Last revised on 2005 JAN 11 by C. H. Acton, N. J. Bachman, B. V.
Semenov.
This document describes how reference frames are treated within SPICE.
The document includes a general discussion of reference frames,
detailed information about various types of frames supported within
SPICE, and instructions on defining additional reference frames to
assist in a user's computations.
This document addresses the needs of several groups of users. Users
looking for a basic discussion of reference frames and a list of the
frames supported by the SPICE system should read the chapter ``Using
Frames.'' Users desiring to customize their environment by adding new
frames should read the chapter ``Creating a Frame Kernel.''
This document assumes you have some familiarity with SPICE concepts and terminology. If you are new to the SPICE system, or just a bit rusty with it, you should consider reviewing ``An Overview of the SPICE System'' and ``An Introduction to SPICE.''
The SPICE frame subsystem facilitates ``behind-the-scenes'' frame
transformations. This allows you to concentrate on questions more
closely related to the problem you are trying to solve instead of the
details of on how to get position or state vectors in the frame of
interest.
Several user-level SPICE routines require that the user supply the name of a reference frame as one of the inputs to the routine. The most important of these is the routine SPKEZR. This routine returns the state (Cartesian position and velocity) of one object relative to another in a user specified reference frame. The choice of reference frame often makes a big difference in the usefulness of a returned state. If the state is given relative to the reference frame of interest to the user, computations involving that state can be much simpler than if the state is returned relative to some other reference frame.
The two user-level interface routines that deal solely with frame transformations are SXFORM and PXFORM. SXFORM supports transformations of Cartesian state vectors (6 components) between reference frames while PXFORM supports transformations of Cartesian position vectors (3 components). PXFORM may be used when only position information is needed , or when the derivatives required for a state transformation are unavailable, for example when one frame is defined by a C-kernel that lacks angular velocity data.
The calling sequences for these routines are
CALL SXFORM ( FROM, TO, ET, XFORM ) CALL PXFORM ( FROM, TO, ET, ROTATE )The output of SXFORM, XFORM, is a 6 by 6 matrix used to transform state vectors relative to a reference frame, the name of which is specified by the FROM input argument, to states relative to another reference frame, the name of which is specified by the TO input argument, at the epoch ET (specified in seconds past J2000).
The output of PXFORM, ROTATE, is a 3 by 3 transformation matrix equivalent to the upper left 3x3 block of XFORM. This matrix transforms position as opposed to state vectors.
In both cases -- with the routines requiring specification of a
reference frame as one of the inputs (for example SPKEZR), and with
the routines computing transformation between two reference frames
(SXFORM and PXFORM) -- you specify the frame or frames of interest
using a character string that contains the name of the reference
frame.
A number of names are automatically recognized by the frame subsystem because the definitions for these frames are ``built into'' SPICE software. Among these frames are:
CALL FURNSH ( 'myframe.tf' )Note that 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.
In many cases data needed to compute transformation of one frame
relative to another is stored in SPICE kernels: PCK, CK, FK, and even
SPK. The appropriate kernels must be loaded for the SPICE system to
compute a frame transformation from a non-inertial frame to any other
frame.
The ``built in'' inertial frames are the only frames the transformations between which can be computed without loading any SPICE kernels.
Since the body-fixed frames are tied to the rotation of planets, satellites, asteroids, etc, the information about how the orientation of these frames is changing with respect to inertial frames is stored in SPICE PCK files. It is important to note that although the names of these frames are ``built in'' their relationship to inertial frames is not. This information must be ``loaded'' into the SPICE system from a PCK file. Without loading this information you cannot compute the transformation to or from a body-fixed frame.
As the name suggests, the orientation of CK-based frames is computed using data provided in CK files and cannot be computed without loading these. In addition to the CKs, an SCLK kernel establishing time correlation for the on-board clock that is used to tag data in the CKs must be loaded to support time time conversion between that clock and ephemeris time.
Because the fixed offset frame definitions stored in text kernels provide all information needed to determine their orientation relative to the frame with respect to which they are defined, only the text kernel containing the definition need be loaded.
Depending on the particular family to which a dynamic frame belongs, no additional data may be needed in order to compute its orientation, or one or more types of SPICE kernels, including SPKs, PCKs, CKs, and SCLK, may have to be loaded.
If you need to create a frame kernel you will need to understand the
concept of a frame class.
The method by which a frame is related to some other frame is a
function of the ``class'' of the frame. You describe the class of a
frame with an integer called the frame's ``class number.'' The
reference frame classes are enumerated below.
In addition to the data/model needed to specify the orientation of a
frame with respect to some other reference frame, you must tell the
SPICE system how to find the data or model. This specification
requires five pieces of information:
Frame Name : 'WALDO' Frame ID code : 1234567 (A number guaranteed to be suitable for private use) Frame Class : 3 (C-kernel) Frame Center : -10001 (Waldo Spacecraft ID code) Frame Class_id: -10000001 (ID code in C-kernel for Waldo)The frame kernel that specifies this frame is given below:
\begindata FRAME_WALDO = 1234567 FRAME_1234567_NAME = 'WALDO' FRAME_1234567_CLASS = 3 FRAME_1234567_CENTER = -10001 FRAME_1234567_CLASS_ID = -10000001 \begintext
The name chosen for a frame must no exceed 26 characters taken from
the set including uppercase letters, numbers, underscore, and plus and
minus signs. It should have some mnemonic value so that users can
recognize what the name means. Finally, it should not be the name of
one of the ``built in'' frames listed above or the name of any other
frame you wish to specify. If you try to use a ``built in'' name, the
frame subsystem will ignore your frame specification. In the example
given above, we chose the name 'WALDO' for the name of our reference
frame. If ``Waldo'' would be a lander and would would need to specify
a local level frame at its landing site, we could have named that
frame 'WALDO_LOCAL_LEVEL'. A good name for for a frame associated with
the camera flown on ``Waldo'' would be 'WALDO_CAMERA'.
What you choose for a frame ID depends upon the class of the frame. If
the class is CK, you may use the same ID as you use for the CLASS_ID.
If the frame is a PCK frame and you are working without consultation
with NAIF, select an integer in the range from 1400000 to 2000000. In
the previous example, we selected the Frame ID to be 1234567. (Since
our example frame is of class 3, a CK frame, we would normally use the
same number for the frame ID as we used for the class ID. However, in
this example, we have chosen a different value to illustrate the
connection between the frame ID and the variables needed to define the
frame.)
For TK frames, the frame and class IDs must be identical. For TK frames associated with an instrument, the instrument ID is used for both frame ID and class ID. For topocentric TK frames at tracking station sites, both frame ID and class ID are created by ``combining'' the ID of the body on which the station is located with the station number (for example frame and class ID 1399012 is used for ``DSS-12'', with the formula used to arrive at this ID being 1000000 + ``Earth ID''*1000 + ``station ID''.) For local level and surface fixed TK frames at a landing site, both frame ID and class ID are based on the ID of the lander (for example frame and class ID of -222999 would be the natural choice for the lander with ID -222.)
This is usually the easiest part of specifying a frame. Presumably you
know how the orientation of the frame with respect to some other frame
will be computed. Simply choose the appropriate class number. In the
example above, the class number is 3 because we are defining a
CK-based frame.
A frame is used to specify the orientation of some object. The frame
consists of a set of coordinate axes relative to some point -- the
origin of the reference frame. When viewed from some other frame the
axes rotate about the origin. The origin about which the rotation
takes place is the center of the frame. For body-fixed frames this is
the center of the body to which they are fixed. For C-kernel frames
the center is often the spacecraft whose orientation is provided by
the C-kernel. Simply find the SPK ID code for the object to which the
frame is attached and use that as the value for the center. In our
example, the SPK ID code for the ``Waldo'' spacecraft is -10001.
Note that this center ID is used to look up the position of the frame origin when SPICE computes frame orientation adjusted for light time. Therefore, only centers for which supporting SPK data are expected to be available should be picked. It is usually an issue only for TK and CK frames associated with instruments because the positions of instruments are rarely available in SPKs. To get around the need to provide the instrument positions, it is appropriate to specify the ID of the spacecraft on which an instrument is mounted as the center of a TK or CK frame associated with it.
A frame's ``CLASS_ID'' is an integer used internally by SPICE
software. It is the integer code used by the SPICE reference frame
subsystem to look up reference frame information.
If your frame is a PCK class frame the CLASS_ID is the ID code for the body described by the PCK file.
If your frame is a CK class frame, the CLASS_ID is the ID code used in the C-kernel to describe the orientation of the spacecraft.
If the frame is a TK frame, the class ID must match the frame ID. For both ID codes you should use a positive integer in the range from 1400000 to 2000000 (unless you are working in an official project capacity in which case you should ask NAIF to provide a CLASS_ID for you). In the example above, the CLASS_ID is the ID code for the C-kernel structure: -10000001.
If the frame is a dynamic frame, the class ID must match the frame ID.
The range 1400000 to 2000000 has been set aside by NAIF as ranges of
Frame IDs that can be used freely by SPICE users without fear of
conflict with ``officially recognized'' frames. However, if you and a
colleague plan to create several such frames, you will need to
coordinate your work to ensure that your definitions are not in
conflict with one another.
When the SPICE software receives a request to compute a frame
transformation, it first translates the name of the frame to the
corresponding frame ID. There is a one to one correspondence between
frame names and frame IDs. Once the frame ID is in hand, the class of
the frame can be located and an appropriate subsystem identified for
carrying out the initial computations needed to construct a frame
transformation matrix. However, the frame subsystem evolved to unify
several distinct reference frame systems. In each of these systems,
reference frames are identified by integer codes. Unfortunately, since
these subsystems evolved independently, the numeric codes used to
identify the reference systems overlapped from one system to the next.
Moreover, to support backward compatibility, NAIF was not free to
change the numeric codes used by the various systems or the meaning of
the frame codes that were already present in existing data products.
To support existing data products and allow extension of the SPICE system, NAIF needed to associate the old ID code with the new frame ID. The CLASS_ID fills this role. When the frame is identified, the ID code suitable for the frame class is located and passed onto the frame's class so that the initial portion of the frame transformation can be carried out.
Once you've determined the name, ID code, center, class and class ID
of your frame, you create the frame specification by filling in the
frame template below. This should be stored in a text kernel called a
Frame Specification Kernel or Frames Kernel (FK).
FRAME_<name> = <ID code> FRAME_<ID code>_NAME = '<name>' FRAME_<ID code>_CLASS = <class> FRAME_<ID code>_CLASS_ID = <classid> FRAME_<ID code>_CENTER = <center>The example we used for the frame 'WALDO' illustrates this.
\begindata FRAME_WALDO = 1234567 FRAME_1234567_NAME = 'WALDO' FRAME_1234567_CLASS = 3 FRAME_1234567_CENTER = -10001 FRAME_1234567_CLASS_ID = -10000001 \begintextOnce you've completed the frame specification you tell the SPICE system about the frame by ``loading'' the frame kernel that contains it. As with all text kernels, you load it via the routine FURNSH. For example if the frame kernel containing your frame specification is contained in the file ``myframe.tf'' you load the kernel via the call
CALL FURNSH ( 'myframe.tf' )
Every extended object has both a position and orientation in space.
