File moon_080317.tf of Package python-skyfield
KPL/FK
SPICE Lunar Reference Frame Specification Kernel
=====================================================================
Original file name: moon_080317.tf
Creation date: 2008 March 17 20:10
Created by: Nat Bachman (NAIF/JPL)
Date of last revision: 2008 March 21 16:07
Purpose of revision:
Changed names of PA system and frame from "principal axis" to
"principal axes."
Version description:
This frame kernel contains lunar frame specifications compatible
with the current lunar binary PCK file
moon_pa_de421_1900-2050.bpc
The above PCK contains lunar orientation data from the DE-421 JPL
Planetary Ephemeris.
The previous NAIF lunar frame specification kernel was
moon_071218.tf
That kernel is compatible with the DE-418-based lunar binary PCK
file
moon_pa_de418_1950-2050.bpc
The comment section below titled "Lunar body-fixed frame
associations" discusses lunar frame association kernels. These
kernels direct portions of the SPICE system that rely on default
body-fixed reference frames to associate with the Moon either the
MOON_ME or MOON_PA reference frames.
This file was modified on 26-FEB-2009 by Nat Bachman. The initial
blank line was removed and this change description was added.
Nothing else has been changed.
Frames Specified by this Kernel
=====================================================================
Frame Name Relative to Type Frame ID
-------------- ----------------- ----- --------
MOON_PA MOON_PA_DE421 FIXED 31000
MOON_ME MOON_ME_DE421 FIXED 31001
MOON_PA_DE421 ICRF/J2000 PCK 31006
MOON_ME_DE421 MOON_PA_DE421 FIXED 31007
Introduction
=====================================================================
This kernel specifies lunar body-fixed reference frames for use by
SPICE-based application software. These reference frames are
associated with high-accuracy lunar orientation data provided by the
JPL Solar System Dynamics Group's planetary ephemerides (both
trajectory and lunar orientation data are stored in these ephemeris
files). These ephemerides have names of the form DE-nnn (DE stands
for "developmental ephemeris").
The frames specified by this kernel are realizations of two different
lunar reference systems:
Principal Axes (PA) system
--------------------------
The axes of this system are defined by the principal axes of the
Moon. Due to the nature of the Moon's orbit and
rotation, the Z axis of this system does not coincide with the
Moon's mean spin axis, nor does the X axis coincide with the mean
direction to the center of the Earth (in contrast with the ME
system defined below).
Lunar principal axes frames realizing the lunar PA system and
specified by this kernel are associated with JPL planetary
ephemerides. Each new JPL planetary ephemeris can (but does not
necessarily) define a new realization of the lunar principal axes
system. Coordinates of lunar surface features expressed in lunar
PA frames can change slightly from one lunar ephemeris version to
the next.
Mean Earth/Polar Axis (ME) system
---------------------------------
The Lunar mean Earth/polar axis system is a lunar body-fixed
reference system used in the IAU/IAG Working Group Report [2] to
describe the orientation of the Moon relative to the ICRF frame.
The +Z axis of this system is aligned with the north mean lunar
rotation axis, while the prime meridian contains the the mean
Earth direction.
This system is also sometimes called the "mean Earth/mean
rotation axis" system or "mean Earth" system.
The mean directions used to define the axes of a mean Earth/polar
axis reference frame realizing the lunar ME system and specified
by this kernel are associated with a given JPL planetary
ephemeris version. The rotation between the mean Earth frame for
a given ephemeris version and the associated principal axes frame
is given by a constant matrix (see [1]).
For the current JPL planetary ephemeris (DE), this kernel includes
specifications of the corresponding principal axes and mean Earth/
polar axis frames. The names of these frames have the form
MOON_PA_DEnnn
and
MOON_ME_DEnnn
respectively, where nnn is the version number of the DE. The set of
DE-dependent frame specifications will grow over time; frame
specifications pertaining to older DEs can be obtained from earlier
versions of this frame kernel.
For each of the two reference systems, there is a corresponding
"generic" frame specification: these generic frames are simply
aliases for the PA and ME frames associated with the latest DE. The
generic frame names are
MOON_PA
MOON_ME
These generic frame names are provided to enable SPICE-based
applications to refer to the latest DE-based (or other) lunar
rotation data without requiring code modifications as new kernels
become available. SPICE users may, if they wish, modify this kernel
to assign these frame aliases to other frames than those selected
here, for example, older DE-based frames. NAIF recommends that, if
this frame kernel is modified, the name of this file also be changed
to avoid confusion.
