KPL/FK uranus_ringframes_rfrench20201201_v1.tf produced on Tue Dec 1 23:46:59 2020 rfrench@maxwell.fios-router.home:/Volumes/PromisePegasus48TBb/dione_raid2/Research/uranus/PDART2014/programs/create_uranus_ringframes_kernel_v1.pro Orbital elements are from Richard G. French unpublished RINGFIT solution extracted from IDL savefile ringfit_v1.8.Ur017L-RF-V0204.sav. This *.tf file contains definitions of Uranus equatorial and ring reference frames. The Uranus equatorial frame is defined by: - The +Z axis is parallel to the spin angular velocity vector of Uranus at the specified epoch (in this case the J2000 epoch). - The +X axis is parallel to the cross product of the +Z axis of the base frame (in this case the J2000 frame) and the +Z axis of the equatorial frame. This frame is implemented as a "TK" (type 4) frame. The Euler angle sequence used here is the inverse of that used to define the orientation of the equatorial frame relative to the base frame. The J2000 Uranus pole direction is given by RA: 77.31114278950268 Dec: 15.17218767654473 \begindata FRAME_URANUS_EQUATORIAL = 1799000 FRAME_1799000_NAME = 'URANUS_EQUATORIAL' FRAME_1799000_CLASS = 4 FRAME_1799000_CLASS_ID = 1799000 FRAME_1799000_CENTER = 799 TKFRAME_1799000_RELATIVE = 'J2000' TKFRAME_1799000_SPEC = 'ANGLES' TKFRAME_1799000_UNITS = 'DEGREES' TKFRAME_1799000_AXES = ( 3, 1, 3 ) TKFRAME_1799000_ANGLES = ( -167.31114278950270, -74.82781232345528, 0 ) \begintext The ring frames are implemented using the Euler family of the parameterized dynamic frame class. The epoch of the elements is UTC Jan 01, 1987 12:00:00 The corresponding TDB date is 1987 JAN 01 12:00:55.183938 TDB The Euler angle sequence for the ring frames is [ arg of periapse ] [ inclination ] [ longitude of node ] 3 1 3 The specific constants for the orientation of the rings are given below (rates are in degrees/day). (Apse and node rates determined from ring orbit fit.) Ring peri(deg) peri_dot inc(deg) node(deg) node_dot ------------------------------------------------------------------- Ring 6 60.015614 2.7619562 0.060692 212.785905 -2.7564015 Ring 5 23.831421 2.6715873 0.055807 90.628064 -2.6663182 Ring 4 77.332414 2.5979483 0.032246 156.502067 -2.5931023 Alpha 244.574805 2.1854434 0.015031 166.937646 -2.1810450 Beta 302.744308 2.0308827 0.004643 245.876368 -2.0288056 Eta 340.231488 1.8107326 0.000605 4.005938 -1.8079209 Gamma 295.826568 1.7534191 0.000304 114.553090 -1.7486374 Delta 125.881692 1.7106647 0.000445 116.400113 -1.6430618 Lambda 0.000000 1.4736325 0.000000 0.000000 -1.4715988 Epsilon 60.131744 1.3632655 0.000190 298.505826 -1.3614672 Euler frames require the inverse of this sequence, since the mapping from the Euler frame to its base frame is what's defined. The required sequence is: [ -longitude of node ] [ -inclination ] [ -arg of periapse ] 3 1 3 Note that in the frame definitions below, the angular rates are scaled from degrees/day to degrees/second, as required by the SPICE frames