KPL/PCK Asteroid Bennu P_constants (PcK) SPICE kernel file ======================================================================= This text PCK contains rotational and ellipsoidal shape constants for asteroid Bennu. Version and Date -------------------------------------------------------- Version 1.7 -- January 26, 2020 -- Michael Nolan, LPL/UA Jason Leonard, KinetX Jeroen Geeraert, KinetX Updated rotational constants based on FDS / nav pole solution in [10] and shape model v042 [8]. Includes updated PM acceleration based on fitting through the course of the mission. Version 1.6 -- September 14, 2020 -- Michael Nolan, LPL/UA Jason Leonard, KinetX Updated rotational constants based on FDS / nav pole solution in [9] and shape model v042 [8]. Version 1.5 -- September 16, 2019 -- Michael Nolan, LPL/UA Jason Leonard, KinetX Updated rotational and ellipsoid constants based on FDS / nav pole solution in [7] and shape model v042 [8]. Version 1.4 -- February 15, 2019 -- Michael Nolan, LPL/UofA Updated rotational constants based on FDS pole solution in [6] along with the acceleration determined in [5]. It matches the solution in [6] at 2019 Jan 01 12:00:00 TDB to within 0.0001 degrees Version 1.3 -- February 3, 2019 -- Michael Nolan, LPL/UofA Updated rotational constants based on shape modelling in [4] along with the acceleration determined in [5]. It matches the solution in [4] at 2019 Jan 01 12:00:00 TDB Version 1.2 -- January 11, 2019 -- Michael Nolan, LPL/UofA Boris Semenov, NAIFJPL Updated prime meridian location (W0) and rotation terms (W1, W2) based on [2], [3], and Bennu lightcurve observations in flight. Updated ellipsoid parameters based on shape modelling in [3]. Version 1.1 -- October 22, 2018 -- Michael Nolan, LPL/UofA Boris Semenov, NAIF/JPL Updated prime meridian location (W0) and rotation terms (W1, W2) based on [2] and Bennu lightcurve observations in flight. Version 1.0 -- November 4, 2014 -- Boris Semenov, NAIF/JPL Initial version released for official use by OSIRIS-Rex project, containing values for the pole direction, rotation period and shape from [1]. Disclaimer -------------------------------------------------------- This constants file may not contain the parameter values that you prefer. Note that this file may be readily modified by you or anyone else. NAIF suggests that you inspect this file visually before proceeding with any critical or extended data processing. NAIF requests that you update the ``by line'' and date if you modify the file. Sources -------------------------------------------------------- The sources for the constants listed in this version of this file are: 1) (101955) Bennu Design Reference Asteroid, Document Number: OREX-XLSX-04.00-00001, Rev_10, Version: 2014 October 10 (OREX-XLSX-04.00-00001_Rev_10_Bennu_DRA_Final.xlsx) 2) M.C. Nolan et al. (2018). Detection of YORP on Bennu using HST Lightcurve Observations. Submitted to Geophysical Research Letters. 3) O.S. Barnouin et al. (2019) Exploring the Shape of (101955) Bennu with OSIRIS-REx. Submitted to Nature. 4) Product report for OSIRIS-REx shape model v020 5) C.W. Hergenrother at al. (2019). Photometric Properties, Rotation State, and Operational Environment of Asteroid (101955) Bennu from OSIRIS-REx Observations. Submitted to Nature Communications. 