles directly, the
call
BODEUL ( BODY, ET, RA, DEC, W, LAMBDA )can be used. The arguments BODY and ET have the same meanings as in the argument lists of TIPBOD and BODMAT. The arguments RA and DEC represent the right ascension and declination of the North pole of body at et with respect to the J2000 inertial reference frame. The argument W is the prime meridian location for BODY at ET, also measured with respect to the J2000 inertial reference frame.
The output LAMBDA is the positive west longitude, measured from the prime meridian of body, of the longest axis of the triaxial ellipsoidal model for body given in a PCK file.
Currently, the only body having a non-zero value of LAMBDA is Mars (see [195]). SPICELIB software does not currently make use of LAMBDA.
SPICELIB provides a routine analogous to TIPBOD for transforming state vectors from inertial to planetocentric coordinates. This routine is called TISBOD; the calling sequence is
CALL TISBOD ( REF, BODY, ET, TSIPM )The input arguments REF, BODY, and ET have the same meanings as in the argument list of TIPBOD. The output argument TSIPM is the 6x6 matrix required to transform state vectors from inertial to body-fixed coordinates. Left multiplication of a state vector by TSIPM will transform it from the frame specified by REF to body-fixed planetocentric coordinates for BODY at time ET.
See ``Transforming a State to Body-Fixed Coordinates'' in the ``Examples'' section for further discussion of use of TISBOD.
WARNING: These low-level access routines for text PCK files only search the
text kernel pool for these values. Values found in loaded binary PCK files
will NOT be found by these routines. The values retrieved from a binary PCK
file take precedence over the values found in the text PCK kernels.
Therefore, if binary kernels have been loaded values returned by these low
level routines may not be the same values used by higher level routines like
TISBOD and TIPBOD. We recommend the user who loads binary PCK kernels NOT USE
these low-level routines!
The lowest-level SPICELIB PCK access routine is RTPOOL. RTPOOL is a general-purpose routine for retrieving any text kernel data loaded via LDPOOL. To obtain data from RTPOOL, use the calling sequence
CALL RTPOOL ( NAME, N, VALUES, FOUND )The meanings of the arguments of RTPOOL are follows:
In text PCK's produced by NAIF, PCK kernel variables will have names conforming to the naming convention used in SPICELIB, that is, the kernel variable names have the form
BODYnnn_<item name>The SPICELIB routine BODVAR can be used in place of RTPOOL to retrieve values for such variables; BODVAR accepts as inputs the NAIF integer code of the body and a string making up the portion of the item's name following the prefix.
BODVAR ( BODY, ITEM, DIM, VALUES ) CALL BODVAR ( 399, 'RADII', DIM, VALUES )which would return the dimension and values associated with the variable
BODY399_RADIInamely
DIM = 3 VALUE(1) = 6378.140 VALUE(2) = 6378.140 VALUE(3) = 6356.755It is possible to test whether a kernel variable has been loaded by calling the SPICELIB logical function BODFND, as long as the variables in question follow the SPICELIB naming convention. The calling sequence is
FOUND = BODFND ( BODY, ITEM )where body is the NAIF integer code of the body, and ITEM is the string making up the portion of the item's name following the prefix
BODYnnn_For example, to test whether values for Jupiter's radii have been loaded, the test
FOUND = BODFND ( 599, 'RADII' )could be used. The variable FOUND would be returned as .TRUE. if a PCK file had been loaded containing an assignment of the variable
BODY599_RADII
This section illustrates some typical applications of SPICELIB PCK software.
In this example, we present a small program that solves a realistic science
analysis geometry problem: finding the sub-observer point on an extended body
at a specified time. We will assume that we have an SPK file available that
contains ephemeris data for the observer and target body at the time of
interest.
PROGRAM SUBOBS
C
C Compute the planetocentric latitude and longitude of the
C sub-observer point on an extended target body at a
C specified UTC epoch. The observer may be a spacecraft,
C planet, or any body for which ephemeris data is available
C in an SPK file.
C
C This example uses text PCK kernels. This program could
C be modified to use binary PCK kernels by replacing the
C LDPOOL call with a call to PCKLOF. Both types of PCK
C kernels could be used if a call to PCKLOF were added to
C this program.