The SPICE ephemeris subsystem (SPK) allows you to specify the location
of such an object. The frame subsystem allows you to name the
body-fixed frame that describes the orientation of the object, and to
retrieve the orientation of the frame relative to some other frame as
a function of time. Given the name or SPK ID code associated with an
object we can locate its position through the SPK subsystem.
Unfortunately, the body-fixed frame of the object cannot always be
determined from the object's name or ID code. For example, we have
already mentioned that there are two ``built in'' reference frames
that describe the orientation of the Earth: 'IAU_EARTH' and 'ITRF93'.
For other objects, such as the asteroid Ceres, there is no ``built
in'' frame associated with the object. The body-fixed frame of Ceres
must be defined through a text kernel. In both cases, the connection
between the object and its body-fixed frame needs to be supplied via a
kernel pool variable. There are two ways to do this.
OBJECT_<name or spk_id>_FRAME = '<frame name>'or
OBJECT_<name or spk_id>_FRAME = <frame ID code>You may use the ID codes for either the object, the frame or both. As example, four of the following assignments could serve to connect the Earth with the 'ITRF93' frame.
OBJECT_399_FRAME = 13000 OBJECT_399_FRAME = 'ITRF93' OBJECT_EARTH_FRAME = 13000 OBJECT_EARTH_FRAME = 'ITRF93'Note: if you use the name of either the object or frame, you must use upper case letters.
Of these four means of specifying an object's body-fixed frame the second (OBJECT_399_FRAME = 'ITRF93') is the most robust.
For the sun, the planets and their satellites the frame subsystem maintains a default connection between the object and its body-fixed frame ``built into'' SPICE. The complete list of ``built in'' body-fixed frames is provided in the ``built in PCK-Based IAU Body-Fixed Reference Frames'' appendix of this document.
The information supplied in the frame specification tells the SPICE
system where to look for a particular frame model. However, the
specification alone doesn't tell the SPICE system how to actually
transform from the specified frame to some other frame of interest. To
do this you need to supply other information. How this information is
supplied depends upon the class of the frame.
Inertial frames are ``built into'' the SPICE system via the routine
CHGIRF. Only the frames defined in that routine are available as
inertial class frames. For this reason there is rarely a need to
specify an inertial frame through a frame specification kernel.
Essentially all you can do by creating a frame specification for an
inertial frame is to supply a second name for one of the ``built in''
frames. For example you might define EME2000 as another name for the
J2000 frame.
NAIF recommends against creating inertial frame specifications. However, if you choose to do so anyway, you are done once you've defined the frame specification. (You may not be done explaining to your colleagues why you've decided to do this.)
In the example cited earlier (EME2000) here's how you'd specify the frame.
\begindata FRAME_EME2000 = 2000000 FRAME_2000000_NAME = 'EME2000' FRAME_2000000_CLASS = 1 FRAME_2000000_CENTER = 0 FRAME_2000000_CLASSID = 1 \begintextEverything else about this frame is ``built into'' the SPICE system.
If you specify a PCK frame, you will need to load either a text or
binary PCK file for the body with which the frame is associated. The
construction of PC kernels is discussed in the SPICE document PCK
Required Reading (pck.req.)
If a frame is defined as a CK frame, you will need both a C-kernel for
the structure identified by the FRAME_..._CLASS_ID variable and an
SCLK kernel for converting ephemeris time to the ``ticks'' used to
represent time in the C-kernel. Both the C-kernel(s) and SCLK kernel
must be loaded prior to attempting to use the CK frame.
For many C-kernels, the spacecraft clock and spacecraft ID codes can
be determined by performing an integer division of the C-kernel ID
code by 1000. However, under some circumstances this numerical
correspondence between C-kernel ID code and the associated SCLK or
spacecraft ID may break down. When the numerical relationship fails
you need to tell the SPICE system the ID code of the SCLK or
spacecraft via two kernel pool variables.
CK_<ck_ID code>_SCLK = <ID code of SCLK> CK_<ck_ID code>_SPK = <SPK ID code>These variables are normally placed in either the SCLK kernel or in the frame specification kernel (FK).
To illustrate how you would create a C-kernel frame, we shall suppose that we have a C-kernel for structure -100001 aboard the fictional spacecraft ``Waldo'' which has ID code -1001. Moreover we shall assume that the clock ID appropriate for this structure is -1002. Below is a frame specification together with the CK_..._SCLK and CK_..._SPK variable definitions for the 'WALDO' frame.
\begindata FRAME_WALDO = -100001 FRAME_-100001_NAME = 'WALDO' FRAME_-100001_CLASS = 3 FRAME_-100001_CLASS_ID = -100001 FRAME_-100001_CENTER = -1001 CK_-100001_SCLK = -1002 CK_-100001_SPK = -1001 \begintext
The relationship between a constant offset Text Kernel (TK) frame and
the frame it is offset from is given via a text kernel that can be
loaded via the kernel pool routine FURNSH. The first five kernel pool
variables required for TK frame specification are the same as for any
other frame defined via a text kernel:
FRAME_<name> = <ID code> FRAME_<ID code>_NAME = '<name>' FRAME_<ID code>_CLASS = 4 FRAME_<ID code>_CLASS_ID = <ID code> FRAME_<ID code>_CENTER = <center>You need to supply information that indicates the frame, RELATIVE, from which the TK frame is offset. It is done using this kernel pool variable:
TKFRAME_<frame>_RELATIVE = '<name of relative frame>'where `frame' is the ID code or name you used in the frame specification.
Because the rotation from the TK frame to the RELATIVE frame is fixed (time invariant) it can be specified in the FK along with the frame specification information described above. This rotation data can be provided in any of three ways:
V_relative = M * V_tkframe
TKFRAME_<frame>_SPEC.To use a matrix to define the rotation, use the assignment:
TKFRAME_<frame>_SPEC = 'MATRIX'To define the rotation via three Euler angles, use the assignment:
TKFRAME_<frame>_SPEC = 'ANGLES'To define the rotation via a SPICE-style quaternion, use the assignment:
TKFRAME_<frame>_SPEC = 'QUATERNION'Depending upon the value of the `SPEC' variable, you need to supply one of the following sets of kernel pool variables.
If you've chosen to define the rotation using a matrix, supply the
matrix using the kernel pool variable assignment below:
TFRAME_<frame>_MATRIX = ( matrix_value(1,1), matrix_value(2,1), matrix_value(3,1), matrix_value(1,2), matrix_value(2,2), matrix_value(3,2), matrix_value(1,3), matrix_value(2,3), matrix_value(3,3) )For example, if the matrix defining your TK frame is
0.4 -0.6 0.0 0.6 0.4 0.0 0.0 0.0 1.0and the ID code you've selected for the frame is 1234567, then you would supply the following information in a text kernel.
TKFRAME_1234567_SPEC = 'MATRIX' TKFRAME_1234567_MATRIX = ( 0.4 0.6 0.0 -0.6 0.4 0.0 0.0 0.0 1.0 )
If you've chosen to define a TK frame as a sequence of three Euler
angle rotations about specified coordinate axes, you need to supply
the following pieces of information:
TKFRAME_<frame>_ANGLES = ( angle_1, angle_2, angle_3 ) TKFRAME_<frame>_AXES = ( axis_1, axis_2, axis_3 ) TKFRAME_<frame>_UNITS = 'units_of_angles'The units must be from the list given above. The axes must be chosen from the set of integers 1,2,3 where 1 stands for the x-axis, 2 for the y-axis, and 3 for the z-axis. If M is the matrix that converts vectors relative to the TK frame to the RELATIVE frame by left multiplication, then the angles and axes must satisfy the following relationship:
M = [angle_1] [angle_2] [angle_3] axis_1 axis_2 axis_3where the symbol
[ A ] istands for a rotation by the angle A about the i'th axis.
+- -+ | 1 0 0 | | 0 cos A sin A | = [ A ] | 0 -sin A cos A | 1 +- -+ +- -+ | cos A 0 -sin A | | 0 1 0 | = [ A ] | sin A 0 cos A | 2 +- -+ +- -+ | cos A sin A 0 | | -sin A cos A 0 | = [ A ] | 0 0 1 | 3 +- -+This method of definition is particularly well suited for defining topocentric frames on the surface of the Earth. For example, suppose you have an SPK (ephemeris) file that specifies the location of some surface point on the Earth, and that the SPK ID code of this point is 399100. Moreover suppose you have the geodetic co-latitude (COLAT) and longitude (LONG) measured in degrees for this point. (Note that the co-latitude is the complement of latitude: latitude + co-latitude = 90 degrees.)
Given this information we can easily define a topocentric reference frame at the point such that the x-axis points north along the local meridian, the y-axis points west along the local latitude and the z-axis points up from the reference spheroid.
The transformation from Earth body-fixed frame to topocentric frame is given by
BF2TP = [180] [COLAT] [LONG] 3 2 3Consequently the transformation from the topocentric frame to the body-fixed frame is given by
M = TP2BF = [-LONG] [-COLAT] [180] 3 2 3Let 1234567 be the ID code for the topocentric frame; let the name of this frame be 'MYTOPO'; and define this relative to the IAU frame for the Earth (one of the ``built in'' frames). The topocentric frame at the ephemeris point 399100 is specified as shown below:
\begindata FRAME_MYTOPO = 1234567 FRAME_1234567_NAME = 'MYTOPO' FRAME_1234567_CLASS = 4 FRAME_1234567_CLASS_ID = 1234567 FRAME_1234567_CENTER = 399100 TKFRAME_1234567_SPEC = 'ANGLES' TKFRAME_1234567_RELATIVE = 'IAU_EARTH' TKFRAME_1234567_ANGLES = ( <-long>, <-colat>, 180 ) TKFRAME_1234567_AXES = ( 3, 2, 3 ) TKFRAME_1234567_UNITS = 'DEGREES' \begintextAs we'll see a bit later, we can make a more flexible definition for this topocentric frame.
If you've chosen to define a TK frame using a SPICE-style quaternion,
supply the quaternion using the kernel pool variable assignment below:
TKFRAME_<frame>_Q = ( q_0, q_1, q_2, q_3 )where component zero is the so-called ``real'' component of the quaternion (the ``cosine'' component of the quaternion). The last 3 components (components 1 through 3) are the ``axis'' components of the quaternion -- the i, j, and k components respectively of the quaternion. The quaternion must be a unit quaternion.
2 2 2 2 (q_0) + (q_1) + (q_2) + (q_3) = 1A more detailed discussion of quaternions is available in the reference document ``Rotations Required Reading'' (rotation.req), and in a ``Quaternions White Paper'' available from NAIF.
