KPL/PCK P_constants (PCK) SPICE kernel file pck00011_n0066_mars_moons.tpc =========================================================================== By: Rafael Andres Blasco (ESAC/ESA) 2023 July 31 Alfredo Escalante Lopez (ESAC/ESA) Data Accuracy Warning -------------------------------------------------------- This file provides reduced accuracy Phobos rotation data compared to those provided in the file pck00011.tpc. This reduction was needed to make this file usable with the N0066 and older versions of the SPICE Toolkit. See the sections "Version Description" and "Software limitations" below. Purpose -------------------------------------------------------- This file makes available for use in SPICE-based application software orientation and size/shape data for Mars and its moons, Phobos and Deimos. The principal source of the data is a published report by the IAU Working Group on Cartographic Coordinates and Rotational Elements In this file, Mars orientation data is taken from the 2009 IAU report [3] (implemented in pck00010.tpc) while Phobos and Deimos orientation is taken from the 2015 IAU report [1] (implemented in pck00011_n0066.tpc). Orientation and size/shape data not provided by this file may be available in mission-specific PCK files. Such PCKs may be the preferred data source for mission-related applications. Mission-specific PCKs can be found in PDS archives or on the NAIF web site at URL: https://naif.jpl.nasa.gov/naif/data.html Version Description -------------------------------------------------------- This file was created on July 31, 2023 by the ESA SPICE Service, located at ESAC. This file contains a subset of data, corresponding to Mars of the file pck00010.tpc and the Mars' moons Phobos and Deimos, of the file pck00011_n0066.tpc in this file, data for the orientation of Phobos have been modified, compared to the original pck00011.tpc, 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. The previous version of the file was pck00010.tpc That file was published October 21, 2011. This version incorporates data from sources listed under "Sources and References" below. The primary sources are [1] and [2]. This file contains size, shape, and orientation data for all objects covered by the previous version of the file. Orientation data for the following objects provided by this file differ from those provided by the previous version: Deimos Phobos WARNING: Mars system orientation data in the PCK files pck00011*.tpc listed above are incompatible with corresponding data from older PCK files. Loading either of the pck00011*.tpc files, and then loading older PCK files, including pck00010.tpc will make Mars system orientation data from the later loaded files unusable. After this sequence of kernel loads, calls to SPICE APIs that require the orientation of Mars, Phobos, or Deimos, for example calls to the SPICE APIs PXFORM or SXFORM, will cause the error SPICE(INSUFFICIENTANGLES) to be signaled. Mars system orientation data in the file pck00011.tpc cannot be used with SPICE Toolkit versions earlier than N0067. This PCK contains variables that enable Mars system orientation data in this file to be safely used when this file is loaded after either pck00011.tpc or pck00011_n0066.tpc. File Organization -------------------------------------------------------- The contents of this file are as follows. Introductory Information: -- Purpose -- Version description -- File Organization -- Disclaimer -- Sources -- Explanatory notes -- Body numbers and names PcK Data: Orientation Data ---------------- -- Orientation constants for Mars, Phobos and Deimos Orientation data provided in this file are used by the SPICE Toolkit to evaluate the orientation of body-fixed, body-centered reference frames with respect to the ICRF frame ("J2000" in SPICE documentation). These body-fixed frames have names of the form IAU_ for example IAU_DEIMOS See the PCK Required Reading file pck.req for details. Radii of Bodies --------------- -- Radii of Mars, Phobos and Deimos Additional data: -- Variables that prevent conflicts with Mars system orientation data in pck00011.tpc and pck00011_n0066.tpc. Disclaimer -------------------------------------------------------- Applicability of Data This P_constants file (PCK) may not contain the parameter values that you prefer. NAIF suggests that you inspect this file visually before proceeding with any