[Spice_discussion] Moon mean equator and equinox of j2000 frame
Nathaniel.Bachman at jpl.nasa.gov
Thu Aug 9 16:23:57 PDT 2007
Aside from the mechanism used to define the lunar reference frame you
describe, there are some basic questions about the frame definition
1) Do you want to use pole and node definitions based on
- the MOON_ME frame
- the MOON_PA frame
- the IAU_MOON frame
- the IAU_MOON frame with trigonometic terms removed
- some other lunar body-fixed frame
I've attached the current SPICE lunar frame kernel; the discussion
in this file describes the differences between the frames named
By the way, a new planetary ephemeris (DE418) has been released by
JPL's Navigation section, and along with this, new rotational
data for the Moon have been released. NAIF will release new
SPICE kernels reflecting these updates shortly. The orientation
of the MOON_PA frame, and possibly that of the MOON_ME frame,
will change with this update.
2) Do you want the inertial frame to remain fixed throughout the mission
lifetime, or do you want to update it? If you want to update
it, do you want it to remain consistent with the underlying
lunar frame on which it's based?
There are a variety of approaches to defining a fixed-offset reference
frame in SPICE. A few logical possibilities are:
1) Obtain the rotation matrix that maps from the desired frame, which I'll
call "F," to to the J2000 frame. Create a frame kernel defining
a "constant offset" (aka "TK") frame using this matrix. Alternately,
use constant Euler angles instead of a rotation matrix. The Frames
Required Reading document in the SPICE Toolkit describes TK frames.
This approach is the best in terms of run-time speed. It has the drawback
that any change to the input data requires the frame kernel to be updated.
2) In this example, for simplicity, we'll select IAU_MOON as the lunar
body-fixed frame. Another lunar frame could be substituted in the discussion
Define the frame as a frozen two-vector dynamic frame: Let the primary
axis be +Z, and define this axis as the vector (0,0,1) of the J2000 frame.
Let the secondary axis be -Y, and associate this axis with the vector
of the IAU_MOON frame (this association means the component of the IAU_MOON
+Z axis orthogonal to the primary axis of F is parallel to the -Y axis
Make the base frame J2000. Set the freeze epoch to 2000 Jan 1 12:00:00 TDB.
This approach is simple in that no computations are involved. Your frame
remain consistent with whatever IAU_MOON frame definition you're using;
you must decide whether that's desirable.
This approach will give you slower run-time performance than approach (1).
There are some restrictions on the more esoteric uses of dynamic
frames, although these are unlikely to affect most applications.
See the SPICE Dynamic Frames tutorial or the Frames Required Reading
for information on two-vector frames. SPICE tutorials are available
on the NAIF web site:
Using the Euler dynamic frame family usually isn't convenient for defining
constant frames; defining a constant frame using constant Euler angles is
best done via a TK frame.
The "of date" dynamic frame family currently can be used only for
frames; SPICE doesn't currently contain any built-in precession or nutation
models for other bodies.
Please feel free to contact me or any of the NAIF team if you have any
-Nat Bachman (JPL/NAIF)
Nathaniel.Bachman at jpl.nasa.gov
Eagle, David C wrote:
> I’m trying to create an inertial frame which we call the moon mean
> equator and equinox of J2000. Essentially, we need the transformation
> performed by the iau_moon transformation but without the effect of the
> motion of the prime meridian (PA and PA rates are zero).
> I have tested the computation by zeroing the PA terms and rates in the
> pck00008.tpc data file. However, we will eventually need both the
> iau_moon and this inertial frame in our trajectory simulations.
> I think this can be done using an Euler frame definition but I’m not
> sure what to do about the PREC_MODEL and NUT_MODEL statements in the
> frame definition. Perhaps these definitions are not needed.
> We have implemented this transformation in Fortran but are attempting
> to “standardize” our scientific simulations using as much of the SPICE
> library as possible.