The use of non-inertial frames gives you an easy means of creating
ephemerides for points on the surface of a body such as the Earth,
Moon or Mars. The ephemeris is simply the body-fixed location of the
object relative to a body-fixed frame for the same object. However,
the model used to relate the body-fixed frame to other reference
frames may not be fixed. Indeed, for the Earth there are several
different methods with varying degrees of accuracy that give the
orientation of the Earth with respect to inertial space. Each of these
different realizations may have a different frame ID code. This
ability to ``plug in'' different orientations is one of the strengths
of the SPICE system. However, if you create an ephemeris relative to
one of these specific models, you won't be able to use it unless
you've loaded the correct model. To make the ephemeris usable
regardless of the orientation model you happen to have at your
disposal, you should define the body-fixed ephemeris relative to a TK
frame. Then define the TK frame so that rotation from the TK frame to
the PCK frame is the identity matrix. For example, you can define a
lunar body-fixed frame as shown below.
\begindata FRAME_MOONFIXED = 3010000 FRAME_3010000_NAME = 'MOONFIXED' FRAME_3010000_CLASS = 4 FRAME_3010000_CLASS_ID = 3010000 FRAME_3010000_CENTER = 301 TKFRAME_3010000_SPEC = 'MATRIX' TKFRAME_3010000_RELATIVE = '<name of base frame>' TKFRAME_3010000_MATRIX = ( 1, 0, 0, 0, 1, 0, 0, 0, 1 ) \begintextBy editing this definition you can make the MOONFIXED frame be the IAU MOON frame or some other model if one is available. Or you can create several such definitions and, at run-time, load the file that best fits your current environment.
Using this indirect method of defining the various frames for which more than one orientation model may be available, you can avoid limiting how various kernels can be used.
In SPICE documentation, the term ``dynamic frame'' designates a
time-dependent reference frame defined via a frame kernel.
A ``parameterized dynamic frame'' is a dynamic frame defined by a formula implemented in SPICELIB code and having user-selectable parameters set via a frame kernel. The formula defining a dynamic frame may rely on data from other SPICE kernels, for example state vectors provided by SPK files or rotation matrices from C-kernels or PCK files.
An example of a parameterized dynamic frame is a nadir-pointing reference frame for a spacecraft orbiting a planet, where the spacecraft's nadir direction and velocity vector define the frame. Using a frame kernel, a SPICE user may specify the planet and spacecraft, the relationship between the nadir and velocity vectors and the frame's axes, and a small set of additional parameters required to define the frame.
Currently parameterized dynamic frames are the only type of dynamic frame supported by SPICELIB. Other types of dynamic frames, such as frames defined by complete formulas (as opposed to parameters) provided in frame kernels, may be implemented in future versions of SPICELIB.
Below we'll discuss the various types of supported dynamic frames, how to create frame kernels that define dynamic frames, and dynamic frame implementation considerations. The appendix ``Frame Definition Examples'' contains frame definition templates for a variety of popular dynamic frames.
The ``family'' to which a parameterized dynamic frame belongs
indicates the underlying mathematical formula by which the frame is
defined. Currently there are four parameterized dynamic frame
families:
A lower case letter `x' is used to designate the cross product
operator, as in
C = A x BDouble vertical bars bracketing the name of a vector indicate the norm of the vector:
||A||Throughout this discussion we'll use text enclosed in angle brackets to indicate values to be filled in by the creator of a frame kernel. Examples are:
Token Replacement Value ------------- ----------------------------------------- <vec_ID> 'PRI' or 'SEC' [See discussion of two-vector frames below.] <frame_name> SPICE frame name, .e.g. 'J2000' <frame_ID> Integer frame ID code <observer_ID> NAIF integer ID for the observing body <aberration correction> String indicating aberration correction, e.g.: 'NONE', 'LT', 'XLT', 'LT+S'
All parameterized dynamic frame kernel definitions contain the
assignments shown here:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = <center_ID> FRAME_<frame_ID>_RELATIVE = <base_frame_name> FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = <frame_family>These first five of the assignments are common to all SPICE frame definitions; the class code 5 indicates that the frame is dynamic. See the section ``Guidelines for Frame Specification'' in the chapter ``Creating a Frame Kernel'' above for a detailed discussion of these assignments.
The sixth assignment (for keyword FRAME_<frame_ID>_RELATIVE) is the ``base frame'' specification; this indicates the frame the transformation defined by the frame kernel ``maps to'': starting with an epoch ET and a state vector S specified relative to the defined frame
<frame name>the frame definition determines the 6x6 state transformation matrix XFORM such that the product
XFORM * Syields the equivalent state specified relative to the base frame at ET.
The seventh assignment (for keyword FRAME_<frame_ID>_DEF_STYLE) is used to simplify future implementation of other dynamic frame definition styles. Only the value
'PARAMETERIZED'is currently supported.
The last assignment indicates the frame family. The possible values are
'TWO_VECTOR' 'MEAN_EQUATOR_AND_EQUINOX_OF_DATE' 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE' 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DATE' 'EULER'Additional, required frame kernel assignments are a function of the family to which a dynamic frame belongs. These are discussed below.
A parameterized dynamic frame definition can specify a frame's
``rotation state'' as ``rotating'' or ``inertial.'' Rotating frames
are nominally time-dependent, although it is possible for them to be
constant (an Euler frame with all Euler angles constant is an
example).
When a parameterized dynamic frame is specified as ``inertial,'' the derivative with respect to time of the transformation between the frame and any inertial frame, for example the J2000 frame, is zero. The rotation between the frame and any inertial frame is still treated as time-dependent. For such a frame F, the call
CALL SXFORM ( 'F', 'J2000', T, XFORM )yields a 6x6 state transformation matrix `xform' having the structure
+-----+-----+ | R(t)| 0 | +-----+-----+ | 0 | R(t)| +-----+-----+where R(t) is the 3x3 rotation matrix that transforms vectors from frame F to the J2000 frame at time `t'. By contrast, when the rotation state of F is ``rotating,'' `xform' has the structure
+-----+-----+ | R(t)| 0 | +-----+-----+ |dR/dt| R(t)| +-----+-----+So, when the rotation state of frame F is ``inertial,'' velocities are transformed from frame F to J2000 by left-multiplication by R(t); the time derivative of the rotation from F to J2000 is simply ignored.
Normally the inertial rotation state makes sense only for slowly rotating frames such as the earth mean equator and equinox of date frame.
A parameterized dynamic frame's rotation state is specified via the assignment
FRAME_<frame_ID>_ROTATION_STATE = <state>where
<state>is one of
'ROTATING' 'INERTIAL'For frames belonging to the parameterized dynamic frame families
'MEAN_EQUATOR_AND_EQUINOX_OF_DATE' 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE' 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DATE'either the rotation state must be specified, or the frame must be frozen (see ``Frozen Frames'' below).
For two-vector and Euler frames, the rotation state specification is optional; these frames are considered to be rotating by default.
When the rotation state of a parameterized frame is specified, the frame cannot be frozen; these options are mutually exclusive.
A parameterized dynamic frame definition can specify a frame as
``frozen'' at a particular epoch. The rotation between a frozen frame
and its base frame is constant; the derivative with respect to time of
this rotation is zero.
A frozen frame whose base frame is time-varying is still time-varying: it is the relationship between the frozen frame and the base frame that is time-independent.
A frame is declared frozen by specifying a ``freeze epoch.'' This is done via the assignment:
FRAME_<frame_ID>_FREEZE_EPOCH = <time_spec>where
<time_spec>is a TDB calendar date whose format conforms to the SPICE text kernel date format specification. These dates
@
@YYYY-MON-DD/HR:MN.SEC.###Literal examples include
@7-MAR-2005 @March-7-2005-3:10:39.221 @2005-MAR-07/3:10:39.221Note that unlike time strings supported by the SPICELIB routine STR2ET, time system tokens such as
UTC TDT TDBare not supported; times are always assumed to be TDB.
For frames belonging to the parameterized dynamic frame families
'MEAN_EQUATOR_AND_EQUINOX_OF_DATE' 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE' 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DATE'either the frame must be frozen or the rotation state must be specified, (see ``Rotation State'' above).
For two-vector and Euler frames, the freeze epoch specification is optional; these frames are considered to be time-varying relative to their base frames by default.
When a parameterized frame is frozen, the rotation state of the frame cannot be specified; these options are mutually exclusive.
Two-vector frames use two user-specified, non-parallel vectors to
define the mutually orthogonal axes of a right-handed reference frame.
In a two-vector frame definition, one defining vector is parallel to a specified axis of the reference frame; this vector is called the ``primary vector.'' The other vector, called the ``secondary vector,'' defines another axis: the component of the secondary vector orthogonal to the primary vector is parallel to a specified axis of the reference frame. The secondary vector itself need not be, and typically is not, aligned with an axis of the defined frame.
Below, we'll call the primary and secondary defining vectors PRI and SEC, and we'll name the axes of the right-handed frame X, Y, and Z. The unit +Z vector is the cross product of the unit +X and +Y vector.
In a two-vector frame definition, the vectors PRI and SEC are specified geometrically; for example, PRI could be the position of the earth relative to a spacecraft, and SEC could be defined by the right ascension and declination of a given star in a specified reference frame.
In a frame kernel, the vectors PRI and SEC are associated with two members of the set of unit vectors
{ X, -X, Y, -Y, Z, -Z }An example: in this case PRI is associated with -Z and SEC is associated with +X. SEC itself is not parallel to the X axis, but the component of SEC orthogonal to PRI points in the +X direction.
The diagram below shows the relationship between PRI, SEC, X, Y, and Z:
Component of SEC orthogonal to PRI | | ^ v | <-----+--+ \ | | \ +--+ \ | SEC \ | +Z = - PRI / ||PRI|| \ | \ | \ +--+ \| | +X = Y x Z <---------+---+--+ / /| +---/ | /| / / |/| / + | -Z = PRI / ||PRI|| / | / | v v PRI Z x SEC +Y = ----------- ||Z x SEC|| = Z x XBy defining PRI and SEC we can create a concrete frame definition. Continuing the above example, we can define a nadir-pointing frame for the Mars Global Surveyor (MGS) spacecraft as follows:
PRI = Vector from MGS to nearest point on Mars reference ellipsoid Z = -PRI / ||PRI|| SEC = Inertially referenced velocity of MGS relative to Mars Y = Z x SEC / ||Z x SEC|| X = Y x ZFor this nadir-pointing frame, -Z is the nadir direction, X points roughly in the direction of the inertially referenced spacecraft velocity, and Y is aligned with the orbital angular velocity vector.
By converting the above definition into the frame kernel ``keyword=value'' format, we can make the definition usable by the SPICE system. Above, for brevity, we've glossed over a few aspects of the vector definitions. Below we'll discuss in detail all of the elements of two-vector frame specifications.
In the following discussion, for brevity, we will use the term
``computable'' to describe frames whose definitions are known to
SPICELIB and for which kernels have been loaded sufficient to enable
computation of the transformations between these frames and their base
frames.
We'll also call a frame transformation between frames F1 and F2 ``computable'' if both frames F1 and F2 are computable and kernels have been loaded sufficient to enable computation of the transformation between F1 and F2. For example, the transformation between the J2000 and IAU_TITAN frames is computable once a PCK containing rotational elements for TITAN has been loaded.
