KPL/PCK P_constants (PCK) SPICE kernel file mars_konopliv_2026_n0066_v1.tpc =========================================================================== By: Nat Bachman (NAIF) 2026 October 3 PCK for Mars rotation, based on data from the 2026 publication by Konopliv et al. [1]. Rotation data for Phobos have been slightly modified for compatibility with the N0066 and older SPICE Toolkits. To assist with PCK interoperability, rotation data for Phobos and Deimos, and triaxial ellipsoid shape models for all three bodies, are included. These data are from sources [2] and [3]. This kernel was created with the assistance of Claude Sonnet 5. Sources and References -------------------------------------------------------- Sources and background references for the constants listed in this file are: [1] Alex. S. Konopliv, Ryan S. Park, Sebastien Le Maistre, Marie Yseboodt, and Rose-Marie Baland, "Updated Mars Orientation and Gravity Field and Indication of Decadal Changes in Rotation Rate." The Planetary Science Journal, 2026, DOI: 10.3847/PSJ/ae9ba7. [2] Archinal, B.A., Acton, C.H., A'Hearn, M.F., Conrad, A., Consolmagno, G.J., Duxbury, T., Hestroffer, D., Hilton, J.L., Kirk, R.L., Klioner, S.A., McCarthy, D., Meech, K., Oberst, J., Ping, J., Seidelmann, P.K., Tholen, D.J., Thomas, P.C., and Williams, I.P., "Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2015," Celestial Mechanics and Dynamical Astronomy 130, Article number 22 (2018). DOI: https://doi.org/10.1007/s10569-017-9805-5 [3] Archinal, B.A., Acton, C.H., Conrad, A., Duxbury, T., Hestroffer, D., Hilton, J.L., Jorda, L., Kirk, R.L., Klioner, S.A., Margot, J.-L., Meech, K., Oberst, J., Paganelli, F., Ping, J., Seidelmann, P.K., Stark, A., Tholen, D.J., Wang, Y., and Williams, I.P., "Correction to: Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2015." Rotation data for Phobos and Deimos, and triaxial ellipsoid radii for all three bodies, are included. These data are from [2] and [3]. Data Accuracy Warning -------------------------------------------------------- This file provides reduced accuracy Phobos rotation data compared to those provided in the file mars_konopliv_2026_v1.tpc This reduction was needed to make this file usable with the N0066 and older versions of the SPICE Toolkit. See the section "Software Limitations" below. All other data in this file match those provided in mars_konopliv_2026_v1.tpc. Software Limitations -------------------------------------------------------- SPICE support for quadratic phase angle polynomials was introduced in the N0067 Toolkit version. Older Toolkits cannot make use of the Mars system orientation data provided by sources [2] and [3]. Older Toolkits are unable to detect and signal a SPICE error if they are used to compute orientation of Mars, Phobos, or Deimos using these data: memory corruption will occur in user applications linked to these Toolkits if the applications attempt such computations. Any results, including those of unrelated computations, may be invalid after such memory corruption occurs. NAIF provides this PCK file mars_konopliv_2026_n0066_v1.tpc for use with older Toolkits. In this file, one of the phase angle polynomials for Phobos is truncated so as to be usable with older Toolkits. See the "Data Modifications" below for details. See the NAIF server at https://naif.jpl.nasa.gov for the file mars_konopliv_2026_v1.tpc, which provides the original constants from [2] and [3] needed to implement the Phobos rotation model defined by those sources. That file can be used by the N0067 or later versions of the SPICE Toolkit. Kernel Interoperability -------------------------------------------------------- This PCK file can be safely loaded after other, older generic text PCKs created by NAIF. Loading it before these or other text PCKs may prevent use of Mars system rotation models from those files. PCK incompatibility can be due to kernel variables defined by this PCK and not overwritten by PCKs loaded later. This problem can be resolved in two ways: 1) After using this kernel, unload it before loading incompatible PCKs. 2) After using this kernel, load the PCK mars_rotation_reset_v1.tpc before loading incompatible PCKs. Loading