Technical description of solution 2005f_astro 1. Purpose of solution: Source catalogue 2. Analysis center: GSF ( NASA Goddard Space Flight Center ) 3. Short narrative description of solution: Solution 2005f_astro estimates station position and velocity parameters in order to obtain a terrestrial reference frame (TRF) for computing EOP time series. Source positions are also estimated. The TRF is defined in such a manner that the positions and velocities of a subset of 35 strong stations have no net translation with respect to positions and velocities of these stations reported in the ITRF2000 catalogue and the resulting series of the Earth orientation parameters has zero shift and drift with respect to the USNO Finals series at the range [1997.01.01, 2005.06.09]. The CRF is defined in such a way that positions of 212 sources, marked as defining source in the ICRF catalogue [1], do not have net rotation with respect to the coordinates reported in this catalogue. All available dual-band Mark-3/Mark-4/Mark-5 VLBI observations from 1979.08.03 through 2005.12.01 (except 3 gravity sessions and 7 K/Q band experiments ) -- 4059 sessions with duration 18 hours and longer, 5,146,640 group delays -- were used in a single solution. The wrms of postfit residuals is 22.970 psec and chi-sq/ndg = 0.946 Parameters are split into three groups: 1) global parameters estimated over all sessions; 2) local parameters estimated for each 24-hour session individually; 3) segmented parameters estimated over 20-60 minute time spans. Positions and velocities of all stations were estimated as global parameters. Positions of 3481 sources were estimated as global parameters. Mean site gradients were computed from the GSFC Data Assimilation Office (DAO) model from met data from 1990-95. The atmospheric gradient delay is modeled as tau = m_grad(el) * [GN*cos(az)+GE*sin(az)], where el and az are the elevation and azimuth of the observation and the gradient mapping function is m_grad. The gradient vector has east and north components GE and GN. Refer to [2] and [3]. 4. Estimated parameters: a. celestial frame: right ascension, declination (global and local) b. terrestrial frame: X, Y, Z, Xdot, Ydot, Zdot (global) c. Earth orientation: x, y, UT1-TAI, xdot, ydot, UT1dot, dpsi, deps (local) d. zenith troposphere: linear spline 20-min interval; rate constraint with reciprocal weights generally 50 ps/hr; NMF wet partial derivative (segmented). e. troposphere gradient: 6-hour east and north linear spline at all stations, except a set of 84 stations (Appendix A); offset and rate constraints with reciprocal weights 0.5 mm and 2.0 mm/day (segmented). f. station clocks: quadratic (local) + linear spline with 1-hr interval (segmented); rate constraint with reciprocal weights generally 5.0E-14 g. baseline clocks: set in initial analysis - usually used (local) h. other: global antenna axis offsets for a set of stations (Appendix B) (global) 5. Celestial reference frame: a. a priori source positions: 2005d_apr.src catalogue. This catalogue was created in the preliminary solution similar to 2005f_astro. However, positions of 212 ICRF defining sources in the apriori list were replaced with the values taken from the ICRF catalogue. b. source positions adjusted in solution: yes If yes, c. definition of orientation: no-net-rotation tie to the ICRF using only the 212 ICRF defining sources d. source position estimation: 3481 sources 6 - Terrestrial reference frame: a. a priori station positions: 2005d_apr.sit . This catalogue was created in the preliminary solution similar to 2005f_astro. However, positions of 35 strong stations