When a two-vector frame F is defined with a base frame F_BASE, and
when the necessary kernels are loaded, the transformation between F
and F_BASE (in both directions) becomes computable by the SPICELIB
frame subsystem. In addition, for any frame F2 such that the
transformation between F2 to F_BASE is computable, the transformation
from F2 to F (in both directions) becomes computable.
For a two-vector frame, the base frame may be any frame F_BASE such that the transformation between F_BASE and the J2000 reference frame is computable at the time the two-vector frame definition is referenced.
Normally for two-vector frames the base frame should be set to 'J2000'; this choice yields optimal run-time efficiency. The assignment is made as follows.
FRAME_<frame_ID>_RELATIVE = 'J2000'Base frame specifications are part of the two-vector frame definition because the base frame can be used to control how SPICELIB chains together two-vector frames with other frames. However, from a mathematical point of view, two-vector frames are fully defined without reference to a base frame. For example, suppose the two-vector frame F1 is defined by the earth-moon position vector and the earth-sun position vector, and the base frame for F1 is IAU_EARTH. Suppose that the two-vector frame F2 is defined by the same vectors and that the base frame of F2 is J2000. Then, ignoring small round-off errors, the transformation between F1 and F2 is the identity transformation.
Base frames should not be confused with other frames occurring in two-vector frame definitions: constant vectors and velocity vectors have associated frames which are also specified by keyword assignments. See the discussion below under the heading ``Constant Vectors'' and ``Velocity Vectors'' for details.
Definitions of two-vector frames include the frame family
specification:
FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR'Further assignments (discussed below) define the primary and secondary vectors and relate these vectors to the frame's axes.
These specifications are optional for two-vector frames. See the
section above titled ``Conditional Keywords for Parameterized Dynamic
Frames'' for details.
This specification applies only to two-vector frames and is optional.
To diagnose near-degenerate geometry, specifically cases where the
defining vectors have angular separation too close to zero or pi
radians, users can specify a limit on these angular separations. This
is done via the keyword assignment
FRAME_<frame_ID>_ANGLE_SEP_TOL = <tolerance>where <tolerance> is the separation limit in radians. If the angular separation of the defining vectors differs from zero or pi radians by less than the specified tolerance, an error will be signaled at run time.
When a two-vector frame definition omits specification of an angular separation tolerance, SPICELIB uses a default value of one milliradian.
The primary defining vector is associated with a frame axis via the
assignment
FRAME_<frame_ID>_PRI_AXIS = <label>Here
<label>may be any of
{ 'X', '-X', 'Y', '-Y', 'Z', '-Z' }Blanks and case in the label are not significant. Unsigned axis designations are treated as positive; optionally '+' signs may be used to prefix positive axis designations. The primary vector is aligned with the indicated axis and has the sense indicated by the implied or explicit sign.
The secondary defining vector is associated with a frame axis via the assignment
FRAME_<frame_ID>_SEC_AXIS = <label>where the axis labels are as above. The assignment means that the component of the secondary vector orthogonal to the primary vector is aligned with the indicated axis and has the sense indicated by the implied or explicit sign.
The vectors used to define a two-vector frame are specified by
geometric means. Each defining vector may be any of:
All keywords comprising the primary vector definition start with the prefix
FRAME_<frame_ID>_PRI_All keywords for the second defining vector are prefixed by
FRAME_<frame_ID>_SEC_Here <frame_ID> is the integer ID code for the frame being defined.
Both the primary and secondary vectors are specified using the sets of keywords described below.
An observer-target position vector is simply the position of one
ephemeris object relative to another. These vectors are defined by an
observer, a target, an aberration correction, a reference frame, and
an epoch. In the frame kernel, there is no need to specify the
reference frame or epoch: the SPICE frame subsystem will determine
which frame to use, and the epoch is supplied by the calling
application at run time.
The observer and target are specified by name or ID code. The aberration correction may be any value accepted by SPKEZR.
The frame kernel assignments used to define an observer-target position vector are:
FRAME_<frame_ID>_<vec_ID>_VECTOR_DEF = 'OBSERVER_TARGET_POSI FRAME_<frame_ID>_<vec_ID>_OBSERVER = <observer name or FRAME_<frame_ID>_<vec_ID>_TARGET = <target name or ID FRAME_<frame_ID>_<vec_ID>_ABCORR = <aberration correcwhere <vec_ID> may be either PRI or SEC, and <frame_ID> is the ID code of the frame established by the generic assignments described above.
In order for a two-vector frame using a position vector as part of its definition to be computable, kernel data must be loaded that enable computation of the specified position vector with respect to the J2000 frame.
For an example of a two-vector frame definition using an observer-target position vector, see the subsection titled ``Geocentric Solar Ecliptic (GSE) Frame'' in the appendix ``Frame Definition Examples.''
Target near point vectors point from an observer to the closest point
on an extended target body to the observer.
Target near point vectors are defined by an observer, a target, an aberration correction, a frame, and an epoch. As with position vectors, the frame and epoch are not specified in the frame kernel.
The observer and target are specified by name or ID code. Aberration corrections may be any supported by the SPICELIB routine SUBPT. Light time corrections are applied both to the observer- target center vector and to the rotation of the target body. The stellar aberration correction, if specified, is applied to the observer-target center vector.
The frame kernel assignments used to define a target near point position vector are:
FRAME_<frame_ID>_<vec_ID>_VECTOR_DEF = 'TARGET_NEAR_POINT' FRAME_<frame_ID>_<vec_ID>_OBSERVER = <observer name or FRAME_<frame_ID>_<vec_ID>_TARGET = <target name or ID FRAME_<frame_ID>_<vec_ID>_ABCORR = <aberration correcIn order for a two-vector frame using a target near point vector as part of its definition to be computable, kernel data must be loaded that enable computation of the target near point vector with respect to the J2000 frame.
For an example of a two-vector frame definition using a target near point vector, see the subsection titled ``Nadir Frame for Mars Orbiting Spacecraft'' in the appendix ``Frame Definition Examples.''
An observer-target velocity vector is the velocity portion of the
state of one ephemeris object relative to another. These vectors are
defined by an observer, a target, an aberration correction, a
reference frame, and an epoch. Of these, only the epoch is not
specified in the frame kernel. Unlike observer-target position
vectors, velocity vectors require a user-supplied frame specification.
The specified frame (we'll call this the ``velocity frame'') will be
used to look up the velocity vector from the SPICE SPK subsystem.
When the velocity frame is non-inertial and aberration corrections are used, the epoch at which the velocity frame is evaluated will be adjusted by the one-way light time between the observer and the frame's center---just as is done by SPKEZR (see the header of that routine for details).
The reason the velocity frame specification is crucial is that, (unlike rotations) state transformations between non-inertial frames don't preserve geometric properties of velocity vectors. Example: compare the specific angular momentum vector of a geosynchronous satellite (obtained by taking the cross product of the satellite's geocentric position and velocity vectors) in both the J2000 frame and in the earth body-fixed frame. In the latter frame, the specific angular momentum is zero. A valid two-vector frame could be defined using the satellite's position and velocity in the J2000 frame, while using the position and velocity in the earth body-fixed frame gives rise to a degenerate case for which the two-vector frame is undefined.
The observer and target defining the velocity vector are specified by name or ID code. The aberration correction may be any value accepted by SPKEZR. The velocity frame may be any computable by SPICE, including a dynamic frame, as long as the transformation between the velocity frame and the J2000 frame doesn't require multiple levels of simulated recursion (see the discussion of recursion in the chapter ``Dynamic Frame Implementation Considerations'' below for details).
The frame kernel assignments used to define an observer-target velocity vector are:
FRAME_<frame_ID>_<vec_ID>_VECTOR_DEF = 'OBSERVER_TARGET_VELO FRAME_<frame_ID>_<vec_ID>_OBSERVER = <observer name or FRAME_<frame_ID>_<vec_ID>_TARGET = <target name or ID FRAME_<frame_ID>_<vec_ID>_FRAME = <frame_name> FRAME_<frame_ID>_<vec_ID>_ABCORR = <aberration correcIn order for a two-vector frame using a velocity vector as part of its definition to be computable, kernel data must be loaded that enable computation of the velocity vector with respect to both the velocity frame and the J2000 frame.
For an example of a two-vector frame definition using an observer-target velocity vector, see the subsection titled ``Geocentric Solar Ecliptic (GSE) Frame'' in the appendix ``Frame Definition Examples.''
Constant vectors are defined by specifying a reference frame and a
vector expressed relative to that frame. Optionally, aberration
corrections may be specified.
The coordinates of a constant vector may be specified in any of the rectangular, latitudinal, or RA/DEC (right ascension and declination) systems. If the coordinates are angular, the associated angular units must be specified; any angular units supported by the SPICELIB routine CONVRT may be used.
All constant vectors require the frame kernel assignments
FRAME_<frame_ID>_<vec_ID>_VECTOR_DEF = 'CONSTANT' FRAME_<frame_ID>_<vec_ID>_SPEC = <coordinate_system FRAME_<frame_ID>_<vec_ID>_FRAME = <frame_name>where <coordinate_system> is one of
'RECTANGULAR' 'LATITUDINAL' 'RA/DEC'and the frame is any computable by SPICE, including a dynamic frame, as long as the transformation between the constant vector's frame and the J2000 frame doesn't require multiple levels of simulated recursion (see the discussion of recursion in the chapter ``Dynamic Frame Implementation Considerations'' below for details).
When the coordinate system is rectangular, the vector is specified by the frame kernel assignment
FRAME_<frame_ID>_<vec_ID>_SPEC = 'RECTANGULAR' FRAME_<frame_ID>_<vec_ID>_VECTOR = ( <X component>, <Y component>, <Z component> )When the coordinate system is latitudinal, the vector is specified by the frame kernel assignments
FRAME_<frame_ID>_<vec_ID>_SPEC = 'LATITUDINAL' FRAME_<frame_ID>_<vec_ID>_UNITS = <angular_units> FRAME_<frame_ID>_<vec_ID>_LONGITUDE = <longitude> FRAME_<frame_ID>_<vec_ID>_LATITUDE = <latitude>where <angular_units> designates one of the units supported by the SPICELIB routine CONVRT. The set of supported units includes
'RADIANS' 'DEGREES' 'ARCSECONDS'When the coordinate system is RA/DEC, the vector is specified by the frame kernel assignments
FRAME_<frame_ID>_<vec_ID>_SPEC = 'RA/DEC' FRAME_<frame_ID>_<vec_ID>_UNITS = <angular_units> FRAME_<frame_ID>_<vec_ID>_RA = <RA> FRAME_<frame_ID>_<vec_ID>_DEC = <DEC>where <angular_units> are as described above.
Aberration corrections are optional for constant vectors. The set of available corrections is unique to this application: either light time correction or stellar aberration correction may be applied, but both cannot be applied together.
Light time corrections adjust the orientation of the constant vector's frame for the one-way light time between the center of the frame and a specified observer. The application to the frame of light time correction is identical to that performed by the SPICELIB routine SPKEZR when it is asked to compute a light-time corrected state relative to a non-inertial reference frame. Supported light time corrections are any of those supported by SPKEZR that don't include stellar aberration correction.