C
C
C SPICELIB functions
C
DOUBLE PRECISION DPR
C
C Local parameters
C
INTEGER FILEN
PARAMETER ( FILEN = 128 )
C
C Local variables
C
CHARACTER*(FILEN) LEAP
CHARACTER*(FILEN) PCK
CHARACTER*(FILEN) SPK
CHARACTER*(30) UTC
CHARACTER*(5) CORR
DOUBLE PRECISION ALT
DOUBLE PRECISION DIST
DOUBLE PRECISION EPOCH
DOUBLE PRECISION ET
DOUBLE PRECISION LT
DOUBLE PRECISION OBSPOS ( 3 )
DOUBLE PRECISION RADII ( 3 )
DOUBLE PRECISION STATE ( 6 )
DOUBLE PRECISION SUBLAT
DOUBLE PRECISION SUBLON
DOUBLE PRECISION SUBPT ( 3 )
DOUBLE PRECISION TIPM ( 3, 3 )
INTEGER HANDLE
INTEGER N
INTEGER OBSRVR
INTEGER TARGET
LOGICAL CONT
DATA CONT / .TRUE. /
C
C Start out by prompting for the names of kernel files.
C Load each kernel as the name is supplied.
C
WRITE (*,*) ' '
WRITE (*,*) 'Enter name of SPK file'
READ (*,FMT='(A)') SPK
CALL SPKLEF ( SPK, HANDLE )
WRITE (*,*) 'Enter name of leapseconds kernel'
READ (*,FMT='(A)') LEAP
CALL LDPOOL ( LEAP )
WRITE (*,*) 'Enter name of text P_constants kernel'
READ (*,FMT='(A)') PCK
CALL LDPOOL ( PCK )
DO WHILE ( CONT )
WRITE (*,*) ' '
WRITE (*,*) 'Enter NAIF integer code of target body'
READ *, TARGET
WRITE (*,*) 'Enter NAIF integer code of observer body'
READ *, OBSRVR
WRITE (*,*) 'Enter UTC epoch of observation'
READ (*,FMT='(A)') UTC
WRITE (*,*) 'Enter aberration correction to use:'
WRITE (*,*) 'NONE, LT, or LT+S'
READ (*,FMT='(A)') CORR
C
C Convert the UTC epoch to ET.
C
CALL UTC2ET ( UTC, ET )
C
C Find the state of the target as seen from the observer at
C ET.
C
CALL SPKEZ ( TARGET, ET, 'J2000', CORR, OBSRVR, STATE,
. LT )
C
C The pure mathematical problem embedded in this application
C is finding the nearest point on a triaxial ellipsoid to a
C specified point. The SPICELIB routine NEARPT solves this
C problem. NEARPT deals with an ellipsoid that is centered
C at the origin and whose axes are lined up with the x, y,
C and z coordinate axes. So to use NEARPT, we'll have to
C convert the problem at hand into a form that NEARPT can
C accept.
C
C The way to do this is to convert all of our vectors into
C body equator and prime meridian coordinates. The body
C equator and prime meridian system is one in which the
C coordinate axes are lined up with the body's geometric
C axes (there may be a few exceptions to the rule--check the
C PCK file to be sure about the body you're working with).
C
C
C Find the epoch for which the inertial to body equator and
C prime meridian transformation should be computed.
C
IF ( CORR .EQ. 'NONE' ) THEN
EPOCH = ET
ELSE
EPOCH = ET - LT
END IF
C
C Find the transformation from inertial to body equator and
C prime meridian coordinates at the appropriate epoch.
C
CALL TIPBOD ( 'J2000', TARGET, EPOCH, TIPM )
C
C Negate the observer-target vector and rotate the result
C into body-fixed coordinates.
C
CALL VMINUS ( STATE, OBSPOS )
CALL MXV ( TIPM, OBSPOS, OBSPOS )
C
C Look up the radii of the target body from the PCK file.
C
CALL BODVAR ( TARGET, 'RADII', N, RADII )
C
C Find the nearest point on the body to the observer.
C
CALL NEARPT ( OBSPOS, RADII(1), RADII(2), RADII(3),
. SUBPT, ALT )
C
C Find the latitude and longitude of the sub-observer point.
C
CALL RECLAT ( SUBPT, DIST, SUBLON, SUBLAT )
C
C Write out the results, converting radians to degrees.