system. \begindata FRAME_URING_6 = 1799001 FRAME_1799001_NAME = 'URING_6' FRAME_1799001_CLASS = 5 FRAME_1799001_CLASS_ID = 1799001 FRAME_1799001_CENTER = 799 FRAME_1799001_RELATIVE = 'URANUS_EQUATORIAL' FRAME_1799001_DEF_STYLE = 'PARAMETERIZED' FRAME_1799001_FAMILY = 'EULER' FRAME_1799001_EPOCH = @1987-JAN-01/12:00:55.183938 FRAME_1799001_AXES = ( 3 1 3 ) FRAME_1799001_UNITS = 'DEGREES' FRAME_1799001_ANGLE_1_COEFFS = (-2.12785905011383E+02 3.19027951828928E-05 ) FRAME_1799001_ANGLE_2_COEFFS = (-6.06924939245691E-02 0.0 ) FRAME_1799001_ANGLE_3_COEFFS = ( 1.52770291080521E+02 -6.38698804843942E-05 ) FRAME_URING_5 = 1799002 FRAME_1799002_NAME = 'URING_5' FRAME_1799002_CLASS = 5 FRAME_1799002_CLASS_ID = 1799002 FRAME_1799002_CENTER = 799 FRAME_1799002_RELATIVE = 'URANUS_EQUATORIAL' FRAME_1799002_DEF_STYLE = 'PARAMETERIZED' FRAME_1799002_FAMILY = 'EULER' FRAME_1799002_EPOCH = @1987-JAN-01/12:00:55.183938 FRAME_1799002_AXES = ( 3 1 3 ) FRAME_1799002_UNITS = 'DEGREES' FRAME_1799002_ANGLE_1_COEFFS = (-9.06280635134931E+01 3.08601642063704E-05 ) FRAME_1799002_ANGLE_2_COEFFS = (-5.58072388254727E-02 0.0 ) FRAME_1799002_ANGLE_3_COEFFS = ( 6.67966421308632E+01 -6.17813139373033E-05 ) FRAME_URING_4 = 1799003 FRAME_1799003_NAME = 'URING_4' FRAME_1799003_CLASS = 5 FRAME_1799003_CLASS_ID = 1799003 FRAME_1799003_CENTER = 799 FRAME_1799003_RELATIVE = 'URANUS_EQUATORIAL' FRAME_1799003_DEF_STYLE = 'PARAMETERIZED' FRAME_1799003_FAMILY = 'EULER' FRAME_1799003_EPOCH = @1987-JAN-01/12:00:55.183938 FRAME_1799003_AXES = ( 3 1 3 ) FRAME_1799003_UNITS = 'DEGREES' FRAME_1799003_ANGLE_1_COEFFS = (-1.56502067289019E+02 3.00127578501259E-05 ) FRAME_1799003_ANGLE_2_COEFFS = (-3.22459732406430E-02 0.0 ) FRAME_1799003_ANGLE_3_COEFFS = ( 7.91696533293513E+01 -6.00816040020889E-05 ) FRAME_URING_ALPHA = 1799004 FRAME_1799004_NAME = 'URING_ALPHA' FRAME_1799004_CLASS = 5 FRAME_1799004_CLASS_ID = 1799004 FRAME_1799004_CENTER = 799 FRAME_1799004_RELATIVE = 'URANUS_EQUATORIAL' FRAME_1799004_DEF_STYLE = 'PARAMETERIZED' FRAME_1799004_FAMILY = 'EULER' FRAME_1799004_EPOCH = @1987-JAN-01/12:00:55.183938 FRAME_1799004_AXES = ( 3 1 3 ) FRAME_1799004_UNITS = 'DEGREES' FRAME_1799004_ANGLE_1_COEFFS = (-1.66937645724649E+02 2.52435760054987E-05 ) FRAME_1799004_ANGLE_2_COEFFS = (-1.50309011440373E-02 0.0 ) FRAME_1799004_ANGLE_3_COEFFS = (-7.76371594127685E+01 -5.05380596621136E-05 ) FRAME_URING_BETA = 1799005 FRAME_1799005_NAME = 'URING_BETA' FRAME_1799005_CLASS = 5 FRAME_1799005_CLASS_ID = 1799005 FRAME_1799005_CENTER = 799 FRAME_1799005_RELATIVE = 'URANUS_EQUATORIAL' FRAME_1799005_DEF_STYLE = 'PARAMETERIZED' FRAME_1799005_FAMILY = 'EULER' FRAME_1799005_EPOCH = @1987-JAN-01/12:00:55.183938 FRAME_1799005_AXES = ( 3 1 3 ) FRAME_1799005_UNITS = 'DEGREES' FRAME_1799005_ANGLE_1_COEFFS = (-2.45876368477633E+02 2.34815468225088E-05 ) FRAME_1799005_ANGLE_2_COEFFS = (-4.64344134743322E-03 0.0 ) FRAME_1799005_ANGLE_3_COEFFS = (-5.68679396613900E+01 -4.69871335772218E-05 ) FRAME_URING_ETA = 1799006 FRAME_1799006_NAME = 'URING_ETA' FRAME_1799006_CLASS = 5 FRAME_1799006_CLASS_ID = 1799006 FRAME_1799006_CENTER = 799 FRAME_1799006_RELATIVE = 'URANUS_EQUATORIAL' FRAME_1799006_DEF_STYLE = 'PARAMETERIZED' FRAME_1799006_FAMILY = 'EULER' FRAME_1799006_EPOCH = @1987-JAN-01/12:00:55.183938 FRAME_1799006_AXES = ( 3 1 3 ) FRAME_1799006_UNITS = 'DEGREES' FRAME_1799006_ANGLE_1_COEFFS = (-4.00593833060133E+00 2.09250105927987E-05 ) FRAME_1799006_ANGLE_2_COEFFS = (-6.04810632716268E-04 0.0 ) FRAME_1799006_ANGLE_3_COEFFS = (-3.36225549243664E+02 -4.18825641772711E-05 ) FRAME_URING_GAMMA = 1799007 FRAME_1799007_NAME = 'URING_GAMMA' FRAME_1799007_CLASS = 5 FRAME_1799007_CLASS_ID = 1799007 FRAME_1799007_CENTER = 799 FRAME_1799007_RELATIVE = 'URANUS_EQUATORIAL' FRAME_1799007_DEF_STYLE = 'PARAMETERIZED' FRAME_1799007_FAMILY = 'EULER' FRAME_1799007_EPOCH = @1987-JAN-01/12:00:55.183938 FRAME_1799007_AXES = ( 3 1 3 ) FRAME_1799007_UNITS = 'DEGREES' FRAME_1799007_ANGLE_1_COEFFS = (-1.14553090208561E+02 2.02388583280239E-05 ) FRAME_1799007_ANGLE_2_COEFFS = (-3.03770502923976E-04 0.0 ) FRAME_1799007_ANGLE_3_COEFFS = (-1.81273477783157E+02 -4.05330603321011E-05 ) FRAME_URING_DELTA = 1799008 FRAME_1799008_NAME = 'URING_DELTA' FRAME_1799008_CLASS = 5 FRAME_1799008_CLASS_ID = 1799008 FRAME_1799008_CENTER = 799 FRAME_1799008_RELATIVE = 'URANUS_EQUATORIAL' FRAME_1799008_DEF_STYLE = 'PARAMETERIZED' FRAME_1799008_FAMILY = 'EULER' FRAME_1799008_EPOCH = @1987-JAN-01/12:00:55.183938 FRAME_1799008_AXES = ( 3 1 3 ) FRAME_1799008_UNITS = 'DEGREES' FRAME_1799008_ANGLE_1_COEFFS = (-1.16400113299068E+02 1.90169187225242E-05 ) FRAME_1799008_ANGLE_2_COEFFS = (-4.45238485812102E-04 0.0 ) FRAME_1799008_ANGLE_3_COEFFS = (-9.48157837188002E+00 -3.88162783622484E-05 ) FRAME_URING_LAMBDA = 1799009 FRAME_1799009_NAME = 'URING_LAMBDA' FRAME_1799009_CLASS = 5 FRAME_1799009_CLASS_ID = 1799009 FRAME_1799009_CENTER = 799 FRAME_1799009_RELATIVE = 'URANUS_EQUATORIAL' FRAME_1799009_DEF_STYLE = 'PARAMETERIZED' FRAME_1799009_FAMILY = 'EULER' FRAME_1799009_EPOCH = @1987-JAN-01/12:00:55.183938 FRAME_1799009_AXES = ( 3 1 3 ) FRAME_1799009_UNITS = 'DEGREES' FRAME_1799009_ANGLE_1_COEFFS = (-0.00000000000000E+00 1.70323932416062E-05 ) FRAME_1799009_ANGLE_2_COEFFS = (-0.00000000000000E+00 0.0 ) FRAME_1799009_ANGLE_3_COEFFS = ( 0.00000000000000E+00 -3.40883250997155E-05 ) FRAME_URING_EPSILON = 1799010 FRAME_1799010_NAME = 'URING_EPSILON' FRAME_1799010_CLASS = 5 FRAME_1799010_CLASS_ID = 1799010 FRAME_1799010_CENTER = 799 FRAME_1799010_RELATIVE = 'URANUS_EQUATORIAL' FRAME_1799010_DEF_STYLE = 'PARAMETERIZED' FRAME_1799010_FAMILY = 'EULER' FRAME_1799010_EPOCH = @1987-JAN-01/12:00:55.183938 FRAME_1799010_AXES = ( 3 1 3 ) FRAME_1799010_UNITS = 'DEGREES' FRAME_1799010_ANGLE_1_COEFFS = (-2.98505826205259E+02 1.57577219305607E-05 ) FRAME_1799010_ANGLE_2_COEFFS = (-1.89789309525958E-04 0.0 ) FRAME_1799010_ANGLE_3_COEFFS = ( 2.38374082225245E+02 -3.15362583767008E-05 ) \begintext