The user may also correct the constant vector for stellar aberration; this correction is a function of the constant vector and the velocity of an observer relative to the solar system barycenter. A typical application would be to correct an inertially referenced star direction vector for the stellar aberration induced by motion of an observing spacecraft. The supported stellar aberration corrections are
'S' {correct for stellar aberration, reception case} 'XS' {correct for stellar aberration, transmission case}In the application above, one would correct the apparent observer-star direction by selecting the 'S' option. See the discussion in the header of the SPICELIB routine SPKEZR for a description of the ``reception'' and ``transmission'' aberration correction cases.
When aberration corrections are desired, the observer and the correction are specified by the frame kernel assignments
FRAME_<frame_ID>_<vec_ID>_OBSERVER = <observer name or I FRAME_<frame_ID>_<vec_ID>_ABCORR = <aberration correctIn order for a two-vector frame using a constant vector as part of its definition to be computable, kernel data must be loaded that enable computation of the specified vector with respect to both the constant vector's frame and the J2000 frame.
For examples of two-vector frame definitions using constant vectors, see the subsections titled ``Geocentric Solar Magnetospheric (GSM) Frame'' and ``Mercury Solar Equatorial (MSEQ) Frame'' in the appendix ``Frame Definition Examples.''
Mean Equator and Equinox of Date Frames are defined for a solar system
body (for example, a planet) using mathematical models of the
orientation of the body's mean equatorial and orbital planes. The term
``mean equator'' indicates that orientation of the equatorial plane is
modeled accounting for precession only. The ``mean equinox'' is the
intersection of the body's mean orbital plane with the mean equatorial
plane. The X-axis of such a frame is aligned with the cross product of
the north-pointing vectors normal to the body's mean equator and mean
orbital plane of date. The Z-axis is aligned with the first of these
normal vectors. The Y axis is the cross product of the Z and X axes.
The resulting reference frame is time-varying; the term ``of date''
means this frame is evaluated at a specified epoch.
The mathematical model for a mean equator and equinox of date frame is typically called a ``precession model''; SPICE adopts this usage.
The SPICE frame subsystem supports mean equator and equinox of date frames via precession models built into SPICELIB. In principle, for any body, a frame kernel definition for a mean equator and equinox of date frame identifies which precession model to use for that body. Currently SPICE supports only one precession model: the 1976 IAU precession model for the earth.
The base frame of a mean equator and equinox of date frame is a
function of the precession model. For the 1976 IAU earth precession
model the base frame is J2000. This association is made via the
assignment:
FRAME_<frame_ID>_RELATIVE = 'J2000'
A mean equator and equinox of date frame is identified by frame family
specification:
FRAME_<frame_ID>_FAMILY = 'MEAN_EQUATOR_AND_EQUINOX_OF_DATE'
The 1976 IAU precession model is ``selected'' via the assignment:
FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976'
Although mean equator and equinox of date frames are, strictly
speaking, non-inertial, their time variation may be very slow. In some
cases it may be desirable to treat them as inertial (specifically,
non-rotating), perhaps in order to simplify computations or to ensure
compatibility with computations from another source.
Users can instruct the SPICELIB frame subsystem to treat a mean equator and equinox of date frame as either inertial or rotating by making a ``rotation state'' assignment. Users can also direct the frame subsystem to treat a mean equator and equinox of date frame as though it were ``frozen'' at a specified epoch. See the section above titled ``Conditional Keywords for Parameterized Dynamic Frames'' for instructions on how to make these assignments.
Definitions of mean equator and equinox of date frames require either, but not both, the rotation state or a freeze epoch to be specified.
For examples of Mean Equator and Equinox of Date frame definitions, see the subsection titled ``Earth Mean Equator and Equinox of Date Frames'' in the appendix ``Frame Definition Examples.''
True Equator and Equinox of Date Frames may be viewed as a refinement
of mean equator and equinox of date frames. The term ``true equator''
indicates that orientation of a body's equatorial plane is modeled
accounting for precession and nutation. The ``true equinox'' is the
intersection of the body's mean orbital plane with the true equatorial
plane. The X-axis of such a frame is aligned with the cross product of
the north-pointing vectors normal to the body's true equator and mean
orbital plane of date. The Z-axis is aligned with the first of these
normal vectors. The Y axis is the cross product of the Z and X axes.
The term ``of date'' means that these axes are evaluated at a
specified epoch.
True Equator and Equinox of date frame definitions are nearly
identical to those for mean of date frames (see above): the only
differences are the frame family specification and the addition of an
assignment identifying the nutation model.
The base frame of a true equator and equinox of date frame is a
function of the precession model. For the 1976 IAU earth precession
model the base frame is J2000. This association is made via the
assignment:
FRAME_<frame_ID>_RELATIVE = 'J2000'
A true equator and equinox of date frame is identified by frame family
specification:
FRAME_<frame_ID>_FAMILY = 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE'
Currently SPICE supports only one precession model: the 1976 IAU
precession model for the earth.
The 1976 IAU precession model is ``selected'' via the assignment:
FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976'
The choice of nutation model is specified by the assignment:
FRAME_<frame_ID>_NUT_MODEL = <nutation_model>Currently the only available nutation model is the 1980 IAU nutation model for the earth. An assignment specifying this model has the form:
FRAME_<frame_ID>_NUT_MODEL = 'EARTH_IAU_1980'
Although true equator and equinox of date frames are, strictly
speaking, non-inertial, their time variation may be very slow. In some
cases it may be desirable to treat them as inertial (specifically,
non-rotating), perhaps in order to simplify computations or to ensure
compatibility with computations from another source.
Users can instruct the SPICELIB frame subsystem to treat a true equator and equinox of date frame as either inertial or rotating by making a ``rotation state'' assignment. Users can also direct the frame subsystem to treat a true equator and equinox of date frame as though it were ``frozen'' at a specified epoch. See the section above titled ``Conditional Keywords for Parameterized Dynamic Frames'' for instructions on how to make these assignments.
Definitions of true equator and equinox of date frames require either, but not both, the rotation state or a freeze epoch to be specified.
For examples of True Equator and Equinox of Date frame definitions, see the subsection titled ``Earth True Equator and Equinox of Date Frames'' in the appendix ``Frame Definition Examples.''
Mean Ecliptic and Equinox of Date Frames are closely related to mean
equator and equinox of date frames: for a given body, the former is
obtained by rotating the latter about the X-axis by the mean obliquity
of date.
The term ``mean equator'' indicates that orientation of a body's equatorial plane is modeled accounting for precession. The ``mean equinox'' is the intersection of the body's mean orbital plane with the mean equatorial plane. The X-axis of such a frame is aligned with the cross product of the north-pointing vectors normal to the body's mean equator and mean orbital plane of date. The Z-axis is aligned with the second of these normal vectors. The Y axis is the cross product of the Z and X axes. The term ``of date'' means that these axes are evaluated at a specified epoch.
Mean Ecliptic and Equinox of date frame definitions are nearly
identical to those for mean of date frames (see above): the only
differences are the frame family specification and the addition of an
assignment identifying the mean obliquity model.
The base frame of a mean ecliptic and equinox of date frame is a
function of the precession model. For the 1976 IAU earth precession
model the base frame is J2000. This association is made via the
assignment:
FRAME_<frame_ID>_RELATIVE = 'J2000'
A mean ecliptic and equinox of date frame is identified by frame
family specification:
FRAME_<frame_ID>_FAMILY = 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DATE'
Currently SPICE supports only one precession model: the 1976 IAU
precession model for the earth.
The 1976 IAU precession model is ``selected'' via the assignment:
FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976'
The choice of mean obliquity model is specified by the assignment:
FRAME_<frame_ID>_OBLIQ_MODEL = <obliquity_model>Currently the only available mean obliquity model is the 1980 IAU obliquity model for the earth. An assignment specifying this model has the form:
FRAME_<frame_ID>_OBLIQ_MODEL = 'EARTH_IAU_1980'
Although mean ecliptic and equinox of date frames are, strictly
speaking, non-inertial, their time variation may be very slow. In some
cases it may be desirable to treat them as inertial (specifically,
non-rotating), perhaps in order to simplify computations or to ensure
compatibility with computations from another source.
Users can instruct the SPICELIB frame subsystem to treat a mean ecliptic and equinox of date frame as either inertial or rotating by making a ``rotation state'' assignment. Users can also direct the frame subsystem to treat a mean ecliptic and equinox of date frame as though it were ``frozen'' at a specified epoch. See the section above titled ``Conditional Keywords for Parameterized Dynamic Frames'' for instructions on how to make these assignments.
Definitions of mean ecliptic and equinox of date frames require either, but not both, the rotation state or a freeze epoch to be specified.
For examples of Mean Ecliptic and Equinox of Date frame definitions, see the subsection titled ``Earth Mean Ecliptic and Equinox of Date Frames'' in the appendix ``Frame Definition Examples.''
An Euler frame is defined by a sequence of rotation axes and
corresponding time-dependent Euler angles. Each angle is defined by a
set of polynomial coefficients. A reference epoch must be provided in
the frame definition; the independent variable of each polynomial
represents ephemeris seconds past the J2000 TDB epoch.
The rotation defined by the Euler angles maps position vectors via left multiplication from the defined Euler reference frame to the base frame:
V = r(t) * V base_frame Euler_frameThis rotation can be considered to be a time-dependent matrix
r(t)where r(t) represents the composition of the rotations defined by the input angle-axis pairs. Naming the axis indices and angles of the Euler angle sequence
axindx_i, angle_i, i = 1, 2, 3r(t) is
r(t) = [ angle_1(t) ] [ angle_2(t) ] [ angle_3(t) ] axindx_1 axindx_2 axindx_3The axis indices axindx_i, for i = 1, 2, 3, are in the set { 1, 2, 3 }; axindx_2 cannot equal axindx_1 or axindx_3. For example, we could have
axindx_1 = 3 axindx_2 = 1 axindx_3 = 3Here the notation
[ A ] jstands for a frame rotation by the angle A radians about the jth axis of a right-handed frame, where we assign the axes {X, Y, Z} the indices {1, 2, 3} respectively:
+- -+ | 1 0 0 | | 0 cos A sin A | = [ A ] | 0 -sin A cos A | 1 +- -+ +- -+ | cos A 0 -sin A | | 0 1 0 | = [ A ] | sin A 0 cos A | 2 +- -+ +- -+ | cos A sin A 0 | | -sin A cos A 0 | = [ A ] | 0 0 1 | 3 +- -+The base frame can be constructed from the Euler frame via a sequence of Euler angle rotations as follows:
The rotation angles are defined as follows: letting t0 represent the reference epoch, and letting
c , i = 1, 2, 3; j = 0, ... , ni i,jbe the polynomial coefficients for the ith angle, we have
n1 angle_1(t) = c + c * (t-t0) + ... + c * (t-t0) 1,0 1,1 1,n1 n2 angle_2(t) = c + c * (t-t0) + ... + c * (t-t0) 2,0 2,1 2,n2 n3 angle_3(t) = c + c * (t-t0) + ... + c * (t-t0) 3,0 3,1 3,n3See the Rotation Required Reading or the header of the SPICELIB routine EUL2M for details concerning definition of rotations via Euler angles. Note however that the referenced document and source code use a different convention for labeling Euler angles and their rotation axes: here the elements of the rotation sequence are numbered left to right; in those documents the order is that in which rotations are performed, namely right to left.