that file after this PCK has been used, and before another PCK is loaded, enables Mars system rotation models from the last-loaded PCK to function properly. See the documentation within mars_rotation_reset_v1.tpc for details. Data Modifications -------------------------------------------------------- 1) Poisson terms in the angular expressions for alpha, delta, and W in the source model have been replaced by asymptotic approximations, in order to represent the expressions in a format compatible with SPICE Toolkit software. The approximation replaces expressions of the form T * sin ( a + b * T ) T * cos ( a + b * T ) with, respectively, sums of expressions of the form constant * scale * sin( T / scale ) * sin ( a + b * T ) constant * scale * sin( T / scale ) * cos ( a + b * T ) Here T represents Julian centuries past J2000 TDB, and scale = 1.0e4 The modified expressions agree with the original ones, over the time range 1970-2050, to these levels: Maximum absolute alpha error (rad) = 5.33e-15 Maximum absolute delta error (rad) = 6.66e-16 Maximum absolute W error (rad) = 1.09e-10 These errors were determined by sampling using a step size of approximately 250 seconds. The modified expressions have been analytically transformed to expressions that satisfy SPICE text PCK requirements. 2) In this file, data for the orientation of Phobos have been modified, at the expense of some loss of accuracy, so that the file is usable by the N0066 and older versions of the SPICE Toolkit. Specifically, in this file, the polynomial defining the M5 phase angle of the Mars system is truncated to first order, and all of the phase angle polynomial coefficient sets for the Mars system have two coefficients. Only the model of the orientation of Phobos is affected by this change. Over the time period 2000 : 2040 the maximum angular error of Phobos' orientation relative to that given by the original model is approximately 0.041 degrees The maximum error occurs at year 2040. Data -------------------------------------------------------- \begintext The first set of angle coefficients below are those supporting rotation models for Phobos and Deimos. Later assignments in this file augment the angle set with data used by the Mars rotation model. \begindata BODY4_MAX_PHASE_DEGREE = 1 BODY4_NUT_PREC_ANGLES = ( 190.72646643 15917.10818695 21.46892470 31834.27934054 332.86082793 19139.89694742 394.93256437 38280.79631835 189.63271560 41215158.18420050 121.46893664 660.22803474 231.05028581 660.99123540 251.37314025 1320.50145245 217.98635955 38279.96125550 196.19729402 19139.83628608 198.991226 19139.4819985 226.292679 38280.8511281 249.663391 57420.7251593 266.183510 76560.6367950 79.398797 0.5042615 122.433576 19139.9407476 43.058401 38280.8753272 57.663379 57420.7517205 79.476401 76560.6495004 166.325722 0.5042615 129.071773 19140.0328244 36.352167 38281.0473591 56.668646 57420.9295360 67.364003 76560.2552215 104.792680 95700.4387578 95.391654 0.5042615 ) \begintext Polynomial terms of expressions for Mars pole RA, pole Dec, and prime meridian angle W. \begindata BODY499_POLE_RA = ( 317.6811001 -0.1085514 -2.99e-5 ) BODY499_POLE_DEC = ( 52.8863461 -0.0614879 4.41e-5 ) BODY499_PM = ( 176.6302669 350.89198247002 -8.5e-15 ) \begintext Nutation precession angles for Mars pole RA: \begindata BODY4_NUT_PREC_ANGLES += ( 226.3 38280.6 198.6 19140.3 248.7 57420.9 266.0 76561.2 194.7 15924.9 285.2 95701.5 305.1 657.5 304.5 114841.8 59.2 38280.594270422051 239.2 38280.605729577946 210.7 19140.294270422048 30.7 19140.305729577951 ) \begintext Nutation precession angles for Mars pole Dec: \begindata BODY4_NUT_PREC_ANGLES += ( 43.0 38280.6 122.7 19140.3 58.7 57420.9 79.8 76561.2 194.7 15924.9 99.3 95701.5 305.1 657.5 118.7 114841.8 80.8 19140.294270422048 260.8 19140.305729577951 212.3 38280.594270422051 32.3 38280.605729577946 ) \begintext Nutation precession angles for Mars prime meridian angle W: \begindata BODY4_NUT_PREC_ANGLES += ( 46.3 38280.6 147.5 19139.9 92.6 1395.3 18.6 19140.3 253.3 38279.7 68.7 57420.9 86.0 76561.2 291.9 57419.6 237.1 76559.4 14.7 15924.9 105.2 95701.5 125.1 657.5 321.0 16105.3 124.5 114841.8 27.6 19140.294270422048 207.6 19140.305729577951 247.7 