C
WRITE(*,*) ' '
WRITE(*,*) 'Sub-observer longitude (deg) ', DPR() * SUBLON
WRITE(*,*) 'Sub-observer latitude (deg) ', DPR() * SUBLAT
WRITE(*,*) ' '
WRITE (*,*) 'Do you wish to continue? (T/F)'
READ *, CONT
END DO
END
Occasionally, it may be useful to transform a state vector into body-fixed
coordinates. To perform the transformation correctly, it is necessary to take
into account the time derivative of the inertial-to-body-fixed coordinate
transformation. A discussion of the error made by ignoring this derivative
term is given in [214].
The following code fragment shows how to use the SPICELIB routine TISBOD to transform state vectors into body-fixed coordinates.
In the following code fragment, TISBOD is used to transform a state in J2000 inertial coordinates to a state in body-fixed coordinates.
The 6-vector STATE represents the inertial state (position and velocity) of an object with respect to the center of the body at time et. The matrix TSIPM is declared as a 6x6 double-precision matrix.
This program loads both a text and a binary PCK file. The question of from which file is the data retieved is answered by the coverage of the files. If a particular requested time and body is covered by the loaded binary file, the binary data will be used. If not, the text data will be used.
For example, say the binary file covers body 301 from 1985 through 1995. It the 'ORIENT_BODY.PCK' file has body 301 during this time period, that data will be used. Otherwise the program will use the data from 'PLANETARY_CONSTANTS.KER.'
C
C First load the kernel pool.
C
CALL LDPOOL ( 'PLANETARY_CONSTANTS.KER' )
C
C We can also load a binary PCK file. The software
C will use values from the binary PCK, if available,
C and the text PCK above, if not.
C
CALL PCKLOF ( 'ORIENT_BODY.PCK', HANDLE )
C
C Next get the inertial to body-fixed transformation
C and its derivative.
C
CALL TISBOD ( 'J2000', BODY, ET, TSIPM )
C
C Convert position and velocity to body-fixed coordinates.
C
CALL MXVG ( TSIPM, STATE, 6, 6, BDSTAT )
We assume that we are creating a new file for this example. In addition, we
will make use of the fictitious subroutine GENREC to generate a type 03 PCK
data record. This is for demonstrative purposes only, and is not intended to
be a complete program.
The following routines will be used in this example:
Variable declarations for the example code fragment.
CHARACTER*(128) FILE CHARACTER*(60) IFNAME CHARACTER*(32) FRAME CHARACTER*(40) SEGID DOUBLE PRECISION ET DOUBLE PRECISION ETSTRT DOUBLE PRECISION ETSTOP DOUBLE PRECISION RECORD(*) DOUBLE PRECISION STEP INTEGER BODY INTEGER CHBDEG INTEGER HANDLE
C THIS IS A CODE FRAGMENT, NOT A PROGRAM!
C
C Assign the name of the file to be created.
C
FILE = 'new_pck.bpc'
C
C Assign an internal filename for the file.
C
IFNAME = 'THIS IS A NEW PCK FILE'
C
C Open the PCK file.
C
CALL PCKOPN ( FILE, IFNAME, 0, HANDLE )
C
C Set the identifier for the segment. This is a character
C string of at most 40 printing ASCII characters. It may
C be blank.
C
SEGID = 'This is a test. This is only a test.'
C
C Set the body for the PCK segment. We will use the the
C Moon, ID code 301.
C
BODY = 301
C
C We will be using the J2000 reference frame for the segment.
C
FRAME = 'J2000'
C
C Set the degree of the Chebyshev polynomials used for the
C segment.
C
CHBDEG = 10
C
C Begin the PCK segment.
C
CALL PCK03B ( HANDLE, SEGID, BODY, FRAME,
. ETSTRT, ETSTOP, CHBDEG )
C
C We have a start time and a stop time available, ETSTRT
C and ETSTOP, and we want to generate records for
C sub-intervals of the interva (ETSTRT, ETSTOP). For
C simplicity, we will assume equal width intervals and
C that (ETSTOP-ETSTRT)/STEP is a positive integer. The
C times are in ET, ephemeris seconds past J2000.
C
C The time step will be one day, 86400 seconds.
C
STEP = 86400.0D0
C
C Set the initial time.