The base frame of an Euler frame specified via the assignment:
FRAME_<frame_ID>_RELATIVE = '<frame_name>'
An Euler frame is identified by frame family specification:
FRAME_<frame_ID>_FAMILY = 'EULER'
The zero epoch for the independent variable of the polynomials is
defined using the SPICE text kernel calendar ephemeris time syntax. A
sample template is shown below:
FRAME_<frame_ID>_EPOCH = @YYYY-MON-DD/HR:MN.SEC.###A concrete example is:
FRAME_<frame_ID>_EPOCH = @2000-JAN-1/12:00:00.000The calendar time string is assumed to represent a TDB epoch.
See the discussion in the section ``Freeze Epoch'' above or the Kernel Required Reading for further information.
Euler angles are specified by an axis sequence, a set of polynomial
coefficients, and associated units. The axes are specified by an
assignment of the form:
FRAME_<frame_ID>_AXES = ( <index of axis 1> <index of axis 2> <index of axis 3> )The axis indices must be taken from the set
{ 1, 2, 3 }and the middle value must differ from its neighbors. The first integer listed is the axis index for angle 1, the second for angle 2, and the last for angle 3, where the role of the angles is as shown in the equation for r(t) above.
Let n1, n2, and n3 represent the maximum degrees of the polynomials for angles 1, 2, and 3 respectively. Then the polynomial coefficients are defined by the assignments
FRAME_<frame_ID>_ANGLE_1_COEFFS = ( <order 0 coefficient> <order 1 coefficient> ... <order n1 coefficient> ) FRAME_<frame_ID>_ANGLE_2_COEFFS = ( <order 0 coefficient> <order 1 coefficient> ... <order n2 coefficient> ) FRAME_<frame_ID>_ANGLE_3_COEFFS = ( <order 0 coefficient> <order 1 coefficient> ... <order n3 coefficient> )Angular units are specified by the frame kernel assignment
FRAME_<frame_ID>_UNITS = <angular_units>where <angular_units> designates one of the units supported by the SPICELIB routine CONVRT. The set of supported units includes
'RADIANS' 'DEGREES' 'ARCSECONDS'For an example of an Euler frame definition, see the subsection titled ``Euler Frames'' in the appendix ``Frame Definition Examples.''
This chapter discusses issues affecting implementation of dynamic
frames:
In the following discussion, we'll use the graph notation below to
indicate that routine A calls routine B:
A -> BA routine R_0 is ``recursive'' if it calls itself
R_0 -> R_0or if some sequence of calls initiated in the routine R_0 results in a call to R_0:
R_0 -> R_1-> ... -> R_0ANSI standard Fortran 77 doesn't permit recursive calls. However, the implementation of two-vector frames requires sequences of calls that at face value are recursive. For example, to look up a state vector in the GSE frame (see the appendix ``Frame Definition Examples''), the routine SPKEZ must initiate the sequence of calls (ellipses indicate omitted portions of the call graph)
SPKEZ -> ... -> FRMGET -> ... -> SPKEZ -> ... -> FRMGEBoth SPKEZ and FRMGET are called recursively in this graph.
This issue affects not only SPICELIB but CSPICE and Icy as well because these products rely on the SPICELIB (Fortran) implementation of the frame subsystem.
SPICELIB solves the recursion problem by providing renamed duplicates
of routines that must be called recursively. For example, the invalid
call graph
SPKEZ -> ... -> FRMGET -> ... -> SPKEZ -> ... -> FRMGEis implemented in (valid) ANSI standard Fortran 77 using the call graph
SPKEZ -> ... -> FRMGET -> ... -> ZZSPKEZ0 -> ... -> ZZTo a limited extent, two levels of simulated recursion are supported in the frame subsystem, so call graphs of the form
SPKEZ -> ... -> FRMGET -> ... -> ZZSPKEZ0 -> ... -& -> ... -> ZZSPKEZ1 -> ... -> ZZFRMGT1are possible.
For brevity, when we refer to recursion in the following discussion, we'll omit the qualifier ``simulated.''
We say a reference frame is ``evaluated'' when the transformation from
the frame to its base frame is computed for some epoch. A
parameterized dynamic frame normally is evaluated each time it is
referenced in a subroutine call. For example, the calls
CALL SPKEZR ( MOON, ET, 'GSE', 'NONE', 'EARTH', STATE, LT ) CALL SXFORM ( 'GSE', 'J2000', ET, XFORM )both cause the GSE parameterized dynamic frame to be evaluated at ET.
When the definition of a parameterized dynamic frame F1 refers to a second frame F2 as
If F2 is not dynamic but its evaluation requires evaluation of a dynamic frame F3, the same restrictions apply to F3.
When a dynamic frame is used as a base frame in either an SPK or CK segment, evaluation of data from that segment may result in a call to the dynamic frame subsystem. That call may result in lookup of another segment whose base frame is dynamic, and so on: the original kernel lookup could easily exhaust the dynamic frame subsystem's ability to handle recursive calls.
Clearly use of dynamic frames in SPK and CK files requires caution. However, there are some ``reasonable'' applications that call for dynamic base frames in kernels, for example: representing ephemerides of earth orbiters expressed relative to the earth true equator and equinox of date frame.
Transformation of state vectors between frames F1 and F2 via a
time-dependent rotation R(t) requires the derivative with respect to
time of R(t): d(R(t))/dt. The accuracy of the velocity portion of a
transformed state is limited by the accuracy of d(R(t))/dt. When
either frame F1 or F2 is dynamic, loss of accuracy in d(R(t))/dt can
occur for a number of reasons, including but not limited to:
Two-vector frame definitions can suffer from singularities: the
defining vectors may, in some cases, become extremely close to
parallel. In such cases the frame evaluation may generate meaningless
results.
Because two-vector frame definitions may be perfectly valid for some epochs and yield degenerate geometry for others, testing can easily fail to reveal problems with these definitions. Careful frame design is the best defense.
As a backup measure, setting the angular separation tolerance in two-vector frame definitions can enable the frame subsystem to diagnose at run time degenerate or near-degenerate geometry. See the section ``Specifying the Angular Separation Tolerance'' above for details.
In many cases, when recursion is required by a frame evaluation, that
evaluation requires a relatively large amount of computation. For
example, when an SPK call results in a two-vector frame evaluation,
several additional SPK calls may be required to support the original
call. The original call may be many times slower than a call requiring
only non-dynamic frame evaluation.
To minimize the performance degradation imposed by recursion, avoid unnecessary references to dynamic frames in frame definitions. When possible, use J2000 or another inertial frame as the base frame, or as the frame relative to which constant or velocity vectors are defined. When it is not possible to use an inertial frame, prefer non-dynamic, non-inertial frames to dynamic frames.
SPICE software includes the definitions of several inertial reference
frames. The numeric IDs and names of the inertial frames defined in
SPICE software are:
ID Name Description ----- -------- ------------------------------------------- 1 J2000 Earth mean equator, dynamical equinox of J2000. The root reference frame for SPICE. 2 B1950 Earth mean equator, dynamical equinox of B1950. The B1950 reference frame is obtained by precessing the J2000 frame backwards from Julian year 2000 to Besselian year 1950, using the 1976 IAU precession model. The rotation from B1950 to J2000 is [ -z ] [ theta ] [ -zeta ] 3 2 3 The values for z, theta, and zeta are taken directly from formulas given in table 5 of [5]. z = 1153.04066200330" theta = -1002.26108439117" zeta = 1152.84248596724" 3 FK4 Fundamental Catalog (4). The FK4 reference frame is derived from the B1950 frame by applying the equinox offset determined by Fricke. [ 0.525" ] 3 4 DE-118 JPL Developmental Ephemeris (118). The DE-118 reference frame is nearly identical to the FK4 frame. It is also derived from the B1950 frame. Only the offset is different [ 0.53155" ] 3 In [2], Standish uses two separate rotations, [ 0.00073" ] P [ 0.5316" ] 3 3 (where P is the precession matrix used above to define the B1950 frame). The major effect of the second rotation is to correct for truncating the magnitude of the first rotation. At his suggestion, we will use the untruncated value, and stick to a single rotation. Most of the other DE historical reference frames are defined relative to either the DE-118 or B1950 frame. The values below are taken from [4]. DE number Offset from DE-118 Offset from B1950 --------- ------------------ ----------------- 96 +0.1209" +0.4107" 102 +0.3956" +0.1359" 108 +0.0541" +0.4775" 111 -0.0564" +0.5880" 114 -0.0213" +0.5529" 122 +0.0000" +0.5316" 125 -0.0438" +0.5754" 130 +0.0069" +0.5247" 5 DE-96 JPL Developmental Ephemeris ( 96). 6 DE-102 JPL Developmental Ephemeris (102). 7 DE-108 JPL Developmental Ephemeris (108). 8 DE-111 JPL Developmental Ephemeris (111). 9 DE-114 JPL Developmental Ephemeris (114). 10 DE-122 JPL Developmental Ephemeris (122). 11 DE-125 JPL Developmental Ephemeris (125). 12 DE-130 JPL Developmental Ephemeris (130). 13 GALACTIC Galactic System II. The Galactic System II reference frame is defined by the following rotations: o o o [ 327 ] [ 62.6 ] [ 282.25 ] 3 1 3 In the absence of better information, we assume the rotations are relative to the FK4 frame. 14 DE-200 JPL Developmental Ephemeris (200). 15 DE-202 JPL Developmental Ephemeris (202). 16 MARSIAU Mars Mean Equator and IAU vector of J2000. The IAU-vector at Mars is the point on the mean equator of Mars where the equator ascends through the earth mean equator. This vector is the cross product of Earth mean north with Mars mean north. 17 ECLIPJ2000 Ecliptic coordinates based upon the J2000 frame. The value for the obliquity of the ecliptic at J2000 is taken from page 114 of [7] equation 3.222-1. This agrees with the expression given in [5]. 18 ECLIPB1950 Ecliptic coordinates based upon the B1950 frame. The value for the obliquity of the ecliptic at B1950 is taken from page 171 of [7]. 19 DE-140 JPL Developmental Ephemeris. (140) The DE-140 frame is the DE-400 frame rotated: 0.9999256765384668 0.0111817701197967 0.0048589521583895 -0.0111817701797229 0.9999374816848701 -0.0000271545195858 -0.0048589520204830 -0.0000271791849815 0.9999881948535965 The DE-400 frame is treated as equivalent to the J2000 frame. 20 DE-142 JPL Developmental Ephemeris. (142) The DE-142 frame is the DE-402 frame rotated: 0.9999256765402605 0.0111817697320531 0.0048589526815484 -0.0111817697907755 0.9999374816892126 -0.0000271547693170 -0.0048589525464121 -0.0000271789392288 0.9999881948510477 The DE-402 frame is treated as equivalent to the J2000 frame. 21 DE-143 JPL Developmental Ephemeris. (143) The DE-143 frame is the DE-403 frame rotated: 0.9999256765435852 0.0111817743077255 0.0048589414674762 -0.0111817743300355 0.9999374816382505 -0.0000271622115251 -0.0048589414161348 -0.0000271713942366 0.9999881949053349 The DE-403 frame is treated as equivalent to the J2000 frame.