were replaced with the values from the ITRF2000 catalogue. b. a priori station velocities: 2005d_apr.vel . This catalogue was created in the preliminary solution similar to 2005f_astro. However, velocities of 35 strong stations were replaced with the values from the ITRF2000 catalogue. c. reference epoch for site positions: 1997.0 d. station positions/velocities adjusted in solution: yes e. definition of origin, orientation, and their time evolution: net-translation and net-rotation of position with respect to ITRF2000 for 35 stations: ALGOPARK BR-VLBA DSS45 FD-VLBA FORTLEZA HARTRAO HATCREEK HAYSTACK HN-VLBA HOBART26 KASHIM34 KASHIMA KAUAI KOKEE KP-VLBA LA-VLBA MATERA MK-VLBA NL-VLBA NOTO NRAO20 NRAO85_3 NYALES20 ONSALA60 OV-VLBA OVRO_130 PIETOWN RICHMOND SANTIA12 SC-VLBA SESHAN25 TSUKUB32 VNDNBERG WESTFORD WETTZELL net-translation and no-net-rotation of velocity with respect to ITRF2000 for the same 35 stations: ALGOPARK BR-VLBA DSS45 FD-VLBA FORTLEZA HARTRAO HATCREEK HAYSTACK HN-VLBA HOBART26 KASHIM34 KASHIMA KAUAI KOKEE KP-VLBA LA-VLBA MATERA MK-VLBA NL-VLBA NOTO NRAO20 NRAO85_3 NYALES20 ONSALA60 OV-VLBA OVRO_130 PIETOWN RICHMOND SANTIA12 SC-VLBA SESHAN25 TSUKUB32 VNDNBERG WESTFORD WETTZELL Values of right-hand side of net-roatation/net-translation constraints: RIGHT_PART 0.03486006 0.09125957 0.07026078 NO EXCEPT \ * nnt_pos RIGHT_PART -0.16130247 0.02886459 0.04911530 NO EXCEPT \ * nnr_pos RIGHT_PART 0.01905997 0.00043868 0.00366869 NO EXCEPT \ * nnt_vel RIGHT_PART -0.00207785 0.02378060 0.01477826 NO EXCEPT \ * nnr_vel Units: meters for nnt_pos, meters/Earth_radius for nnr_pos, mm/yr for nnt_vel, mm/(yr*Earth_radius) for nnr_vel f. station parameter estimation: X, Y, Z, Xdot, Ydot, Zdot globally for all stations, some with constraints g. stations with constraints: A priori velocity for U, E, and N components of the stations listed in Appendix C were constrained to the ITRF2000 velocities with reciprocal weights 0.1, 3.0, and 3.0 mm/yr respectively because the stations have a very short history of observations, in many cases only one occupation. The velocities of the 20 groups of stations listed in Appendix D are constrained to be the same. h. stations with discontinuous positions and date of discontinuity: YAKATAGA 871201 * Earthquake SOURDOGH 871201 * Earthquake WHTHORSE 871201 * Earthquake FORTORDS 891001 * Seismic event PRESIDIO 891001 * Seismic event MOJAVE12 920627 * Earthquake DSS15 920627 * Earthquake MEDICINA 960601 * Rail reparing EFLSBERG 961001 * Rail reparing DSS65 970415 * Rail reparing MIURA 000601 * Seismic event TATEYAMA 000601 * Seismic event GGAO7108 030101 * Station relocation Besides, the eccentricity vector for station TSUKUB32 was assigned to (-0.0437, 0.0, 0.0) meters in Up, East, North in local topocentric reference frame before 1999.05.01 and (0.0, 0.0, 0.0) after 1999.05.01 according to results of geodetic surveys [4]. Changes in the eccentricity vector are caused by repairing of the concrete foundation slab. Discontinuity in position of station GILCREEK was modeled with B-spline of the 2-rd degree which a node with multiplicity 2 at 2002.11.03_22:12:42 i. stations with nonlinear velocities: HRAS_085, GILCREEK, PIETOWN Non-linear constituent of their position is modeled with expansion on B-sline basis. j. relativity scale: the terrestrial reference frame is defined using the following metric tensor: G_oo = -(1 - (2W/c^2 + W^2/c^4) + 2L_g ) G_oa = -4W^a/c^3 G_ab = \delta_ab (1 + 2W/c^2 - 2L_g) ) Specifically, the old formula 29 in IERS Conventions 1992, page 127-136 was used, although it is known to have a deficiency. THIS METRIC TENSOR DOES