6) 190215_Pole_Final in the OSIRIS-REx FDS to ALTWG/JPL/SPOC POLE PRODUCT FILE RELEASE FORM 7) bennu_pck_fds_v42_final.tpc in the OSIRIS-REx INTERNAL FDS to ALTWG ITERATION PRODUCT FILE RELEASE FORM FOR V42 8) Product report for OSIRIS-REx shape mode v042 9) bennu_pck_fds_v42_final_v3.tpc in the OSIRIS-REx FDS FILE RELEASE FORM FOR UPDATED V42 PCK (V3) 10) FDS V42 Prime Meridian Estimation Results Powerpoint. Orientation constants for asteroid Bennu -------------------------------------------------------- The inertial reference frame for the Bennu rotation constants is J2000; this is the default reference frame for PCK orientation data. The epoch of the Bennu rotation constants is J2000; this is Julian ephemeris date (JED) 2451545.0. The NAIF integer code for Bennu is 2101955. See the NAIF_IDs required reading for further information on NAIF integer codes. The LONG_AXIS keyword providing the offset between the longest axis of the triaxial ellipsoid used to model Bennu and the Bennu prime meridian is not used by SPICE geometry software. It is considered deprecated and provided solely for backwards compatibility. Values in the Version 1.0 The pole direction, prime meridian location, and rotation period in this version are set to the following values from [1]: " 3.1.1 Rotation Period 4.297461 hours 3.1.6 Pole Position (J200 RA/DEC) (+86.6388, -65.1086) deg 3.1.7 Location of Prime Meridian 89.6456 deg (epoch J2000) " The rotation rate (W1) below was derived from the period and is provided in degrees/day. The corresponding keywords were set as follows (saved in comments for trace-ability, lower-cased to prevent accidental use): body2101955_pole_ra = ( 86.6388 0. 0. ) body2101955_pole_dec = ( -65.1086 0. 0. ) body2101955_pm = ( 89.6456 2010.4894494679531 0. ) body2101955_long_axis = ( 0. ) Values in the Version 1.1 The pole direction in this version is the same as in the version 1.0, based on [1]. The prime meridian location (W0) and rotation terms (W1 and W2) in this version are from [2], computed from fitting lightcurves, and adjusting W0 until the phase at 2005 Sep 14 (epoch of Radar model) matches the version 1.0 based on the phase difference between rq36.v.mod1002-submitted and rq36.p5.pdot30.mod models. The corresponding keywords were set as follows (saved in comments for traceability, lower-cased to prevent accidental use): body2101955_pole_ra = ( 86.6388 0. 0. ) body2101955_pole_dec = ( -65.1086 0. 0. ) body2101955_pm = ( 154.9182 2011.14576050637 1.5e-06 ) body2101955_long_axis = ( 0. ) Values in the Version 1.2 The pole direction in this version is from [3], based on the Nav solution from 2019 Jan 09. The rotation terms (W1 and W2) use the method of [2] but include data through approach. The prime meridian location (W0) was determined by fixing W1 and W2 and then adjusting W0 in ISIS until rendered Approach images visually showed the chosen Prime Meridian feature from [3] at 0 longitude. The corresponding keywords were set as follows (saved in comments for traceability, lower-cased to prevent accidental use): body2101955_pole_ra = ( 85.3400 0. 0. ) body2101955_pole_dec = ( -60.1600 0. 0. ) body2101955_pm = ( 146.8404 2011.146953279 1.5e-06 ) body2101955_long_axis = ( 0. ) Values in Version 1.3 The rotation terms and pole direction in this version are from [4], based on the Nav solution from 2019 Jan 16, OD90. These rotation coefficients were used in creating shape model v020. The rotation terms use the acceleration from [5] along with the rotation phase and rate from [4] recast to give the same rate and phase as [4] at 2019 Jan 01 12:00:00 TDB ("J2019"). [4] has rotation constants of ( 45.6089 2011.17201568 0 ). J2019 is 6940 days later than J2000. The T^2 term W2 from [5] is 0.000001815. W1 = 2011.17201568 - (2 * W2 * 6940) = 2011.14682348 W0 = 45.6089 + (2011.17201568 - 2011.14682348) * 6940 - 0.000001815 * 6940 * 6940 = 133.0258 The corresponding keywords were set as follows (saved in comments for traceability, lower-cased to prevent accidental use): body2101955_pole_ra = ( 85.6474 0. 0. ) body2101955_pole_dec = ( -60.1697 0. 