KPL/FK
BepiColombo Supplementary Frames FK
===============================================================================
This frame kernel contains a set of supplementary frame definitions
for the BepiColombo mission.
Version and Date
-------------------------------------------------------------------------------
Version 0.0 -- February 26, 2015 -- Boris Semenov, NAIF
Initial version.
References
-------------------------------------------------------------------------------
1. ``Frames Required Reading''
2. ``Kernel Pool Required Reading''
3. ``C-Kernel Required Reading''
4. pck00009.tpc, based on IAU 2006 constants
5. pck00010.tpc, based on IAU 2009 constants
6. MERCURY_MME/999999 frame definition provided by Dr. Jonathan
McAuliffe, ESA, 20 Feb 2015
BepiColombo Supplementary Frames
-------------------------------------------------------------------------------
The following BepiColombo supplementary frames are defined in FK:
Name Relative to Type NAIF ID
====================== ===================== ============ =======
Mercury Mean Equator Frames:
---------------------------
BC_MME_IAU2006_OF_DATE J2000 DYNAMIC -69921
BC_MME_IAU2006_J2000 J2000 FIXED -69922
BC_MME_IAU2009_OF_DATE J2000 DYNAMIC -69923
BC_MME_IAU2009_J2000 J2000 FIXED -69924
Mercury Mean Equator of Date Frame based on IAU2006 Constants
--------------------------------------------------------------
The BC_MME_IAU2006_OF_DATE frame is based on Mean Mercury Equator
and IAU vector of date computed using IAU 2006 Mercury rotation
constants
The BC_MME_IAU2006_OF_DATE frame is implemented as an Euler frame
mathematically identical to the PCK frame IAU_MERCURY based on IAU
2006 Mercury rotation constants but without prime meridian rotation
terms.
The IAU 2006 PCK data from [4] defining the IAU_MERCURY frame are:
BODY199_POLE_RA = ( 281.01 -0.033 0. )
BODY199_POLE_DEC = ( 61.45 -0.005 0. )
BODY199_PM = ( 329.548 6.1385025 0. )
Here pole RA/Dec terms in the PCK are in degrees and degrees/century;
the rates here have been converted to degrees/sec ( = (rate deg/cen)/
(86400.0 * 36525.0)). Prime meridia terms from the PCK are disregarded.
The 3x3 transformation matrix M defined by the angles is
M = [ 0.0] [angle_2] [angle_3]
3 1 3
Vectors are mapped from the J2000 base frame to the
BC_MME_IAU2006_OF_DATE frame via left multiplication by M.
The relationship of these Euler angles to RA/Dec for the
J2000-to-IAU Mercury Mean Equator and IAU vector of date
transformation is as follows:
angle_1 is 0.0
angle_2 is 90 - Dec
angle_3 is 90 + RA, mapped into the range 0 < angle_3 < 2*pi
Since when we define the BC_MME_IAU2006_OF_DATE 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 -90 - RA, mapped into the range 0 < angle_3 < 2*pi
angle_2 is -90 + Dec
angle_3 is 0.0
Then our frame definition is:
\begindata
FRAME_BC_MME_IAU2006_OF_DATE = -69921
FRAME_-69921_NAME = 'BC_MME_IAU2006_OF_DATE'
FRAME_-69921_CLASS = 5
FRAME_-69921_CLASS_ID = -69921
FRAME_-69921_CENTER = 199
FRAME_-69921_RELATIVE = 'J2000'
FRAME_-69921_DEF_STYLE = 'PARAMETERIZED'
FRAME_-69921_FAMILY = 'EULER'
FRAME_-69921_EPOCH = @2000-JAN-1/12:00:00
FRAME_-69921_AXES = ( 3 1 3 )
FRAME_-69921_UNITS = 'DEGREES'
FRAME_-69921_ANGLE_1_COEFFS = ( -11.01
1.0457068978629554e-11 )
FRAME_-69921_ANGLE_2_COEFFS = ( -28.55
-1.5844043907014476e-12 )
FRAME_-69921_ANGLE_3_COEFFS = ( 0.0 )
FRAME_-69921_ROTATION_STATE = 'INERTIAL'
\begintext
Mercury Mean Equator at J2000 Frame based on IAU2006 Constants
--------------------------------------------------------------
The BC_MME_IAU2006_J2000 frame is the BC_MME_IAU2006_OF_DATE frame
frozen at J2000 TDB. For efficiency it is defined as a offset frame
using pre-computed rotation matrix transforming vectors from
BC_MME_IAU2006_OF_DATE to J2000 at J2000 TDB.
For consistency with earlier BepiColombo usage the matrix below is
from [6].