Comparison of PA and ME frames
------------------------------
The rotation between the mean Earth frame for a given DE and the
associated principal axes frame for the same DE is given by a
constant matrix (see [1]). For DE-421, the rotation angle of this
matrix is approximately 0.0288473 degrees; this is equivalent to
approximately 875 m when expressed as a displacement along a great
circle on the Moon's surface.
Comparison of DE-based and IAU/IAG report-based ME frames
---------------------------------------------------------
Within the SPICE system, a lunar ME frame specified by the
rotational elements from the IAU/IAG Working Group report [2] is
given the name IAU_MOON; the data defining this frame are provided
in a generic text PCK.
The orientation of the lunar ME frame obtained by applying the
DE-based PA-to-ME rotation described above to the DE-based lunar
libration data does not agree closely with the lunar ME frame
orientation given by the rotational elements from the IAU/IAG
Working Group report (that is, the IAU_MOON frame). The difference
is due to truncation of the libration series used in the report's
formula for lunar orientation (see [1]).
In the case of DE-421, for the time period ~2000-2020, the
time-dependent difference of these ME frame implementations has an
amplitude of approximately 0.0051 degrees, which is equivalent to
approximately 155 m, measured along a great circle on the Moon's
surface, while the average value is approximately 0.00249 degrees,
or 76 m.
Comparison of DE-421 and DE-418 Lunar Reference Frames
======================================================
The magnitudes of the rotational offsets between the
DE-418 and DE-421 realizations of the MOON_PA and MOON_ME
frames are discussed below.
Note that the angle ranges shown below are ordered as signed values,
*not* by absolute value.
MOON_PA frame orientation differences
-------------------------------------
Tests performed by NAIF indicate an approximately 0.45 microradian
maximum rotation between the MOON_PA_DE418 and MOON_PA_DE421 frames,
based on a sampling of orientation data over the time period
2000-2020. This offset corresponds to a displacement of about 0.79 m
along a great circle on the Moon's surface.
When the transformation from the MOON_PA_DE418 frame to the
MOON_PA_DE421 frame is decomposed as a 1-2-3 Euler angle sequence,
the offset angle ranges for each axis are:
X axis: -3.8063e-07 to -2.9746e-07 radians
Y axis: -2.5322e-07 to -1.8399e-07 radians
Z axis: -9.9373e-08 to 6.0046e-08 radians
MOON_ME frame orientation differences
-------------------------------------
Tests performed by NAIF indicate an approximately 0.27 microradian
maximum rotation between the MOON_ME_DE418 and MOON_ME_DE421 frames,
based on a sampling of orientation data over the time period
2000-2020. This offset corresponds to a displacement of about 0.46 m
along a great circle on the Moon's surface.
When the transformation from the MOON_ME_DE418 frame to the
MOON_ME_DE421 frame is decomposed as a 1-2-3 Euler angle sequence,
the offset angle ranges for each axis are:
X axis: 7.2260e-09 to 9.0391e-08 radians
Y axis: 3.7643e-08 to 1.0691e-07 radians
Z axis: -2.4471e-07 to -8.5296e-08 radians
Regarding Use of the ICRF in SPICE
==================================
The IERS Celestial Reference Frame (ICRF) is offset from the J2000
reference frame (equivalent to EME 2000) by a small rotation: the
J2000 pole offset magnitude is about 18 milliarcseconds (mas) and
the equinox offset magnitude is approximately 78 milliarcseconds
(see [3]).
Certain SPICE data products use the frame label "J2000" for data
that actually are referenced to the ICRF. This is the case for SPK
files containing JPL version DE-4nn planetary ephemerides, for
orientation data from generic text PCKs, and for binary PCKs,
including binary lunar PCKs used in conjunction with this lunar
frame kernel.
Consequently, when SPICE computes the rotation between the "J2000"
frame and either of the lunar PA or ME frames, what's computed is
actually the rotation between the ICRF and the respective lunar
frame.
Similarly, when SPICE is used to compute the state given by a JPL DE
planetary ephemeris SPK file of one ephemeris object relative to
another (for example, the state of the Moon with respect to the
Earth), expressed relative to the frame "J2000," the state is
actually expressed relative to the ICRF.
Because SPICE is already using the ICRF, users normally need not
use the J2000-to-ICRF transformation to adjust results computed
with SPICE.