0. ) body2101955_pm = ( 133.0258 2011.14682348 1.815e-06 ) body2101955_long_axis = ( 0. ) Values in Version 1.4 The rotation terms and pole direction in this version are from [6], Delivered from FDS to SPOC on 2019 Feb 15. The rotation terms use the acceleration from [5] along with the rotation phase and rate from [6] recast to give the same rate and phase as [6] at 2019 Jan 01 12:00:00 TDB ("J2019"). [6] has rotation constants of: Pole_RA : 8.545674147094455E+01 deg Pole_Dec :-6.035739923373426E+01 deg PM : 4.839868214726448E+01 deg (j2000) Rotation_Rate : 2.011171643153616E+03 deg/day J2019 is 6940 days later than J2000. The T^2 term W2 from [5] is 0.000001815. W2 is half the acceleration rate. W1 = 2011.17164315 - (2 * .000001815 * 6940) = 2011.14645095 W0 = 48.3987 + (2011.17164315 - 2011.14645095) * 6940 - 0.000001815 * 6940 * 6940 = 135.8156 The corresponding keywords were set as follows (saved in comments for traceability, lower-cased to prevent accidental use): body2101955_pole_ra = ( 85.4567 0. 0. ) body2101955_pole_dec = ( -60.3574 0. 0. ) body2101955_pm = ( 135.8156 2011.14645095 1.815e-06 ) body2101955_long_axis = ( 0. ) Values in Previous Version 1.5 The rotation terms and pole direction in this version are from [7], Delivered from FDS to SPOC on 2019 Sep 15. The rotation terms include the acceleration from [5] as part of the solution in [7], however it was not fit and no uncertainty was calculated. The additional corrections used in Version 1.4 were therefore not needed or applied. From [7], the uncertainties in the rotational constants are: " SIG_Pole_RA : 0.00034 deg SIG_Pole_Dec : 0.00010 deg SIG_PM : 0.00034 deg SIG_Rotation_Rate : 2.778e-11 deg/sec " The rotation sigma converted to deg/day is 2.778E-11 * 86400 = 0.000002400 deg/day Those are all formal fit uncertainties. Estimated actual uncertainties are: SIG_RA = 0.005 deg SIG_Dec = 0.010 deg SIG_Spin = 1.0e-08 deg/s (0.00086 deg/day) SIG_PM = 0.1 deg (~50 cm) The corresponding keywords were set as follows (saved in comments for traceability, lower-cased to prevent accidental use): body2101955_pole_ra = ( 85.45218 0. 0. ) body2101955_pole_dec = ( -60.36780 0. 0. ) body2101955_pm = ( 139.13621 2011.1459760340 1.815e-06 ) body2101955_long_axis = ( 0. ) Values in Previous Version 1.6 The rotation terms and pole direction in this version are from [9], Delivered from FDS to SPOC via the orx FOB on 2020 Sep 4. The rotation terms include the acceleration from [5] as part of the solution in [9], however it was not fit and no uncertainty was calculated. The additional corrections used in Version 1.4 were therefore not needed or applied. From [9], the formal fit uncertainties in the rotational constants are: SIG_Pole_RA : 0.0013 deg SIG_Pole_Dec : 0.00058 deg SIG_PM : 0.0012 deg SIG_Rotation_Rate : 2.5e-06 deg/day Estimated actual uncertainties are: SIG_Pole_RA : 0.005 deg (same as v15) SIG_Pole_Dec : 0.010 deg (same as v15) SIG_PM(j2000) : 0.025 deg SIG_Rotation_Rate : 2.5e-06 deg/day The rotational acceleration is from [5] and was not fit; no uncertainty was estimated. These updated pck Bennu orientation parameters are based on combined OD filter of Detailed Survey, Recon B, CP/R and MP/R. This OD solution assumed the V42 shape model with landmarks scaled at 0.99896 and radio/landmark tracking spans as follows: Detailed Survey March 5-30, 2019, April 2-20, 2019 Recon-B Jan 14-23, 2020 CP Rehearsal Apr 1-18, 2020 MP Rehearsal July 9-August 11, 2020 The corresponding keywords were set as follows (saved in comments for traceability, lower-cased to prevent accidental use): body2101955_pole_ra = ( 85.46097 0. 0. ) body2101955_pole_dec = ( -60.35860 0. 