NOT CONFORM IAU 2000 RESOLUTIONS! k. permanent tide correction: yes "Yes" means that both the permanent and the periodic tides have been included in the model, so that the output station position is for after the removal of both the permanent and the periodic tidal effect. The model used includes tide displacements for zero frequency with Love numbers h2(freq=0) = 0.6074, l2(freq=0) = 0.0852 7. Earth orientation: a. a priori precession model: heo_06c b. a priori nutation model: heo_06c c. a priori short-period tidal variations in x, y, UT1 were taken into account in accordance with the empirical model heo_06c (Appendix E) d. EOP estimation: X, Y, UT1, Xdot, Ydot, UT1dot, deps, dpsi each day with a priori error of 45 mas for pole and 3 ms for UT1, 45 mas/day and 3 ms/day for pole rate and UT1 rate to allow estimation for one-baseline sessions; deps and dpsi are relative to IAU 1976 precession and IAU 1980 nutation models. Time tag of EOP series is the middle epoch of the observing session. The empirical model of high frequency variations in polar motion and UT1, including nutation derived from VLBI solutions heo_06c was used. The reported values of polar motion and UT1 are the sum of the adjustments and the apriori EOP without contribution due to the high frequency variations. Thus, the final series of polar motion and UT1 do not contain contributions due to the high frequency variations. A network of each individual session falls into 4 categories: 1) very small network: baselines shorter than 150 km; 2) small network: baselines in the range 150-1500 km; 3) singular network: single baseline network with baseline length longer than 1500 km; 4) global network: three or more stations with baselines longer than 1500 km. The EOPs were not estimated for very small networks. The EOPs were estimated for small networks but applying strong constraints. The records related to these experiments were eliminated from the output EOP file. EOP from other series were put in file 2005f_astro.eops . The pole coordinates and UT1 from singular networks were substantially affected by weak constraints. They were removed from the output file 2005f_astro.eops and their values and formal uncertainties were replaced with "-0 ". The singular networks provided reasonable estimates of nutation angles. 8. A priori geophysical models: a. troposphere: NMF dry mapping function; Saastamoinen zenith delay calculated using logged pressure, temperature; a priori mean gradients from DAO weather model. b. solid Earth tide: IERS Conventions 1996, p.56-65, step 1 and step 2, anelasticity variant, including tides of the 3-rd order. c. ocean loading: 3D ocean loading displacements computed by SPOTL software. The model of displacements caused by ocean loading contains 28 constituents. The following ocean tide models were used: Harmonic Phase rad Frequency rad/sec Model Comment k2-a 1.324501D+00 1.458530140651D-04 GOT00 admittance k2 3.506941D+00 1.458423171028D-04 GOT00 s2 6.283185D+00 1.454441043329D-04 GOT00 s2-a 4.312500D-02 1.452450074576D-04 GOT00 admittance m2 2.169437D+00 1.405189027044D-04 GOT00 m2-a 1.210284D+00 1.405082057420D-04 GOT00 admittance n2 6.097067D+00 1.378796996516D-04 GOT00 k1-a 1.141827D+00 7.293185551375D-05 GOT00 admittance k1 3.324267D+00 7.292115855138D-05 GOT00 k1-b 2.365113D+00 7.291046158901D-05 GOT00 admittance p1 2.958919D+00 7.252294578148D-05 GOT00 p1-a 3.002044D+00 7.232384890619D-05 GOT00 admittance o1 5.128356D+00 6.759774415297D-05 GOT00 o1-a 1.027610D+00 6.758704719061D-05 GOT00 admittance q1 2.772800D+00 6.495854110023D-05 GOT00 q1-a 4.955240D+00 6.494784413786D-05 GOT00 