Lunar body-fixed frame associations
=====================================================================
By default, the SPICE system considers the body-fixed reference
frame associated with the Moon to be the one named IAU_MOON. This
body-frame association affects the outputs of the SPICE frame system
routines
CIDFRM
CNMFRM
and of the SPICE time conversion and geometry routines
ET2LST
ILLUM
SRFXPT
SUBPT
SUBSOL
Also, any code that calls these routines to obtain results involving
lunar body-fixed frames are affected. Within SPICE, the only
higher-level system that is affected is the dynamic frame system.
NAIF provides "frame association" kernels that simplify changing the
body-fixed frame associated with the Moon. Using FURNSH to load
either of the kernels named below changes the Moon's body-fixed
frame from its current value, which initially is IAU_MOON, to that
shown in the right-hand column:
Kernel name Lunar body-fixed frame
----------- ----------------------
moon_assoc_me.tf MOON_ME
moon_assoc_pa.tf MOON_PA
For further information see the in-line comments in the association
kernels themselves. Also see the Frames Required Reading section
titled "Connecting an Object to its Body-fixed Frame."
In the N0062 SPICE Toolkit, the routines
ILLUM
SRFXPT
SUBPT
SUBSOL
are superseded, respectively, by the routines
ILUMIN
SINCPT
SUBPNT
SUBSLR
The newer routines don't require frame association kernels: the name
of the target body's body-fixed reference frame is an input argument
to these routines.
Using this Kernel
=====================================================================
In order for a SPICE-based application to use reference frames
specified by this kernel, the application must load both this kernel
and a binary lunar PCK containing lunar orientation data for the
time of interest. Normally the kernels need be loaded only once
during program initialization.
SPICE users may find it convenient to use a meta-kernel (also called
a "FURNSH kernel") to name the kernels to be loaded. Below, we show
an example of such a meta-kernel, as well as the source code of a
small Fortran program that uses lunar body fixed frames. The
program's output is included as well.
The kernel names shown here are simply used as examples; users must
select the kernels appropriate for their applications.
Numeric results shown below may differ very slightly from those
obtained on users' computer systems.
Meta-kernel
-----------
KPL/MK
Example meta-kernel showing use of
- binary lunar PCK
- generic lunar frame kernel (FK)
- leapseconds kernel (LSK)
- planetary SPK
17-MAR-2008 (NJB)
Note: to actually use this kernel, replace the @ characters
below with backslashes (\). The backslash character cannot be
used here, within the comments of this frame kernel, because the
begindata and begintext strings would be interpreted as
directives bracketing actual load commands.
This meta-kernel assumes that the referenced kernels exist
in the user's current working directory.
@begindata
KERNELS_TO_LOAD = ( 'moon_pa_de421_1900-2050.bpc'
'moon_080317.tf'
'leapseconds.ker'
'de421.bsp' )
@begintext
Example program
---------------
PROGRAM EX1
IMPLICIT NONE
INTEGER FILSIZ
PARAMETER ( FILSIZ = 255 )
CHARACTER*(FILSIZ) META
DOUBLE PRECISION ET
DOUBLE PRECISION LT
DOUBLE PRECISION STME ( 6 )
DOUBLE PRECISION STPA ( 6 )
C
C Prompt user for meta-kernel name.
C
CALL PROMPT ( 'Enter name of meta-kernel > ', META )
C
C Load lunar PCK, generic lunar frame kernel,
C leapseconds kernel, and planetary ephemeris
C via metakernel.
C
CALL FURNSH ( META )
C
C Convert a time of interest from UTC to ET.
C
CALL STR2ET ( '2008 MAR 17 20:10:00', ET )
WRITE (*,*) 'ET (sec past J2000 TDB): ', ET
WRITE (*,*) ' State of Earth relative to Moon'
C
C Find the geometric state of the Earth relative to the
C Moon at ET, expressed relative to the ME frame.
C
CALL SPKEZR ( 'Earth', ET, 'MOON_ME',
. 'NONE', 'Moon', STME, LT )
WRITE (*,*) ' In MOON_ME frame:'
WRITE (*,*) STME
C
C Find the geometric state of the Earth relative to the
C Moon at ET, expressed relative to the PA frame.
C
CALL SPKEZR ( 'Earth', ET, 'MOON_PA',
. 'NONE', 'Moon', STPA, LT )
WRITE (*,*) ' In MOON_PA frame:'
WRITE (*,*) STPA
END
Program output
--------------
Enter name of meta-kernel > meta
ET (sec past J2000 TDB): 259056665.