C
ET = ETSTRT
C
C Loop until we have processed all of the time intervals,
c i.e., when ET >= ETSTOP.
C
DO WHILE ( ET .LT. ETSTOP )
C
C Get a type 03 PCK record for the interval ET, ET+STEP
C
CALL GETREC ( ET, ET+STEP, RECORD )
C
C Add the record to the segment.
C
CALL PCK03A ( HANDLE, 1, RECORD, ET )
C
C Increment the time interval.
C
ET = ET + STEP
END DO
C
C End the segment.
C
CALL PCK03E ( HANDLE )
C
C Close the PCK file.
C
CALL PCKCLS ( HANDLE )
Loading files:
LDPOOL ( FILE ) for text PCK kernels PCKLOF ( FILE, HANDLE ) for binary PCK kernelsUnloading binary PCK files:
PCKUOF ( HANDLE ) for binary PCK kernelsSearching binary PCK files for appropriate information:
PCKSFS ( BODY, TIME, HANDLE, DESCR, IDENT, FOUND )Testing for the presence of variables in the text kernel pool:
BODFND ( BODY, ITEM )Obtaining values associated with variables from the text kernel pool:
BODVAR ( NAME, BODY, N, VALUES ) RTPOOL ( NAME, N, VALUES, FOUND )Obtaining Euler angles and their derivatives from a binary PCK file:
PCKEUL ( BODY, ET, FOUND, REF, EULANG )Obtaining inertial-to-body-fixed coordinate transformation matrices:
TIPBOD ( REF, BODY, ET, TIPM ) BODMAT ( BODY, ET, TIPM )Obtaining Euler angles defining inertial-to-body-fixed coordinate transformations:
Obtaining inertial-to-body-fixed state transformation matrices:
TISBOD ( REF, BODY, ET, TSIPM )Opening a binary PCK file for writing:
PCKOPN ( NAME, IFNAME, NCOMCH, HANDLE )Writing type 2 segment to a binary PCK file:
PCKW02 ( HANDLE, BODY, FRAME, FIRST, LAST, SEGID, INTLEN,
N, POLYDG, CDATA, BTIME )
Writing type 3 segment to a binary PCK file:
To begin a type 3 segment: PCK03B ( HANDLE, SEGID, BODY, FRAME, FIRST, LAST, CHBDEG ) To add data to a type 3 sgement: PCK03A ( HANDLE, NRECS, RECRDS, EPOCHS ) To end a type 3 segment: PCK03E ( HANDLE )Close a binary PCK file after writing:
PCKCLS ( HANDLE )Reading a type 2 segment from a binary PCK file:
PCKE02 ( ET, RECORD, EULANG )Evaluating a type 2 segment from a binary PCK file:
PCKE02 ( ET, RECORD, EULANG )Reading a type 3 segment from a binary PCK file:
PCKR03 ( HANDLE, DESCR, ET, RECORD )Evaluating a type 3 segment from a binary PCK file:
PCKE03 ( ET, RECORD, ROTMAT )
The file shown here is an example of a text PCK file. This file is intended
only for use as an example; it should not be used as a source of data.
The label set shown here is (as the comments in the PCK file indicate) a draft set. The label set is shown to complete the qualitative description of the PCK format; PCKs produced by NAIF will contain label sets, but the form and contents of those sets will differ from that of the label set shown below.
\beginlabel
; ***********DRAFT**DRAFT**DRAFT**DRAFT**DRAFT*****************
; This is a draft and incomplete prototype label set, for
; discussion.
; Do NOT write any code using this information or assuming the
; structure used here.