admittance mtm-a 4.652212D+00 7.973314413516D-06 NAO99.l admittance mtm 5.514660D-01 7.962617451151D-06 NAO99.l mf-a 2.296657D+00 5.334111360775D-06 NAO99.l admittance mf 4.479096D+00 5.323414398410D-06 NAO99.l msf 9.721550D-01 4.925201628510D-06 NAO99.l mm 5.497148D+00 2.639203052741D-06 NAO99.l msm 4.899785D+00 2.285998575769D-06 NAO99.l ssa 3.653480D-01 3.982127698995D-07 NAO99.l paw 5.012885D+00 1.991063797295D-07 equilibrium sa 3.098467D+00 1.990968752920D-07 NAO99.l pcw 2.003605D+00 1.671771314171D-07 equilibrium 18.6 4.100746D+00 1.069696236521D-08 equilibrium d. atmosphere loading: 3D displacements computed by convolving global surface pressure field on 2.5x2.5 degrees grid with 6 hour temporal resolution using the NCEP Reanalysis model [5]. 9. Data type: three indepdent solutions: inosphere-free combination of group delays, X-band group delays only S-band group delays only 10. Data editing: 5 deg elevation cutoff 11. Data weighting. Weights are defined as follows: 1/sqrt ( f**2 + a**2 ) where "f" is formal uncertainty of the ionosphere free linear combination of group delays at X- and S-band obtained by fringe fitting on the base of achieved signal to noise ratio. The station-dependent parameter "a" was computed for each session by an iterative procedure such that the ratio of the sum of squares of weighted residuals to the estimate of their mathematical expectation is about unity. 12. Standard errors reported: all errors derived from least-squares estimation propagated from the data weights and the constraints applied to the estimated parameters. 13. Software: Calc 9.12, SOLVE revision date 2005.10.05 14. Other information: Mean pole coordinates used for computation of pole tide deformation were set to 0.0, 0.0 References: 1. Coordinates of the defining sources in ICRF http://hpiers.obspm.fr/webiers/results/icrf/icrfdef.html 2. MacMillan, D.S. and C. Ma, Atmospheric gradients from very long baseline interferometry observations, Geophys. Res. Lett., 22, 1041-1044, 1995. 3. MacMillan, D.S. and C. Ma, Atmospheric gradients and the VLBI terrestrial and celestial reference frames, Geophys. Res. Lett., 24, 453-456, 1997. 4. Takashima, K., et al., "Status and Results of GSI Domestic VLBI Network", Bulletin of the Geographical survey Institute, Vol. 46, March 2000, p. 1-9. 5. Petrov, L. and J.-P. Boy, "Study of the atmospheric pressure loading signal in VLBI observations", J. Geophys. Res., 10.1029/2003JB002500, vol. 109, No. B03405, 2004. 2005.12.04_19:54:13 ---------------------------------------------------------------------------- Appendix A. ~~~~~~~~~~~ List of 111 stations for which troposphere gradients were not estimated: AIRA AUSTINTX AZORES BERMUDA BLKBUTTE BLOOMIND BREST CARNUSTY CARROLGA CHICHI10 CHLBOLTN CTVASBAY CTVASTJ DAITO DEADMANL DSS15 ELY FLAGSTAF FORTORDS FORT_ORD FTD_7900 GBT-VLBA GGAO7108 GIFU11 GIFU3 GOLDVENU GORF7102 GRASSE HALEAKAL HOFN HOHENFRG HOHNBERG JPL_MV1 KAINAN KANOZAN KARLBURG KASHIM11 KIRSBERG KODIAK KOGANEI KOGANEI3 KWAJAL26 LEONRDOK MAMMOTHL MARCUS MARPOINT MCD_7850 METSHOVI MIAMI20 MILESMON MIURA MIYAZAKI MIZNAO10 MIZUSGSI MOJ_7288 MON_PEAK MV2ONSLA NOBEY_6M NOME NRAO85_1 OCOTILLO OHIGGINS ONSALA85 OVR_7853 PARKES PBLOSSOM PENTICTN PINFLATS PLATTVIL PRESIDIO PT_REYES PVERDES QUINCY ROBLED32 SAGARA SANPAULA SEATTLE1 SESHAN25 SEST SHANGHAI SINTOTU SINTOTU3 SNDPOINT SOURDOGH SUWON SYOWA TATEYAMA TITIJIMA TOMAKO11 TOULOUSE TROMSONO TRYSILNO TIDBIN64 TIGOWTZL TSUKUBA TSUKU3 URUMQI USSURISK USUDA64 VERAMZSW VERNAL VICTORIA VLA VLA-N8 WHTHORSE YAKATAGA YEBES YELLOWKN YLOW7296 YUMA Appendix B. ~~~~~~~~~~~ List of 61 stations with axis offsets