State of Earth relative to Moon
In MOON_ME frame:
379892.825 33510.118 -12661.5278 0.0400357582 0.0117963334 0.115130508
In MOON_PA frame:
379908.634 33385.003 -12516.8859 0.0399957879 0.0117833314 0.115145731
References
=====================================================================
[1] J.G. Williams, D.H. Boggs and W.M. Folkner. "DE421 Lunar
Orbit, Physical Librations, and Surface Coordinates,"
preprint of JPL IOM 335-JW,DB,WF-20080314-001, dated
March 14, 2008.
[2] 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.
[3] Roncoli, R. (2005). "Lunar Constants and Models Document,"
JPL D-32296.
Frame Specifications
=====================================================================
MOON_PA is the name of the generic lunar principal axes (PA) reference
frame. This frame is an alias for the principal axes frame defined
by the latest version of the JPL Solar System Dynamics Group's
planetary ephemeris.
In this instance of the lunar reference frames kernel, MOON_PA is an
alias for the lunar principal axes frame associated with the
planetary ephemeris DE-421.
\begindata
FRAME_MOON_PA = 31000
FRAME_31000_NAME = 'MOON_PA'
FRAME_31000_CLASS = 4
FRAME_31000_CLASS_ID = 31000
FRAME_31000_CENTER = 301
TKFRAME_31000_SPEC = 'MATRIX'
TKFRAME_31000_RELATIVE = 'MOON_PA_DE421'
TKFRAME_31000_MATRIX = ( 1 0 0
0 1 0
0 0 1 )
\begintext
MOON_ME is the name of the generic lunar mean Earth/polar axis (ME)
reference frame. This frame is an alias for the mean Earth/polar
axis frame defined by the latest version of the JPL Solar System
Dynamics Group's planetary ephemeris.
In this instance of the lunar reference frames kernel, MOON_ME is an
alias for the lunar mean Earth/polar axis frame associated with the
planetary ephemeris DE-421.
\begindata
FRAME_MOON_ME = 31001
FRAME_31001_NAME = 'MOON_ME'
FRAME_31001_CLASS = 4
FRAME_31001_CLASS_ID = 31001
FRAME_31001_CENTER = 301
TKFRAME_31001_SPEC = 'MATRIX'
TKFRAME_31001_RELATIVE = 'MOON_ME_DE421'
TKFRAME_31001_MATRIX = ( 1 0 0
0 1 0
0 0 1 )
\begintext
MOON_PA_DE421 is the name of the lunar principal axes
reference frame defined by JPL's DE-421 planetary ephemeris.
\begindata
FRAME_MOON_PA_DE421 = 31006
FRAME_31006_NAME = 'MOON_PA_DE421'
FRAME_31006_CLASS = 2
FRAME_31006_CLASS_ID = 31006
FRAME_31006_CENTER = 301
FRAME_MOON_PA_DE403 = 31002
FRAME_31002_NAME = 'MOON_PA_DE403'
FRAME_31002_CLASS = 2
FRAME_31002_CLASS_ID = 31002
FRAME_31002_CENTER = 301
\begintext
MOON_ME_DE421 is the name of the lunar mean Earth/polar
axis reference frame defined by JPL's DE-421 planetary ephemeris.
Rotation angles are from reference [1].
\begindata
FRAME_MOON_ME_DE421 = 31007
FRAME_31007_NAME = 'MOON_ME_DE421'
FRAME_31007_CLASS = 4
FRAME_31007_CLASS_ID = 31007
FRAME_31007_CENTER = 301
TKFRAME_31007_SPEC = 'ANGLES'
TKFRAME_31007_RELATIVE = 'MOON_PA_DE421'
TKFRAME_31007_ANGLES = ( 67.92 78.56 0.30 )
TKFRAME_31007_AXES = ( 3, 2, 1 )
TKFRAME_31007_UNITS = 'ARCSECONDS'
\begintext
Updating this Kernel
--------------------
When a new JPL DE providing lunar rotation data becomes available,
the new lunar PA frame associated with that data set will be named
MOON_PA_DEnnn
where nnn is the version number of the DE.
The PCK body ID code associated with that data set will be
31008
The frame ID and class ID for this frame will also be 31008.
The generic PA frame specification will be updated to point to the
new DE-specific PA frame. The rest of this frame specification
is unchanged.
The ME frame name associated with the new data set will be named
MOON_ME_DEnnn
The frame ID and class ID for this frame will be
31009
The rotational offset between this frame and the new DE-specific PA
frame will need to be updated; this offset is DE-dependent.
The generic ME frame specification will be updated to point to the
new DE-specific ME frame. The rest of this frame specification
is unchanged.
=====================================================================
End of kernel