; PDS Labels
PDS_VERSION_ID = PDS3
RECORD_TYPE = STREAM
RECORD_BYTES = n/a
^SPICE_KERNEL = "value"
MISSION_NAME = GALILEO
SPACECRAFT_NAME = GALILEO_ORBITER
DATA_SET_ID = "value"
KERNEL_TYPE_ID = PCK
PRODUCT_ID = "value"
ORIGINAL_FILE_NAME = "value"
PRODUCT_CREATION_TIME = 1994-03-30T16:45:00
PRODUCER_ID = PDS_NAIF
MISSION_PHASE_NAME = value
MISSION_PHASE_TYPE = value
PRODUCT_VERSION_TYPE = value
PRODUCT_VERSION_ID = value
HARDWARE_MODEL_ID = "value"
SOFTWARE_VERSION_ID = "value"
PLATFORM_OR_MOUNTING_NAME = n/a
FLIGHT_SEQUENCE_NAME = "value"
START_TIME = n/a
STOP_TIME = n/a
SPACECRAFT_CLOCK_START_COUNT = n/a
SPACECRAFT_CLOCK_STOP_COUNT = n/a
TARGET_NAME = n/a
INSTRUMENT_NAME = n/a
INSTRUMENT_ID = n/a
SOURCE_PRODUCT_ID = "value"
NOTE = "value"
OBJECT = SPICE_KERNEL
INTERCHANGE_FORMAT = ASCII
KERNEL_TYPE = TARGET_CONSTANTS
DESCRIPTION = 1991 IAU cartgraphic values
END_OBJECT = SPICE_KERNEL
END
; end PDS Labels
\endlabel
P_constants (PcK) SPICE kernel file
===================================================================
Update by: Karen Zukor (NAIF) 1994 March 30
First draft of a PCK with internal labels included.
NOTE: some of the label keywords, values, syntax and overall
organization are likely to change. Do not write any code that
uses the above labels.
Organization
--------------------------------------------------------
The sections of this file are as follows.
Introductory Information:
-- Version description
-- Disclaimer
-- Sources
-- Explanation of the PcK contents
-- Body numbers and names
Pck Data:
-- Orientation constants for the Sun and planets
-- Orientation constants for satellites
-- Radii for all bodies
Version description
--------------------------------------------------------
This is a prototype PcK, for use in SPICE training and
constants evaluation only.
This file is based on the 1991 IAU report,
NAIF document [306].
Disclaimer
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This constants file may not contain the parameter values that
you prefer. Note that this file may be readily modified by
you or anyone else. NAIF suggests that you inspect this file
visually before proceeding with any critical or extended data
processing.
NAIF requests that you update the `by line' and date if
you modify the file.
Sources
--------------------------------------------------------
The sources for the constants listed in this file are:
1. ``Report of the IAU/IAG/COSPAR Working Group on
Cartographic Coordinates and Rotational Elements of
the Planets and Satellites: 1991,'' March 3, 1992.
2. ``The Astronomical Almanac,'' 1990.
3. ``Planetary Geodetic Control Using Satellite
Imaging,'' Journal of Geophysical Research, Vol. 84,
No. B3, March 10, 1979, by Thomas C. Duxbury. This
paper is cataloged as NAIF document 190.0.
4. Letter from Thomas C. Duxbury to Dr. Ephraim
Lazeryevich Akim, Keldish Institute of Applied
Mathematics, USSR Academy of Sciences, Moscow,
USSR. This letter is catalogued as NAIF document
number 195.0.
5. Mars Observer Planetary Constants and Models,
November 1990, Mars Observer Document No. 642-321,
JPL Document No. D-3444.
Most values are from [1], and these are generally taken from
[1]. All exceptions are commented where they occur in this
file. The exceptions are:
-- The second nutation precession angle (M2) for Mars is
represented by a quadratic polynomial in the 1991
IAU report. The SPICE subroutine BODEUL can not
handle this term (which is extremely small), so we
truncate the polynomial to a linear one.
-- The expression for the prime meridian of Deimos (
body 402 ) includes a cosine term, which BODEUL
doesn't yet handle. The amplitude of the term is
0.19 degrees. We simply ignore this term.
Body numbers and names
(Contains only information pertinent to Mars Observer)
----------------------------------------------------------
Barycenters:
3 Earth barycenter
4 Mars barycenter
While not relevant to the P_constants kernel, we note here
for completeness that 0 is used to represent the solar
system barycenter.