estimated as global parameters: AIRA ALGOPARK BR-VLBA CHICHI10 DSS15 \ DSS45 DSS65 FD-VLBA FORTLEZA GBT-VLBA \ GGAO7108 GIFU11 GILCREEK GOLDVENU HARTRAO \ HATCREEK HAYSTACK HN-VLBA HRAS_085 KASHIM11 \ KASHIM34 KASHIMA KAUAI KOGANEI KOKEE \ KP-VLBA LA-VLBA MARPOINT MATERA MIAMI20 \ MIURA MIZNAO10 MK-VLBA MOJAVE12 NL-VLBA \ NOTO NRAO_140 NRAO20 NRAO85_1 NRAO85_3 \ OHIGGINS OV-VLBA OVRO_130 PIETOWN RICHMOND \ SANTIA12 SC-VLBA SESHAN25 SINTOTU3 SVETLOE \ TATEYAMA TIGOCONC TIGOWTZL TOMAKO11 TSUKUB32 \ URUMQI VNDNBERG WESTFORD YEBES YLOW7296 \ YUMA Appendix C. ~~~~~~~~~~~ 35 stations with constraints on velocity: AUSTINTX AZORES BERMUDA BLOOMIND BREST \ CARNUSTY CARROLGA CHLBOLTN CTVASBAY CTVASTJ \ DAITO GRASSE HOFN HOHENFRG HOHNBERG \ KAINAN KANOZAN KARLBURG KIRSBERG LEONRDOK \ MCD_7850 METSHOVI MILESMON NOBEY_6M OCOTILLO \ SAGARA SEST SUWON TIDBIN64 TITIJIMA \ TOMAKO11 TOULOUSE USSURISK USUDA64 VICTORIA Appendix D. ~~~~~~~~~~~ Velocities of these 23 pairs or triplets of stations were constrainted to be the same: DSS15 GOLDMARS \ DSS45 TIDBIN64 \ DSS65 ROBLED32 MADRID64 \ FORTORDS FORT_ORD FTD_7900 \ GIFU11 GIFU3 \ GGAO7108 GORF7102 \ KASHIM34 KASHIM11 \ KAUAI HALEAKAL \ KOGANEI KOGANEI3 \ METSAHOV METSHOVI \ MIZNAO10 MIZUSGSI VERAMZSW \ MOJAVE12 MOJ_7288 \ NRAO20 GBT-VLBA \ NRAO_140 NRAO85_1 \ ONSALA60 MV2ONSLA ONSALA85 \ OVRO_130 OVR_7853 \ RICHMOND MIAMI20 \ SESHAN25 SHANGHAI \ SINTOTU SINTOTU3 \ TSUKUB32 TSUKU3 TSUKUBA \ PIETOWN VLA VLA-N8 \ WETTZELL TIGOWTZL \ YLOW7296 YELLOWKN Appendix E. ~~~~~~~~~~~ HEO Format version of 2004.03.12 # # Created by nut_res # run by Leonid Petrov ( lpetrov@lacerta.gsfc.nasa.gov ) # on lacerta at 2005.03.01-09:21:29 local time # # Result of VLBI solution heo_05c # Corrections with respect to IERS96 expansion. # #============================ Beginning of format description: ================= # # Specifications of HEO format version of 2004.03.12 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # # HEO format is for describing small harmonic variations in the Earth # orientation. "Small" means that the squares of the rotation angles # can be neglected. # # A file in HEO format consists of records of variable length in # ASCII coding. The records are separated by a character with decimal # code 13. The records of the following types are supported: # # 1) Header record; # 2) Model name record; # 3) Time epoch record; # 4) Harmonic definition records; # 5) Amplitude definition records; # 6) Velocities definition records; # 7) Trailer record. # # Records which start from # character are considered as comments. # # The first record of a valid file in HEO format is the header record. # It is followed by the model name record, time epoch record and then by one # or more harmonic definition records and one or more harmonic definition # records. The last record is a trailer record. All harmonic definition records # should precede amplitude and velocity definition records. Names of a harmonic # in the amplitude or velocity records should be defined in the harmonic # definition record. The number of velocity records can be less than the number # of amplitude records, and the number of amplitude records can be less than # the number of harmonic records. If a harmonic is not defined in an amplitude # records, its amplitude is considered to be zero. If a harmonic is not defined # in a velocity records, the rate of change of the amplitude of that harmonic # is considered to be zero. # # Records format: # # 1) A header record contains the string # "HEO Format version of 2004.03.12" # # The header record allows to distinguish the valid file in the # HEO