> C. David Eagle
> Senior Staff Systems Engineer
> Orion Mission Analysis
> Lockheed Martin Space Systems
> david.c.eagle at lmco.com <mailto:david.c.eagle at lmco.com>
> P.O. Box 179 MS W3003
> Denver, CO 80201-0179
> subroutine mm2000 (xjdate, tmatrix)
> c eme2000 to moon mean equator and equinox of j2000
> c input
> c xjdate = julian date
> c output
> c tmatrix = transformation matrix
> c ************************************
> implicit double precision (a-h, o-z)
> dimension phat_moon(3), rmoon(3), vmoon(3)
> dimension xvec(3), xhat(3), yvec(3), yhat(3)
> dimension zhat(3), hv(3), hhat(3), tmatrix(3, 3)
> data dtr /1.745329251994330d-2/
> c time arguments
> t = (xjdate - 2451545.0d0) / 36525.0d0
> d = xjdate - 2451545.0d0
> c iau 2000 pole orientation
> e1 = 125.045d0 - 0.0529921d0 * d
> e2 = 250.089d0 - 0.1059842d0 * d
> e3 = 260.008d0 + 13.0120009d0 * d
> e4 = 176.625d0 + 13.3407154d0 * d
> e5 = 357.529d0 + 0.9856003d0 * d
> e6 = 311.589d0 + 26.4057084d0 * d
> e7 = 134.963d0 + 13.0649930d0 * d
> e8 = 276.617d0 + 0.3287146d0 * d
> e10 = 15.134d0 - 0.1589763d0 * d
> e13 = 25.053d0 + 12.9590088d0 * d
> rasc_pole = 269.9949d0 + 0.0031d0 * t
> & - 3.8787d0 * sin(dtr * e1)
> & - 0.1204d0 * sin(dtr * e2)
> & + 0.0700d0 * sin(dtr * e3)
> & - 0.0172d0 * sin(dtr * e4)
> & + 0.0072d0 * sin(dtr * e6)
> & - 0.0052d0 * sin(dtr * e10)
> & + 0.0043d0 * sin(dtr * e13)
> decl_pole = 66.5392d0 + 0.0130d0 * t
> & + 1.5419d0 * cos(dtr * e1)
> & + 0.0239d0 * cos(dtr * e2)
> & - 0.0278d0 * cos(dtr * e3)
> & + 0.0068d0 * cos(dtr * e4)
> & - 0.0029d0 * cos(dtr * e6)
> & + 0.0009d0 * cos(dtr * e7)
> & + 0.0008d0 * cos(dtr * e10)
> & - 0.0009d0 * cos(dtr * e13)
> c compute the unit vector in the direction of the moon's pole
> phat_moon(1) = cos(rasc_pole * dtr) * cos(decl_pole * dtr)
> phat_moon(2) = sin(rasc_pole * dtr) * cos(decl_pole * dtr)
> phat_moon(3) = sin(decl_pole * dtr)
> zhat(1) = 0.0d0
> zhat(2) = 0.0d0
> zhat(3) = 1.0d0
> c x-direction
> call vcross (zhat, phat_moon, xvec)
> call uvector(xvec, xhat)
> c y-direction
> call vcross (phat_moon, xhat, yvec)
> call uvector(yvec, yhat)
> c load elements of transformation matrix
> tmatrix(1, 1) = xhat(1)
> tmatrix(1, 2) = xhat(2)
> tmatrix(1, 3) = xhat(3)
> tmatrix(2, 1) = yhat(1)
> tmatrix(2, 2) = yhat(2)
> tmatrix(2, 3) = yhat(3)
> tmatrix(3, 1) = phat_moon(1)
> tmatrix(3, 2) = phat_moon(2)
> tmatrix(3, 3) = phat_moon(3)
> Spice_discussion mailing list
> Spice_discussion at naif.jpl.nasa.gov
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SPICE Lunar Reference Frame Specification Kernel
Original file name: moon_060721.tf
Creation date: 2006 July 21 16:52
Revision date: 2007 February 12 03:14
Created by: Nat Bachman (NAIF/JPL)
The comments in this kernel have been updated to refer to the
current lunar binary PCK. Also, this kernel now refers to
the lunar frame association kernels which direct the SPICE
system to associate with the Moon either the MOON_ME or MOON_PA
The data (that is, the "keyword = value" assignments) in this
kernel are unchanged.
Frames Defined by this Kernel
Frame Name Relative to Type Frame ID
-------------- ----------------- ----- --------
MOON_PA MOON_PA_DE403 FIXED 31000
MOON_ME MOON_ME_DE403 FIXED 31001
MOON_PA_DE403 ICRF/J2000 PCK 31002
MOON_ME_DE403 MOON_PA_DE403 FIXED 31003
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
Mean Earth/polar axis (ME) system
The Lunar mean Earth/axis system is a lunar body-fixed reference
system used in the IAU/IAG Working Group Report  to describe
the orientation of the Moon relative to the ICRF frame. The +Z
axis of this system is aligned with the mean lunar north pole,
while the prime meridian contains the the mean Earth direction.
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 ).
For each 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
respectively, where nnn is the version number of the DE. This set of
DE-dependent frame specifications will grow over time; frame
specifications pertaining to older DEs will be retained in later
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
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 data
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
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 ). For DE-403, the rotation angle of this matrix is
approximately 0.028241 degrees; this is equivalent to approximately 860 m
when expressed as a displacement along a great circle on the Moon's
Comparison of DE-based and IAU/IAG report rotation data
Within the SPICE system, the lunar ME frame specified by the
rotational elements from the IAU/IAG Working Group report  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 ).
In the case of DE-403, for the time period ~2000-2020, this
time-dependent difference has an amplitude of approximately 0.005
degrees, which is equivalent to approximately 150 m, measured along
a great circle on the Moon's surface, while the average value is
approximately 0.0025 degrees, or 75 m.