[1] Jay Lieske, ``Precession Matrix Based on IAU (1976) System of Astronomical Constants,'' Astron. Astrophys. 73, 282-284 (1979). [2] E.M. Standish, Jr., ``Orientation of the JPL Ephemerides, DE 200/LE 200, to the Dynamical Equinox of J2000,'' Astron. Astrophys. 114, 297-302 (1982). [3] E.M. Standish, Jr., ``Conversion of Ephemeris Coordinates from the B1950 System to the J2000 System,'' JPL IOM 314.6-581, 24 June 1985. [4] E.M. Standish, Jr., ``The Equinox Offsets of the JPL Ephemeris,'' JPL IOM 314.6-929, 26 February 1988. [5] Jay Lieske, ``Expressions for the Precession Quantities Based upon the IAU (1976) System of Astronomical Constants'' Astron. Astrophys. 58, 1-16 (1977). [6] Laura Bass and Robert Cesarone "Mars Observer Planetary Constants and Models" JPL D-3444 November 1990. [7] "Explanatory Supplement to the Astronomical Almanac" edited by P. Kenneth Seidelmann. University Science Books, 20 Edgehill Road, Mill Valley, CA 94941 (1992)
You may obtain the rotation between any two ``built in'' inertial
frames using the SPICE routine IRFROT and supplying the IDs for the
frames of interest. The module header for IRFROT, and this document,
always contain the definitive list of recognized frames.
This example shows how to rotate a position vector from FK4 coordinates to J2000 coordinates (the ID for the FK4 frame is 3, the ID for the J2000 frame is 1);
INTEGER FROM INTEGER TO FROM = 3 TO = 1 CALL IRFROT ( FROM, TO, ROT ) CALL MXV ( ROT, OLD, NEW )(ROT is a 3-by-3 matrix, OLD and NEW are 3-vectors; subroutine MXV multiplies a matrix and a vector to produce a vector.)
Two additional subroutines can be used to convert a frame name to ID and vice versa. This example shows how to find the index of the DE-125 frame:
CALL IRFNUM ( 'DE-125', FRID )This example shows how to find the name corresponding to ID 11:
INTEGER FRAME FRID = 11 CALL IRFNAM ( FRID, FRNAME )
SPICE software includes the definitions of body-fixed frames for all
natural bodies -- planets, satellites, and some asteroids -- listed in
International Astronomical Union (IAU) reports on cartographic
constants. These frames are fixed to and do not move with respect to
``surface'' features of a natural object, but they do move with
respect to inertial frames as the object rotates. The complete list of
body-fixed frames ``built into'' SPICE is given below. Each name is
constructed by adding the prefix ``IAU_'' to the name of the body. The
prefix ``IAU_'' indicates that the orientation of this frame is
typically determined from the IAU model for the body in question. The
constants associated with this model are stored in one or more text
PCK files, which, therefore, must be loaded in order for orientation
of these frames to be computed.
IAU_ADRASTEA IAU_AMALTHEA IAU_ANANKE IAU_ARIEL IAU_ATLAS IAU_BELINDA IAU_BIANCA IAU_CALLIRRHOE IAU_CALLISTO IAU_CALYPSO IAU_CARME IAU_CHALDENE IAU_CHARON IAU_CORDELIA IAU_CRESSIDA IAU_DEIMOS IAU_DESDEMONA IAU_DESPINA IAU_DIONE IAU_EARTH IAU_EARTH_BARYCENTER IAU_ELARA IAU_ENCELADUS IAU_EPIMETHEUS IAU_ERINOME IAU_EROS IAU_EUROPA IAU_GALATEA IAU_GANYMEDE IAU_GASPRA IAU_HARPALYKE IAU_HELENE IAU_HIMALIA IAU_HYPERION IAU_IAPETUS IAU_IDA IAU_IO IAU_IOCASTE IAU_ISONOE IAU_JANUS IAU_JULIET IAU_JUPITER IAU_JUPITER_BARYCENTER IAU_KALYKE IAU_LARISSA IAU_LEDA IAU_LYSITHEA IAU_MAGACLITE IAU_MARS IAU_MARS_BARYCENTER IAU_MERCURY IAU_MERCURY_BARYCENTER IAU_METIS IAU_MIMAS IAU_MIRANDA IAU_MOON IAU_NAIAD IAU_NEPTUNE IAU_NEPTUNE_BARYCENTER IAU_NEREID IAU_OBERON IAU_OPHELIA IAU_PAN IAU_PANDORA IAU_PASIPHAE IAU_PHOBOS IAU_PHOEBE IAU_PLUTO IAU_PLUTO_BARYCENTER IAU_PORTIA IAU_PRAXIDIKE IAU_PROMETHEUS IAU_PROTEUS IAU_PUCK IAU_RHEA IAU_ROSALIND IAU_SATURN IAU_SATURN_BARYCENTER IAU_SINOPE IAU_SUN IAU_TAYGETE IAU_TELESTO IAU_TETHYS IAU_THALASSA IAU_THEBE IAU_THEMISTO IAU_TITAN IAU_TITANIA IAU_TRITON IAU_UMBRIEL IAU_URANUS IAU_URANUS_BARYCENTER IAU_VENUS IAU_VENUS_BARYCENTER
In addition to the text PCK based IAU body-fixed frame for Earth,
'IAU_EARTH', these two body-fixed frames for Earth are also ``built
into'' the SPICE system:
ITRF93 EARTH_FIXED'ITRF93' is a frame ``fixed'' to the Earth's crust. It provides a high precision model for the orientation of the Earth with respect to J2000. In SPICE this is also a PCK type frame but its orientation is provided in a binary PCK file.
'EARTH_FIXED' is a ``generic frame'' that gives the orientation of the Earth with respect to some other frame (usually 'IAU_EARTH' or 'ITRF93') via a constant rotational offset. Such frames are called Text Kernel (TK) frames. See the subsection `` Gaining Flexibility via TK Frames'' for a discussion of the use of TK frames.
NAIF has set aside a range of frame ID codes for Earth fixed frames to
be added in the future when/if additional high precision Earth
orientation model become available and are implemented in SPICE. This
reserved range is from 13000 to 13999. The ID assigned to 'ITRF93',
which is only currently implemented frame of this kind, is 13000. All
of these frames are PCK based frames. They model the orientation of
the Earth with respect to an inertial reference frame such as the
J2000 frame. Since the primary customer of these frames is NASA's Deep
Space Network (DSN), we shall refer to any frame with ID code in this
reserved range as a DSN Earth Fixed frame or simply DSN frame.
The class ID to associate with any DSN frame is the frame ID minus 10000. For example, the class ID associated with frame 13003 is 3003. It is this class ID that should be placed in the PCK file that implements the relationship between the DSN frame and the corresponding inertial frame.
The center of any DSN frame is the center of mass of the Earth, which has SPK ID code 399.
These frames are partially ``built in''. Given a frame ID in the range from 13001 to 13999, the frame subsystem ``knows'' that the frame is a PCK frame, the center of the frame is 399 and the class ID of the frame is the frame ID - 10000. This knowledge cannot be overridden. However, the frame subsystem does not ``know'' the relationship between the names of these frames and their ID codes. The relationship must be specified via the appropriate kernel pool frame definition.
FRAME_<name> = <DSN Frame-ID> FRAME_<DSN Frame-ID>_NAME = '<name>' OBJECT_EARTH_FRAME = <DSN Frame-ID>Note that this specification leaves out the items below
FRAME_<DSN Frame-ID>_CENTER = 399 FRAME_<DSN Frame-ID>_CLASS = 2 FRAME_<DSN Frame-ID>_CLASSID = <DSN Frame-ID - 10000>You may supply these values if you like, but they have no effect on the frame subsystem's recognition and interpretation of the frame with the specified frame ID.
Below are examples that you can modify to create frame specifications
for similar situations.
Inertial frames can be defined only as aliases for the ``built in''
inertial frames. This example defines EME50 to be the same frame as
B1950.
\begindata FRAME_EME50 = 2000000 FRAME_2000000_NAME = 'EME50' FRAME_2000000_CLASS = 1 FRAME_2000000_CLASS_ID = 2 FRAME_2000000_CENTER = 0 \begintext
This definition shows how you create a frame definition for the
asteroid Eros. Note we also define which frame is associated with the
asteroid Eros.
\begindata FRAME_EROS_FIXED = 2000433 FRAME_2000433_NAME = 'EROS_FIXED' FRAME_2000433_CLASS = 2 FRAME_2000433_CLASS_ID = 2000433 FRAME_2000433_CENTER = 2000433 OBJECT_2000433_FRAME = 'EROS_FIXED' \begintext
This definition shows how you create a frame definition for the MGS
spacecraft. Note this frame definition includes the appropriate SCLK
definition as well as which frame to attach to the MGS spacecraft.
\begindata FRAME_MGS_SPACECRAFT = -94000 FRAME_-94000_NAME = 'MGS_SPACECRAFT' FRAME_-94000_CLASS = 3 FRAME_-94000_CLASS_ID = -94000 FRAME_-94000_CENTER = -94 CK_-94000_SCLK = -94 CK_-94000_SPK = -94 OBJECT_-94_FRAME = 'MGS_SPACECRAFT' \begintext
This example shows how you can make up an alias for a frame using a TK
frame. Note we make the reference frame to associate with Mars the
MARS_FIXED frame.
\begindata FRAME_MARS_FIXED = 1400499 FRAME_1400499_NAME = 'MARS_FIXED' FRAME_1400499_CLASS = 4 FRAME_1400499_CLASS_ID = 1400499 FRAME_1400499_CENTER = 499 OBJECT_499_FRAME = 'MARS_FIXED' \begintext To make this point to another frame just replace 'IAU_MARS' below with the name of that frame. \begindata TKFRAME_1400499_RELATIVE = 'IAU_MARS' TKFRAME_1400499_SPEC = 'MATRIX' TKFRAME_1400499_MATRIX = ( 1 0 0 0 1 0 0 0 1 ) \begintext
This example shows how you could create a topographic frame for the
DSN Station DSS-17.