38280.594270422051 67.7 38280.605729577946 ) \begintext Nutation precession angle coefficients for Mars pole RA: \begindata BODY499_NUT_PREC_RA = ( 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ) BODY499_NUT_PREC_RA += ( 0.0002383 0.0000682 0.0000519 0.0000088 0.0000019 0.0000014 0.0000007 0.0000002 0.006 0.006 0.005 0.005 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ) \begintext Nutation precession angle coefficients for Mars pole Dec: \begindata BODY499_NUT_PREC_DEC = ( 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ) BODY499_NUT_PREC_DEC += ( 0 0 0 0 0 0 0 0 0 0 0 0 0.0001414 0.0000519 0.0000310 0.0000053 0.0000012 0.0000008 0.0000004 0.0000001 0.002 0.002 0.004 0.004 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ) \begintext Nutation precession angle coefficients for Mars prime meridian angle W: \begindata BODY499_NUT_PREC_PM = ( 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ) BODY499_NUT_PREC_PM += ( 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0001900 0.0001448 0.0000683 0.0000544 0.0000467 0.0000414 0.0000070 0.0000055 0.0000030 0.0000015 0.0000011 0.0000006 0.0000002 0.0000002 0.004 0.004 0.005 0.005 ) \begintext Rotation data for Phobos and Deimos follow. Satellites of Mars Phobos Old values are from the 2009 IAU report. body401_pole_ra = ( 317.68 -0.108 0. ) body401_pole_dec = ( 52.90 -0.061 0. ) body401_pm = ( 35.06 1128.8445850 6.6443009930565219e-09 ) body401_long_axis = ( 0. ) body401_nut_prec_ra = ( 1.79 0. 0. 0. ) body401_nut_prec_dec = ( -1.08 0. 0. 0. ) body401_nut_prec_pm = ( -1.42 -0.78 0. 0. ) The quadratic prime meridian term is scaled by 1/36525**2: 8.864000000000000 ---> 6.6443009930565219E-09 Current values: Values from the 2015 IAU report [2] were corrected by [3], which is used as the source for the data below. The quadratic prime meridian term is scaled by 1/36525**2: 12.72192797000000000000 ---> 9.536137031212154e-09 \begindata BODY401_POLE_RA = ( 317.67071657 -0.10844326 0. ) BODY401_POLE_DEC = ( 52.88627266 -0.06134706 0. ) BODY401_PM = ( 35.18774440 1128.84475928 9.536137031212154e-09 ) BODY401_LONG_AXIS = ( 0. ) BODY401_NUT_PREC_RA = ( -1.78428399 0.02212824 -0.01028251 -0.00475595 ) BODY401_NUT_PREC_DEC = ( -1.07516537 0.00668626 -0.00648740 0.00281576 ) BODY401_NUT_PREC_PM = ( 1.42421769 -0.02273783 0.00410711 0.00631964 -1.143 ) \begintext Deimos Old values are from the 2009 IAU report. The Deimos prime meridian expression from that report is: 2 W = 79.41 + 285.1618970 d - 0.520 T - 2.58 sin M 3 + 0.19 cos M . 3 At the present time, the PCK kernel software (the routine BODEUL in particular) cannot handle the cosine term directly, but we can represent it as 0.19 sin M 4 where M = 90.D0 - M 4 3 Therefore, the old nutation precession angle assignments for Phobos and Deimos contain four coefficients rather than three. The quadratic prime meridian term is scaled by 1/36525**2: -0.5200000000000000 ---> -3.8978300049519307E-10 body402_pole_ra = ( 316.65 -0.108 0. ) body402_pole_dec = ( 53.52 -0.061 0. ) body402_pm = ( 79.41 285.1618970 -3.897830d-10 ) body402_long_axis = ( 0. ) body402_nut_prec_ra = ( 0. 0. 2.98 0. ) body402_nut_prec_dec = ( 0. 0. -1.78 0. ) body402_nut_prec_pm = ( 0. 0. -2.58 0.19 ) New values: \begindata BODY402_POLE_RA = ( 316.65705808 -0.10518014 0. ) BODY402_POLE_DEC = ( 53.50992033 -0.05979094 0. ) BODY402_PM = ( 79.39932954 285.16188899 0. ) BODY402_LONG_AXIS = ( 0. ) BODY402_NUT_PREC_RA = ( 0 0 0 0 0 3.09217726 0.22980637 0.06418655 0.02533537 0.00778695 ) BODY402_NUT_PREC_DEC = ( 0 0 0 0 0 1.83936004 0.14325320 0.01911409 -0.01482590 0.00192430 ) BODY402_NUT_PREC_PM = ( 0 0 0 0 0 -2.73954829 -0.39968606 -0.06563259 -0.02912940 0.01699160 ) \begintext Radii of Mars System Objects -------------------------------------------------------- Values are from [2]. Mars \begindata BODY499_RADII = ( 3396.19 3396.19 3376.20 ) \begintext Phobos \begindata BODY401_RADII = ( 13.0 11.4 9.1 ) \begintext Deimos \begindata BODY402_RADII = ( 7.8 6.0 5.1 ) \begintext =========================================================================== End of file mars_konopliv_2026_n0066_v1.tpc ===========================================================================