\begindata
FRAME_BC_MME_IAU2006_J2000 = -69922
FRAME_-69922_NAME = 'BC_MME_IAU2006_J2000'
FRAME_-69922_CLASS = 4
FRAME_-69922_CLASS_ID = -69922
FRAME_-69922_CENTER = 199
TKFRAME_-69922_RELATIVE = 'J2000'
TKFRAME_-69922_SPEC = 'MATRIX'
TKFRAME_-69922_MATRIX = (
0.981593866044678, 0.190980318733265, 1.45064023353692E-15,
-0.167757184264224, 0.862232423481673, 0.477925491080635,
0.0912743626173337, -0.469128730471140, 0.878400378515027
)
\begintext
Mercury Mean Equator of Date Frame based on IAU2009 Constants
-------------------------------------------------------------
The BC_MME_IAU2009_OF_DATE frame is based on Mean Mercury Equator
and IAU vector of date computed using IAU 2009 Mercury rotation
constants
The BC_MME_IAU2009_OF_DATE frame is implemented as as Euler frame
mathematically identical to the PCK frame IAU_MERCURY based on IAU
2009 Mercury rotation constants but without prime meridian rotation
terms.
The IAU 2009 PCK data from [5] defining the IAU_MERCURY frame are:
BODY199_POLE_RA = ( 281.0097 -0.0328 0. )
BODY199_POLE_DEC = ( 61.4143 -0.0049 0. )
BODY199_PM = ( 329.5469 6.1385025 0. )
Here pole RA/Dec terms in the PCK are in degrees and degreeS/Century;
the rates here have been converted to degrees/sec ( = (rate deg/cen)/
(86400.0 * 36525.0)). Prime meridia terms from the PCK are disregarded.
The 3x3 transformation matrix M defined by the angles is
M = [ 0.0] [angle_2] [angle_3]
3 1 3
Vectors are mapped from the J2000 base frame to the
BC_MME_IAU2009_OF_DATE frame via left multiplication by M.
The relationship of these Euler angles to RA/Dec for the
J2000-to-IAU Mercury Mean Equator and IAU vector of date
transformation is as follows:
angle_1 is 0.0
angle_2 is 90 - Dec
angle_3 is 90 + RA, mapped into the range 0 < angle_3 < 2*pi
Since when we define the BC_MME_IAU2009_OF_DATE 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 -90 - RA, mapped into the range 0 < angle_3 < 2*pi
angle_2 is -90 + Dec
angle_3 is 0.0
Then our frame definition is:
\begindata
FRAME_BC_MME_IAU2009_OF_DATE = -69923
FRAME_-69923_NAME = 'BC_MME_IAU2009_OF_DATE'
FRAME_-69923_CLASS = 5
FRAME_-69923_CLASS_ID = -69923
FRAME_-69923_CENTER = 199
FRAME_-69923_RELATIVE = 'J2000'
FRAME_-69923_DEF_STYLE = 'PARAMETERIZED'
FRAME_-69923_FAMILY = 'EULER'
FRAME_-69923_EPOCH = @2000-JAN-1/12:00:00
FRAME_-69923_AXES = ( 3 1 3 )
FRAME_-69923_UNITS = 'DEGREES'
FRAME_-69923_ANGLE_1_COEFFS = ( -11.0097
1.0393692803001496e-11 )
FRAME_-69923_ANGLE_2_COEFFS = ( -28.5857
-1.5527163028874185e-12 )
FRAME_-69923_ANGLE_3_COEFFS = ( 0.0 )
FRAME_-69921_ROTATION_STATE = 'INERTIAL'
\begintext
Mercury Mean Equator at J2000 Frame based on IAU2009 Constants
--------------------------------------------------------------
The BC_MME_IAU2009_J2000 frame is the BC_MME_IAU2009_OF_DATE frame
frozen at J2000 TDB. For efficiency it is defined as a offset frame
using pre-computed rotation matrix transforming vectors from
BC_MME_IAU2009_OF_DATE to J2000 at J2000 TDB.
\begindata
FRAME_BC_MME_IAU2009_J2000 = -69924
FRAME_-69924_NAME = 'BC_MME_IAU2009_J2000'
FRAME_-69924_CLASS = 4
FRAME_-69924_CLASS_ID = -69924
FRAME_-69924_CENTER = 199
TKFRAME_-69924_RELATIVE = 'J2000'
TKFRAME_-69924_SPEC = 'MATRIX'
TKFRAME_-69924_MATRIX = (
+9.8159486600183365E-01 +1.9097517911718839E-01 +0.0000000000000000E+00
-1.6769576713227249E-01 +8.6194082826998297E-01 +4.7847271421385607E-01
+9.1376412299678439E-02 -4.6966635979428373E-01 +8.7810242099246349E-01
)
\begintext
End of FK file.