\begindata FRAME_DSS-17_TOPO = 1399017 FRAME_1399017_NAME = 'DSS-17_TOPO' FRAME_1399017_CLASS = 4 FRAME_1399017_CLASS_ID = 1399017 FRAME_1399017_CENTER = 399017 OBJECT_399017_FRAME = 'DSS-17_TOPO' \begintext Note that the geodetic longitude and co-latitude of the DSS-17 tracking station are: 243.126496675 and 54.657822839 respectively. \begindata TKFRAME_DSS-17_TOPO_RELATIVE = 'EARTH_FIXED' TKFRAME_DSS-17_TOPO_SPEC = 'ANGLES' TKFRAME_DSS-17_TOPO_UNITS = 'DEGREES' TKFRAME_DSS-17_TOPO_AXES = ( 3, 2, 3 ) TKFRAME_DSS-17_TOPO_ANGLES = ( -243.126496675, -54.657822839, 180.0 ) \begintext Recall that the frame `EARTH_FIXED' is a TK frame. As a result its relationship to other frames must be specified via a kernel pool variable. We make that specification here. If the ITRF93 PCK kernel is not available we can simply rename the "RELATIVE" frame to be IAU_EARTH and still have the topocentric frame well defined. \begindata TKFRAME_EARTH_FIXED_RELATIVE = 'ITRF93' TKFRAME_EARTH_FIXED_SPEC = 'MATRIX' TKFRAME_EARTH_FIXED_MATRIX = ( 1 0 0 0 1 0 0 0 1 ) \begintext
Definition of the Geocentric Solar Ecliptic frame:
FRAME_GSE = <frame_ID> FRAME_<frame_ID>_NAME = 'GSE' FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR' FRAME_<frame_ID>_PRI_AXIS = 'X' FRAME_<frame_ID>_PRI_VECTOR_DEF = 'OBSERVER_TARGET_POSITION' FRAME_<frame_ID>_PRI_OBSERVER = 'EARTH' FRAME_<frame_ID>_PRI_TARGET = 'SUN' FRAME_<frame_ID>_PRI_ABCORR = 'NONE' FRAME_<frame_ID>_SEC_AXIS = 'Y' FRAME_<frame_ID>_SEC_VECTOR_DEF = 'OBSERVER_TARGET_VELOCITY' FRAME_<frame_ID>_SEC_OBSERVER = 'EARTH' FRAME_<frame_ID>_SEC_TARGET = 'SUN' FRAME_<frame_ID>_SEC_ABCORR = 'NONE' FRAME_<frame_ID>_SEC_FRAME = 'J2000'
Definition of the Geocentric Solar Magnetospheric frame:
FRAME_GSM = <frame_ID> FRAME_<frame_ID>_NAME = 'GSM' FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR' FRAME_<frame_ID>_PRI_AXIS = 'X' FRAME_<frame_ID>_PRI_VECTOR_DEF = 'OBSERVER_TARGET_POSITION' FRAME_<frame_ID>_PRI_OBSERVER = 'EARTH' FRAME_<frame_ID>_PRI_TARGET = 'SUN' FRAME_<frame_ID>_PRI_ABCORR = 'NONE' FRAME_<frame_ID>_SEC_AXIS = 'Z' FRAME_<frame_ID>_SEC_VECTOR_DEF = 'CONSTANT' FRAME_<frame_ID>_SEC_FRAME = 'IAU_EARTH' FRAME_<frame_ID>_SEC_SPEC = 'LATITUDINAL' FRAME_<frame_ID>_SEC_UNITS = 'DEGREES' FRAME_<frame_ID>_SEC_LONGITUDE = 288.43 FRAME_<frame_ID>_SEC_LATITUDE = 79.54
Definition of the Mercury Solar Equatorial Frame:
The MSEQ frame can be defined using the following assignments, where <frame_ID> must be replaced by an integer ID code.
FRAME_MSEQ = <frame_ID> FRAME_<frame_ID>_NAME = 'MSEQ' FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 199 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR' FRAME_<frame_ID>_PRI_AXIS = 'Z' FRAME_<frame_ID>_PRI_VECTOR_DEF = 'CONSTANT' FRAME_<frame_ID>_PRI_FRAME = 'IAU_SUN' FRAME_<frame_ID>_PRI_SPEC = 'RECTANGULAR' FRAME_<frame_ID>_PRI_VECTOR = ( 0, 0, 1 ) FRAME_<frame_ID>_SEC_AXIS = 'X' FRAME_<frame_ID>_SEC_VECTOR_DEF = 'OBSERVER_TARGET_POSITION' FRAME_<frame_ID>_SEC_OBSERVER = 'MERCURY' FRAME_<frame_ID>_SEC_TARGET = 'SUN' FRAME_<frame_ID>_SEC_ABCORR = 'NONE'
Definition of the nadir frame:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = <orbiter_ID> FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR' FRAME_<frame_ID>_PRI_AXIS = 'Z' FRAME_<frame_ID>_PRI_VECTOR_DEF = 'TARGET_NEAR_POINT' FRAME_<frame_ID>_PRI_OBSERVER = <orbiter_ID/name> FRAME_<frame_ID>_PRI_TARGET = 'MARS' FRAME_<frame_ID>_PRI_ABCORR = 'NONE' FRAME_<frame_ID>_SEC_AXIS = '-X' FRAME_<frame_ID>_SEC_VECTOR_DEF = 'OBSERVER_TARGET_VELOCITY' FRAME_<frame_ID>_SEC_OBSERVER = <orbiter_ID/name> FRAME_<frame_ID>_SEC_TARGET = 'MARS' FRAME_<frame_ID>_SEC_ABCORR = 'NONE' FRAME_<frame_ID>_SEC_FRAME = 'J2000'
There are a variety of roll-celestial frames in use. This example may
not match frame definitions used for any specific flight project; it
is intended to demonstrate how to define this category of frame.
Definition of the roll-celestial frame:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = <spacecraft_ID> FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR' FRAME_<frame_ID>_PRI_AXIS = 'Z' FRAME_<frame_ID>_PRI_VECTOR_DEF = 'OBSEVER_TARGET_POSITION' FRAME_<frame_ID>_PRI_OBSERVER = <spacecraft_ID/name> FRAME_<frame_ID>_PRI_TARGET = 'EARTH' FRAME_<frame_ID>_PRI_ABCORR = 'NONE' FRAME_<frame_ID>_SEC_AXIS = 'X' FRAME_<frame_ID>_SEC_VECTOR_DEF = 'CONSTANT' FRAME_<frame_ID>_SEC_FRAME = 'J2000' FRAME_<frame_ID>_SEC_SPEC = 'RA/DEC' FRAME_<frame_ID>_SEC_UNITS = 'DEGREES' FRAME_<frame_ID>_SEC_RA = <star RA in degrees> FRAME_<frame_ID>_SEC_DEC = <star DEC in degrees> FRAME_<frame_ID>_SEC_ABCORR = 'S' FRAME_<frame_ID>_SEC_OBSERVER = <spacecraft_ID/name>
Definition of a non-inertial Earth Mean Equator and Equinox of Date
frame using 1976 IAU precession model. Here <frame_name> must be
replaced by a string containing the name of the frame, and
<frame_ID> must be replaced by an integer ID code:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'MEAN_EQUATOR_AND_EQUINOX_OF_DATE FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_ROTATION_STATE= 'ROTATING'Definition for the inertial version of the above frame:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'MEAN_EQUATOR_AND_EQUINOX_OF_DATE FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_ROTATION_STATE= 'INERTIAL'Definition for the frozen version of the above frame, where the ``freeze epoch'' is B1950 TDB. The resulting frame should match the inertial frame B1950 to round-off level:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'MEAN_EQUATOR_AND_EQUINOX_OF_DATE FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_FREEZE_EPOCH = @1949-DEC-31/22:09:46.861901
Definition of the Earth True Equator and Equinox of Date frame:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_NUT_MODEL = 'EARTH_IAU_1980' FRAME_<frame_ID>_ROTATION_STATE= 'ROTATING'Definition for the inertial version of the above frame:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_NUT_MODEL = 'EARTH_IAU_1980' FRAME_<frame_ID>_ROTATION_STATE= 'INERTIAL'Definition for the frozen version of the above frame, where the ``freeze epoch'' is B1950 TDB.
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_NUT_MODEL = 'EARTH_IAU_1980' FRAME_<frame_ID>_FREEZE_EPOCH = @1949-DEC-31/22:09:46.861901
Definition of the Earth Mean Ecliptic and Equinox of Date frame:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DAT FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_OBLIQ_MODEL = 'EARTH_IAU_1980' FRAME_<frame_ID>_ROTATION_STATE= 'ROTATING'Definition for the inertial version of the above frame:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DAT FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_OBLIQ_MODEL = 'EARTH_IAU_1980' FRAME_<frame_ID>_ROTATION_STATE= 'INERTIAL'Definition for the frozen version of the above frame, where the ``freeze epoch'' is B1950 TDB.
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DAT FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_OBLIQ_MODEL = 'EARTH_IAU_1980' FRAME_<frame_ID>_FREEZE_EPOCH = @1949-DEC-31/22:09:46.861901
As an example, we construct an Euler frame called IAU_MARS_EULER.
Frame IAU_MARS_EULER is mathematically identical to the PCK frame as
IAU_MARS.
The PCK data defining the underlying IAU_MARS frame are:
BODY499_POLE_RA = ( 317.68143 -0.1061 0. ) BODY499_POLE_DEC = ( 52.88650 -0.0609 0. ) BODY499_PM = ( 176.630 350.89198226 0. )These values are from:
Seidelmann, P.K., Abalakin, V.K., Bursa, M., Davies, M.E., Bergh, C. de, Lieske, J.H., Oberst, J., Simon, J.L., Standish, E.M., Stooke, P., and Thomas, P.C. (2002). "Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: 2000," Celestial Mechanics and Dynamical Astronomy, v.82, Issue 1, pp. 83-111.Here pole RA/Dec terms in the PCK are in degrees and degrees/century; the rates here have been converted to degrees/sec. Prime meridian terms in the PCK are in degrees and degrees/day; the rate here has been converted to degrees/sec.
The 3x3 transformation matrix M defined by the angles is
M = [angle_1] [angle_2] [angle_3] 3 1 3Vectors are mapped from the J2000 base frame to the IAU_MARS frame via left multiplication by M.
The relationship of these Euler angles to RA/Dec/PM for the J2000-to-IAU Mars body-fixed transformation is as follows:
angle_1 is PM * (radians/degree) angle_2 is pi/2 - Dec * (radians/degree) angle_3 is pi/2 + RA * (radians/degree), mapped into the range 0 < angle_3 < 2*pi -Since when we define the IAU_MARS_EULER frame we're defining the *inverse* of the above transformation, the angles for our Euler frame definition are reversed and the signs negated:
angle_1 is -pi/2 - RA * (radians/degree), mapped into the range 0 < angle_3 < 2*p - angle_2 is -pi/2 + Dec * (radians/degree) angle_3 is - PM * (radians/degree)Then our frame definition is:
FRAME_IAU_MARS_EULER = <frame_ID> FRAME_<frame_ID>_NAME = 'IAU_MARS_EULER' FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 499 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'EULER' FRAME_<frame_ID>_EPOCH = @2000-JAN-1/12:00:00 FRAME_<frame_ID>_AXES = ( 3 1 3 ) FRAME_<frame_ID>_UNITS = 'DEGREES' FRAME_<frame_ID>_ANGLE_1_COEFFS = ( -47.68143 0.33621061170684714E-10 ) FRAME_<frame_ID>_ANGLE_2_COEFFS = ( -37.1135 -0.19298045478743630E-10 ) FRAME_<frame_ID>_ANGLE_3_COEFFS = ( -176.630 -0.40612497946759260E-02 )