critical or extended data processing. File Modifications by Users Note that this file may be readily modified by you to change values or add/delete parameters. NAIF requests that you update the "by line," date, version description section, and file name if you modify this file. A user-modified file should be thoroughly tested before being published or otherwise distributed. P_constants files must conform to the standards described in the two SPICE technical reference documents: PCK Required Reading Kernel Required Reading Known Limitations and Caveats Accuracy -------- In general, the orientation models given here are claimed by the IAU Working Group Report [1] to be accurate to 0.1 degree ([1], p. 9). However, NAIF notes that orientation models for natural satellites and asteroids have in some cases changed substantially with the availability of new observational data, so users are urged to investigate the suitability for their applications of the models presented here. Software limitations -------------------- SPICE Toolkits prior to version N0067 cannot make use of the Mars system orientation data provided in the file pck00011.tpc These 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 these Toolkits if the applications attempt such computations. Any results, including those of unrelated computations, may be invalid after such memory corruption occurs. ESA SPICE Service provides this PCK file pck00011_n0066_mars_moons.tpc based on the NAIF PCK file pck00011_n0066.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 "Version Description" above for details. Sources and References -------------------------------------------------------- Sources and background references for the constants listed in this file are: [1] 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., Klinoner, 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 [2] Archinal, B.A., Acton, C.H., Conrad, A., Duxbury, T., Hestroffer, D., Hilton, J.L., Jorda, L., Kirk, R.L., Klinoner, Margot, J.-L., S.A., Meech, K., Oberst, Paganelli, F., J., Ping., J., Seidelmann, P.K., Stark, A., Tholen, Wang, Y., and Williams, I.P., "Correction to: Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2015." [3] Archinal, B.A., A'Hearn, M.F., Bowell, E., Conrad, A., Consolmagno, G.J., Courtin, R., Fukushima, T., Hestroffer, D., Hilton, J.L., Krasinsky, G.A., Neumann, G., Oberst, J., Seidelmann, P.K., Stooke, P., Tholen, D.J., Thomas, P.C., and Williams, I.P. "Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2009." [4] Archinal, B.A., A'Hearn, M.F., Conrad, A., Consolmagno, G.J., Courtin, R., Fukushima, T., Hestroffer, D., Hilton, J.L., Krasinsky, G.A., Neumann, G., Oberst, J., Seidelmann, P.K., Stooke, P., Tholen, D.J., Thomas, P.C., and Williams, I.P. "Erratum to: Reports of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2006 & 2009." [5] Seidelmann, P.K., Archinal, B.A., A'Hearn, M.F., Conrad, A., Consolmagno, G.J., Hestroffer, D., Hilton, J.L., Krasinsky, G.A., Neumann, G., Oberst, J., Stooke, P., Tedesco, E.F., Tholen, D.J., and Thomas, P.C. "Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements: 2006." Most values are from [1]. All exceptions are commented where they occur in this file. The exceptions are: -- Phobos prime meridian constants are from [2]. "Old values" listed are from the SPICE PCK file pck00010.tpc dated October 21, 2011. Most of these values came from the 2009 IAU report [3]. Explanatory Notes -------------------------------------------------------- This file, which is logically part of the SPICE P-kernel, contains constants used to model the orientation, size and shape of Mars and its moons, Phobos and Deimos. The orientation models express the direction of the pole and location of the prime meridian of a body as a function of time. The size/shape models ("shape models" for short) represent all bodies as ellipsoids, using two equatorial radii and a polar radius. Spheroids and spheres are obtained when two or all three radii are equal. The SPICE Toolkit routines that use this file are documented in the SPICE "Required Reading" file pck.req. They are also documented in the "PCK" SPICE tutorial, which is available on the NAIF web site. File Format A terse description of the PCK file format is given here. See the SPICE "Required Reading" files pck.req and kernel.req for a detailed explanation of the SPICE text kernel file format. The