0. ) body2101955_pm = ( 140.68835 2011.145755336826 1.815E-06 ) body2101955_long_axis = ( 0. ) Values in Version 1.7 The rotation terms and pole direction in this version are from [10], Delivered from FDS to SPOC on 2021 Jan 14. From [10], the formal fit uncertainties in the rotational constants are: SIG_Pole_RA : 0.00107 deg SIG_Pole_Dec : 0.00056 deg SIG_PM : 0.0012 deg SIG_Rotation_Rate : 2.5e-06 deg/day SIG_Rotation_Accel : 7.5e-08 deg/day/day Estimated actual uncertainties are: SIG_Pole_RA : 0.006 deg SIG_Pole_Dec : 0.004 deg SIG_PM(j2000) : 0.0085 Deg SIG_Rotation_Rate : 1.32899e-4 deg/day SIG_Rotation_Accel : 1.0e-7 deg/day/day The rotational acceleration was estimated by examining a number of different weightings of the data. The uncertainty is estimated as 1.0e-7 deg/day/day for the W2 term of the PCK (0.2 deg/day/day for the actual acceleration) based on the variability of the estimate. The phase residuals during proximity operations show a ~sinusoidal variation with an amplitude of 0.023 degrees. This residual is believed to result from the change in the YORP torque over the Bennu year. This residual is not included in the uncertainties listed above. Also note that, because they are multiplied by large numbers, the acceleration and rate are reported below to many more digits than the uncertainties given above so that the final computed phase is accurate to the specified tolerance. These updated pck Bennu orientation parameters are based on combined OD filter of Approach, Orbital A (2 points) Detailed Survey, Orbital B, Orbital C, Recon R, Recon B, CP/R (2 points), MP/R, and pre-TAG (2 points) combined with the ground-based data from [1-3]. This OD solution assumed the V42 shape model with landmarks scaled at 0.99896 and radio/landmark tracking spans as follows: Approach Oct 30-Nov 20, 2018 Orbital A Jan 1-31, 2019, Feb 1-28, 2019 Detailed Survey March 5-30, 2019 Orbital B Jun 28-Aug 2, 2019 Orbital C Aug 9-Sep 14, 2019 Orbital R Nov 1-Dec 25, 2019 Recon-B Jan 14-Feb 14, 2020 Recon-C Mar 15-Apr 14, 2019 CP Rehearsal Apr 1-14, 2020 CP Rehearsal May 1-Jun, 2020 MP Rehearsal Jul 10-Aug 11, 2020 Pre-TAG 28 Aug-27 Sep, 2020 Pre-TAG 22 Sep-20 Oct, 2020. The ground-based lightcurve data from Sep 1999, Sep 2005, and HST photometry from 2012 [2] were also refit with the same scaled V42 shape model. \begindata BODY2101955_POLE_RA = ( 85.45864 0. 0. ) BODY2101955_POLE_DEC = ( -60.36468 0. 0. ) BODY2101955_PM = ( 150.48977 2011.143058731885 2.0E-06 ) BODY2101955_LONG_AXIS = ( 0. ) \begintext Radii for asteroid Bennu -------------------------------------------------------- Values in Versions 1.0 and 1.1 The radii in this version are set based on following values from [1]: " 2.1.2 Polar Dimension 508 meters 2.1.3 Equatorial Dimensions 565 x 535 meters " The radii below are 1/2 of the polar and equatorial dimensions provided in kilometers. The corresponding keywords were set as follows (saved in comments for trace-ability, lower-cased to prevent accidental use): body2101955_radii = ( 0.2825 0.2675 0.254 ) Values in Version 1.2 and Version 1.3 The radii in this version are set based on following values from [3]: "The extent of the GDTM is (563.87 +/- 0.17) x (536.09 +/- 0.17) x (498.42 +/- 0.17) m." The radii below are 1/2s of the polar and equatorial dimensions provided in kilometers. The corresponding keywords were set as follows (saved in comments for trace-ability, lower-cased to prevent accidental use): body2101955_radii = ( 0.281935 0.268045 0.24921 ) Values in Version 1.4 From [4]: "Extent (km): X: [-0.27915000915527344, 0.28558000922203064] Y: [-0.263949990272522, 0.2721500098705292] Z: [-0.2445800006389618, 0.25391000509262085] " The radii below are the mean of the + and - extents, ignoring the floating point rounding errors. The corresponding keywords were set as follows (saved in comments for trace-ability, lower-cased to prevent accidental use): body2101955_radii = ( 0.282365 0.268050 0.249245 ) Values in the Version 1.5, 1.6, and Current Version 1.7 From [8]: "Extent (km): X: [-0.27955999970436096, 0.2865700125694275] Y: [-0.2648099958896637, 0.27761998772621155] Z: [-0.2448599934577942, 0.25457999110221863] " The radii below are the mean of the + and - extents, ignoring the floating point rounding errors. \begindata BODY2101955_RADII = ( 0.283065 0.271215 0.249720 ) \begintext End of PCK file.