Mass centers:
399 Earth
401 Phobos
402 Deimos
499 Mars
10 Sun
Orientation constants for the Sun and planets
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Sun
\begindata
BODY10_POLE_RA = ( 286.13 0. 0. )
BODY10_POLE_DEC = ( 63.87 0. 0. )
BODY10_PM = ( 84.10 +14.18440 0. )
BODY10_LONG_AXIS = ( 0. )
\begintext
Earth
\begindata
BODY399_POLE_RA = ( 0. -0.641 0. )
BODY399_POLE_DEC = ( +90. -0.557 0. )
BODY399_PM = ( 190.16 +360.9856235 0. )
BODY399_LONG_AXIS = ( 0. )
\begintext
The linear terms before and after scaling:
-.052992 --> -1935.5328
-.105984 --> -3871.0656
-13.012 --> -475263.3
13.340716 --> +487269.6519
-.9856 --> -35999.04
\begindata
BODY3_NUT_PREC_ANGLES = ( 125.045 -1935.5328
250.090 -3871.0656
260.008 475263.3
176.625 487269.6519
357.529 35999.04 )
\begintext
Mars
\begindata
BODY499_POLE_RA = ( 317.681 -0.108 0. )
BODY499_POLE_DEC = ( +52.886 -0.061 0. )
BODY499_PM = ( 176.868 +350.8919830 0. )
\begintext
Source [3] specifies the following value for the lambda_a
term ( BODY4_LONG_AXIS ) for Mars.
This term is the POSITIVE WEST LONGITUDE, measured from the
prime meridian, of the longest axis of the ellipsoid
representing the `mean planet surface', as the article states.
body499_long_axis = ( 110. )
Source [4] specifies the lambda_a value
body499_long_axis = ( 104.9194 )
We list these lambda_a values for completeness. [5] gives
equal values for both equatorial radii, so the lambda_a
offset does not apply.
The 1991 IAU report defines M2, the second nutation
precession angle, by:
2
192.93 + 1128.4096700 d + 8.864 T
We truncate the M2 series to a linear expression.
Again, the linear terms are scaled by 36525.0:
-0.4357640000000000 --> -15916.28010000000
1128.409670000000 --> 41215163.19675000
-1.8151000000000000E-02 --> -662.9652750000000
\begindata
BODY4_NUT_PREC_ANGLES = ( 169.51 -15916.2801
192.93 +41215163.19675
53.47 -662.965275 )
\begintext
Orientation constants for the satellites
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Satellites of Mars
Phobos:
The quadratic prime meridian term is scaled by 1/36525**2:
8.864000000000000 ---> 6.6443009930565219E-09
\begindata
BODY401_POLE_RA = (317.68 -0.108 0. )
BODY401_POLE_DEC = (+52.90 -0.061 0. )
BODY401_PM = ( 35.06 +1128.8445850 8.864 )
BODY401_LONG_AXIS = ( 0. )
BODY401_NUT_PREC_RA = ( +1.79 0. 0. )
BODY401_NUT_PREC_DEC = ( -1.08 0. 0. )
BODY401_NUT_PREC_PM = ( -1.42 -0.78 0. )
\begintext
Deimos:
There's a new wrinkle in the Deimos prime meridian
expression, which is:
2
W = 79.41 + 285.1618970 d - 0.520 T - 2.58 sin M
3
+ 0.19 cos M .
3
^
(new wrinkle)
At the present time, the constants kernel software (the
routine bodeul_ in particular) cannot handle the cosine term;
we omit this term for the time being. The maximum error we
can make is 0.19 degrees.
The quadratic prime meridian term is scaled by 1/36525**2:
-0.5200000000000000 ---> -3.8978300049519307E-10
\begindata
BODY402_POLE_RA = (316.65 -0.108 0. )
BODY402_POLE_DEC = (+53.52 -0.061 0. )
BODY402_PM = ( 79.41 +285.1618970 -3.897830D-10 )
BODY402_LONG_AXIS = ( 0. )
BODY402_NUT_PREC_RA = ( 0. 0. +2.98 )
BODY402_NUT_PREC_DEC = ( 0. 0. -1.78 )
BODY402_NUT_PREC_PM = ( 0. 0. -2.58 )
\begintext
Radii of bodies
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Sun
Value for the Sun is from the 1990 Almanac (page K7).
\begindata
BODY10_RADII = ( 696000. 696000. 696000. )
\begintext
Earth
Values for the Earth are unchanged in the 1991 IAU report.
\begindata
BODY399_RADII = ( 6378.140 6378.140 6356.75 )
\begintext
Mars
Current values taken from [5]:
\begindata
BODY499_RADII = ( 3393.4 3393.4 3375.7 )
\begintext
Satellites of Mars
\begindata
BODY401_RADII = ( 13.4 11.2 9.2 )
BODY402_RADII = ( 7.5 6.1 5.2 )