files pck.req and kernel.req are included in the documentation provided with the SPICE Toolkit. The file starts out with the ``ID word'' string KPL/PCK This string identifies the file as a text kernel containing PCK data. This file consists of a series of comment blocks and data blocks. Comment blocks, which contain free-form descriptive or explanatory text, are preceded by a \begintext token. Data blocks follow a \begindata token. In order to be recognized, each of these tokens must be placed on a line by itself. The portion of the file preceding the first data block is treated as a comment block; it doesn't require an initial \begintext token. This file identifies data using a series of KEYWORD = VALUE assignments. The left hand side of each assignment is a "kernel variable" name; the right hand side is an associated value or list of values. SPICE kernel pool access routines (see kernel.req) enable other SPICE routines and user applications to retrieve the set of values associated with each kernel variable name. Kernel variable names are case-sensitive and are limited to 32 characters in length. Numeric values may be integer or floating point. String values are normally limited to 80 characters in length; however, SPICE provides a mechanism for identifying longer, "continued" strings. See the SPICE routine STPOOL for details. String values are single quoted. When the right hand side of an assignment is a list of values, the list items may be separated by commas or simply by blanks. The list must be bracketed by parentheses. Example: BODY399_RADII = ( 6378.1366 6378.1366 6356.7519 ) Any blanks preceding or following keyword names, values and equal signs are ignored. Assignments may be spread over multiple lines, for example: BODY399_RADII = ( 6378.1366 6378.1366 6356.7519 ) This file may contain blank lines anywhere. Non-printing characters including TAB should not be present in the file: the presence of such characters may cause formatting errors when the file is viewed. Time systems and reference frames The 2015 IAU Working Group Report [1] states the time scale used as the independent variable for the rotation formulas is Barycentric Dynamical Time (TDB) and that the epoch of variable quantities is J2000 TDB (2000 Jan 1 12:00:00 TDB, Julian ephemeris date 2451545.0 TDB). Throughout SPICE documentation and in this file, we use the names "J2000 TDB" and "J2000" for this epoch. The name "J2000.0" is equivalent. SPICE documentation refers to the time system used in this file as either "ET" or "TDB." SPICE software makes no distinction between TDB and the time system associated with the independent variable of the JPL planetary ephemerides T_eph. The inertial reference frame used for the rotational elements in this file is identified by [1] as the ICRF (International Celestial Reference Frame). The SPICE PCK software that reads this file uses the label "J2000" to refer to the ICRF; this is actually a mislabeling which has been retained in the interest of backward compatibility. Using data from this file, by means of calls to the SPICE frame transformation routines, will actually compute orientation relative to the ICRF. The difference between the J2000 frame and the ICRF is on the order of 100 milliarcseconds and is well below the accuracy level of the formulas in this file. Orientation models All of the complete orientation models use three Euler angles to describe the orientation of the coordinate axes of the "Body Equator and Prime Meridian" system with respect to an inertial system. By default, the inertial system is the ICRF (labeled as "J2000"), but other inertial frames can be specified in the file. See the PCK Required Reading for details. The first two angles, in order, are the ICRF right ascension and declination (henceforth RA and DEC) of the north pole of a body as a function of time. The third angle is the prime meridian location (represented by "W"), which is expressed as a rotation about the north pole, and is also a function of time. For each body, the expressions for the north pole's right ascension and declination, as well as prime meridian location, are sums (as far as the models that appear in this file are concerned) of quadratic polynomials and trigonometric polynomials, where the independent variable is time. In this file, the time arguments in expressions always refer to Barycentric Dynamical Time (TDB), measured in centuries or days past a reference epoch. By default, the reference epoch is the J2000 epoch, which is Julian ephemeris date 2451545.0 (2000 Jan 1 12:00:00 TDB), but other epochs can be specified in the file. See the PCK Required Reading for details. Orientation models for satellites and some planets (including Jupiter) involve both polynomial terms and trigonometric terms. The arguments of the trigonometric terms are linear or quadratic polynomials. In this file, we call the arguments of these trigonometric terms "nutation precession angles" or "phase angles." Example: 2015 IAU Model for orientation of Jupiter. Note that these values are used as an example only; see the data area below for current values. Right ascension --------------- alpha = 268.056595 - 0.006499 T + 0.000117 sin(Ja) 0 + 0.000938 sin(Jb) + 0.001432 sin(Jc) + 0.000030 sin(Jd) + 0.002150 sin(Je) Declination ----------- delta = 64.495303 + 0.002413 T + 0.000050 cos(Ja) 0 + 0.000404 cos(Jb) + 0.000617 cos(Jc) - 0.000013 cos(Jd) + 0.000926 cos(Je) Prime meridian -------------- W = 284.95 + 870.5366420 d Here T represents centuries past J2000 ( TDB ), d represents days past J2000 ( TDB ). Ja-Je are nutation precession angles. In this file, the polynomials' coefficients above are assigned to kernel variable names (left-hand-side symbols) as follows BODY599_POLE_RA = ( 268.056595 -0.006499 0. ) BODY599_POLE_DEC = ( 64.495303 0.002413 0. ) BODY599_PM = ( 284.95 870.5360000 0. ) and the trigonometric polynomials' coefficients are assigned as follows BODY599_NUT_PREC_RA = ( 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.000117 0.000938 0.001432 0.000030 0.002150 ) BODY599_NUT_PREC_DEC = ( 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.000050 0.000404 0.000617 -0.000013 0.000926 ) BODY599_NUT_PREC_PM = ( 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.0 0.0 0.0 0.0 0.0 ) Note the number "599"; this is the NAIF ID code for Jupiter. In this file, the polynomial expressions for the nutation precession angles are listed along with the planet's RA, DEC, and prime meridian terms. Below are the 2006 IAU nutation precession angles for the Jupiter system. J1 = 73.32 + 91472.9 T J2 = 24.62 + 45137.2 T J3 = 283.90 + 4850.7 T J4 = 355.80 + 1191.3 T J5 = 119.90 + 262.1 T J6 = 229.80 + 64.3 T J7 = 352.25 + 2382.6 T J8 = 113.35 + 6070.0 T J9 = 146.64 + 182945.8 T J10 = 49.24 + 90274.4 T Ja = 99.360714 + 4850.4046 T Jb = 175.895369 + 1191.9605 T Jc = 300.323162 + 262.5475 T Jd = 114.012305 + 6070.2476 T Je = 49.511251 + 64.3000 T Here T represents centuries past J2000 ( TDB ) J1-J10 and Ja-Je are the nutation precession angles. The angles J9 and J10 are equal to 2*J1 and 2*J2, respectively. Angles J9 and J10 are not present in [1]; they have been added to fit the terms 2*J1 and 2*J2, which appear in the orientation models of several satellites, into a form that can be accepted by the PCK system. The assignment of the nutation precession angles for the Jupiter system is as follows: BODY5_NUT_PREC_ANGLES = ( 73.32 91472.9 24.62 45137.2 283.90 4850.7 355.80 1191.3 119.90 262.1 229.80 64.3 352.25 2382.6 113.35 6070.0 146.64 182945.8 49.24 90274.4 99.360714 4850.4046 175.895369 1191.9605 300.323162 262.5475 114.012305 6070.2476 49.511251 64.3000 ) You'll see an additional symbol grouped with the ones listed above; it is BODY599_LONG_AXIS This is a deprecated feature; see the note on "Prime meridian offsets" under "Known Limitations and Caveats" above. The pattern of the formulas for satellite orientation is similar to that for Jupiter. Example: 2006 IAU values for Io. Again, these values are used as an example only; see the data area below for current values. Right ascension --------------- alpha = 268.05 - 0.009 T + 0.094 sin(J3) + 0.024 sin(J4) 0 Declination ----------- delta = 64.50 + 0.003 T + 0.040 cos(J3) + 0.011 cos(J4) 0 Prime meridian -------------- W = 200.39 + 203.4889538 d - 0.085 sin(J3) - 0.022 sin(J4) d represents days past J2000. J3 and J4 are nutation precession angles. The polynomial terms are assigned to symbols by the statements BODY501_POLE_RA = ( 268.05 -0.009 0. ) BODY501_POLE_DEC = ( 64.50 0.003 0. ) BODY501_PM = ( 200.39 203.4889538 0. ) The coefficients of the trigonometric terms are assigned to symbols by the statements BODY501_NUT_PREC_RA = ( 0. 0. 0.094 0.024 ) BODY501_NUT_PREC_DEC = ( 0. 0. 0.040 0.011 ) BODY501_NUT_PREC_PM = ( 0. 