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
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
Consequently, when SPICE computes the rotation between the "J2000"
frame and the either of the lunar PA or ME frames, what's computed
is actually the rotation between the ICRF and the respective
Similarly, when a 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
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
and of the SPICE time conversion and geometry routines
Finally, 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
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 sets the Moon's body-fixed frame
to that shown in the right-hand column:
Kernel name Lunar body-fixed frame
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."
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.
Example meta-kernel showing use of
- binary lunar PCK
- generic lunar frame kernel (FK)
- leapseconds kernel (LSK)
- planetary SPK
Note: to actually use this kernel, replace the @
characters below with backslashes (\). The
backslash character cannot be used here because these
comments would be interpreted as actual load commands.
This meta-kernel assumes that the referenced kernels exist
in the user's current working directory.
KERNELS_TO_LOAD = ( 'moon_pa_de403_1950-2198.bpc'
PARAMETER ( FILSIZ = 255 )
DOUBLE PRECISION ET
DOUBLE PRECISION LT
DOUBLE PRECISION STME ( 6 )
DOUBLE PRECISION STPA ( 6 )
C Prompt user for meta-kernel name.
CALL PROMPT ( 'Enter name of meta-kernel > ', META )
C Load lunar PCK, generic lunar frame kernel,
C leapseconds kernel, and planetary ephemeris
C via metakernel.
CALL FURNSH ( META )
C Convert a time of interest from UTC to ET.
CALL STR2ET ( '2006 jun 8 06:50:00', ET )
WRITE (*,*) 'ET (sec past J2000 TDB): ', ET
WRITE (*,*) ' State of Earth relative to Moon'
C Find the geometric state of the Earth relative to the
C Moon at ET, expressed relative to the ME frame.
CALL SPKEZR ( 'Earth', ET, 'MOON_ME',
. 'NONE', 'Moon', STME, LT )
WRITE (*,*) ' In MOON_ME frame:'
WRITE (*,*) STME
C Find the geometric state of the Earth relative to the
C Moon at ET, expressed relative to the PA frame.
CALL SPKEZR ( 'Earth', ET, 'MOON_PA',
. 'NONE', 'Moon', STPA, LT )
WRITE (*,*) ' In MOON_PA frame:'
WRITE (*,*) STPA
Enter name of meta-kernel > meta
ET (sec past J2000 TDB): 203021465.
State of Earth relative to Moon
In MOON_ME frame:
391739.183 -33210.254 25299.0887 -0.0592286405 -0.048721834 0.0917188552
In MOON_PA frame:
391719.148 -33331.588 25449.2934 -0.0592788895 -0.0487034073 0.0916961762
 A.S. Konopliv, S.W. Asmar, E. Carranza, W.L. Sjogren, and D.N.
Yuan (2001). "Recent Gravity Models as a Result of the Lunar
Prospector Mission," Icarus 150, pp. 1-18.
 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.
 Roncoli, R. (2005). "Lunar Constants and Models Document,"
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
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-403.
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_DE403'
TKFRAME_31000_MATRIX = ( 1 0 0
0 1 0
0 0 1 )
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-403.
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_DE403'
TKFRAME_31001_MATRIX = ( 1 0 0
0 1 0
0 0 1 )
MOON_PA_DE403 is the name of the lunar principal axes
reference frame defined by JPL's DE-403 planetary ephemeris.
FRAME_MOON_PA_DE403 = 31002
FRAME_31002_NAME = 'MOON_PA_DE403'
FRAME_31002_CLASS = 2
FRAME_31002_CLASS_ID = 31002
FRAME_31002_CENTER = 301
MOON_ME_DE403 is the name of the lunar mean Earth/polar
axis reference frame defined by JPL's DE-403 planetary ephemeris.
Rotation angles are from reference .
FRAME_MOON_ME_DE403 = 31003
FRAME_31003_NAME = 'MOON_ME_DE403'
FRAME_31003_CLASS = 4
FRAME_31003_CLASS_ID = 31003
FRAME_31003_CENTER = 301
TKFRAME_31003_SPEC = 'ANGLES'
TKFRAME_31003_RELATIVE = 'MOON_PA_DE403'
TKFRAME_31003_ANGLES = ( 63.8986 79.0768 0.1462 )
TKFRAME_31003_AXES = ( 3, 2, 1 )
TKFRAME_31003_UNITS = 'ARCSECONDS'
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
where nnn is the version number of the DE.
The PCK body ID code associated with that data set will be
The frame ID and class ID for this frame will also be 31004.
The generic PA frame specification will be updated to point to the
new DE-specific PA frame. The rest of this frame specification
The ME frame name associated with the new data set will be named
The frame ID and class ID for this frame will be
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
End of kernel
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