0. -0.085 -0.022 ) 501 is the NAIF ID code for Io. SPICE software expects the models for satellite orientation to follow the form of the model shown here: the polynomial portions of the RA, DEC, and W expressions are expected to be quadratic, the trigonometric terms for RA and W (satellite prime meridian) are expected to be linear combinations of sines of nutation precession angles, the trigonometric terms for DEC are expected to be linear combinations of cosines of nutation precession angles, and the polynomials for the nutation precession angles themselves are expected to be linear or quadratic. Eventually, the software will handle more complex expressions, we expect. Shape models There is only one kind of shape model supported by the SPICE Toolkit software at present: the triaxial ellipsoid. The 2015 IAU report [1] does not use any other models, except in the case of Mars, where separate values are given for the north and south polar radii. In this file, we provide as a datum the mean Mars polar radius provided by [1]. The North and South values are included as comments. For each body, three radii are listed: The first number is the largest equatorial radius, the second number is the smaller equatorial radius, and the third is the polar radius. Example: Radii of the Earth. BODY399_RADII = ( 6378.1366 6378.1366 6356.7519 ) Body Numbers and Names -------------------------------------------------------- The following NAIF body ID codes and body names appear in this file. See the NAIF IDs Required Reading file naif_ids.req for a detailed discussion and a complete list of ID codes and names. 4 Mars barycenter 499 Mars 401 Phobos 402 Deimos Orientation constants for Mars and its natural satellites --------------------------------------------------------- Mars In this file, the Mars rotation model from pck00010.tpc is maintained, implementing orientation from the 2009 IAU report [3]. Current values: \begindata BODY499_POLE_RA = ( 317.68143 -0.1061 0. ) BODY499_POLE_DEC = ( 52.88650 -0.0609 0. ) BODY499_PM = ( 176.630 350.89198226 0. ) \begintext Source [5] specifies the following value for the lambda_a term (BODY499_LONG_AXIS ) for Mars. This term is the POSITIVE EAST LONGITUDE, measured from the prime meridian, of the meridian containing the longest axis of the reference ellipsoid. (CAUTION: previous values were POSITIVE WEST.) body499_long_axis = ( 252. ) We list this lambda_a value for completeness. The IAU report [1] gives equal values for both equatorial radii, so the lambda_a offset does not apply to the IAU model. SPICE support for quadratic phase angle polynomials was introduced in the N0067 Toolkit version. Older Toolkits cannot use the constants for the Mars phase angles given by [1]. In this file, the polynomial for the M5 phase angle has been truncated to first order. Only the model of the orientation of Phobos is degraded by this change. See the SPICE server at https://naif.jpl.nasa.gov/naif/ for the file pck00011.tpc, which has the original model given by [1]. \begindata 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 ) \begintext 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 [1] were corrected by [2], 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: 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 for Mars and its natural satellites -------------------------------------------------------- Mars Old values: Values for Mars are unchanged in the 2015 report. Current values: The 2015 IAU report [4] gives separate values for the north and south polar radii: north: 3373.19 south: 3379.21 The report provides the average of these values as well, which we use as the polar radius for the triaxial model. \begindata BODY499_RADII = ( 3396.19 3396.19 3376.20 ) \begintext Satellites of Mars Old values: Values are unchanged in the 2015 IAU report. Current values: \begindata BODY401_RADII = ( 13.0 11.4 9.1 ) BODY402_RADII = ( 7.8 6.0 5.1 ) \begintext Variables that prevent conflicts with PCKs pck00011*.tpc -------------------------------------------------------- \begindata BODY4_MAX_PHASE_DEGREE = 1 BODY499_NUT_PREC_DEC = ( 0 ) BODY499_NUT_PREC_PM = ( 0 ) BODY499_NUT_PREC_RA = ( 0 ) \begintext =========================================================================== End of file pck00011_n0066_mars_moons.tpc ===========================================================================