format from files in other formats and tells to a parsing software # that is the version of the format. # # # 2) A name record defines the name of the model of the harmonic Earth # orientation variations. # # Format of an N-record: # ---------------------- # # Field 1:1 A1 -- Records ID: letter N (decimal code 78). # field 2:3 a2 -- delimiters: blanks. # Field 4:80 A77 -- 77-letter long model name. May contain any # characters in the decimal range [32, 255]. # # 3) An epoch record defines the epoch of the expansion. # An expansion may have mixed terms (t-t0)*sin(at+p), (t-t0)*cos(at+p), # where t is time. The E-record defines the epoch t0 in mixed terms. # If an expansion does not have mixed terms, then the epoch defined in # this record is not used. Time scale TDT is used for defining the # reference epoch. # # Format of a E-record: # --------------------- # # Field 1:1 A1 -- Records ID: letter E (decimal code 69). # field 2:2 a2 -- delimiters: blanks. # Field 4:7 I4 -- Year # field 8:8 a1 -- delimiter: letter . (decimal code 46). # Field 9:10 I2 -- The index of the month in the year in the range [1,12] # field 11:11 a1 -- delimiter: letter . (decimal code 46). # Field 12:13 I2 -- The index of the day in the month in the range [1,31] # field 14:14 a1 -- delimiter: letter - (decimal code 45). # Field 15:16 I2 -- Hour in the range [0,23] # field 17:17 a1 -- delimiter: letter : (decimal code 58). # Field 18:19 I2 -- Minute in the range [0,23] # field 20:20 a1 -- delimiter: letter : (decimal code 58). # Field 21:24 F4.1 -- Seconds in the range [0.0, 59.9] # # # 4) A harmonic definition record defines the argument of the harmonic in # the form {phase + freq*(t-tr) + 1/2*accel*(t-tr)**2} where t is # time in TDT time scale and tr is the reference epoch J2000.0, # 01 January 2000, 12 hours TDT. The file cannot contain more than one # definition of the same harmonic. # # # Format of an H-record: # ---------------------- # # Field 1:1 A1 -- Records ID: letter H (decimal code 72). # field 2:3 a2 -- delimiters: blanks. # Field 4:11 A8 -- 8-letter long harmonic name. May contain any # characters with decimal codes 32-255, but blanks # are allowed only at the end of the harmonic name. # This field should not necessarily have a special # meaning. Parsing software should not try to # interpret this name. # field 12:13 a2 -- delimiters: blanks. # Field 14:25 F11.9 -- Phase of the harmonic in float format. # Units: rad. # field 26:27 a2 -- delimiters: blanks. # Field 28:46 D19.12 -- Frequency of the harmonic in float format. # Units: rad/sec. # field 47:48 a2 -- delimiters: blanks. # Field 49:59 D11.4 -- Acceleration of the harmonic in float format. # Units: rad/sec**2. # field 60:60 a1 -- delimiters: blanks. # field 61:80 A20 -- Comment. Parser ignores contents of this field. # # # 5) An amplitude record specifies the harmonic and 4 amplitudes of # the variation of the Earth orientation: in phase polar motion # (PM_amp_cos), out_of_phase polar motion (PM_amp_sin), in_phase # rotation around E3 axis (E3_amp_cos), out_of_phase rotation around # E3 axis (E3_amp_sin). A file cannot contain more than one amplitude # record for the same harmonic. The harmonic referred in an amplitude record # must be defined in the preceding harmonic definition record. # # These amplitudes allows to define instantaneous small Euler angles of # the perturbations in the Earth rotation with respect to an apriori model # in this way: # # E1 = [ PM_amp_cos + PM_vel_cos*(t-t0) ] * # cos { (ut1-tdt)*2*pi/86400 + phase + freq*(t-tr) + 1/2*accel*(t-tr)**2 } # + [ PM_amp_sin + PM_vel_sin*(t-t0) ] * # sin { (ut1-tdt)*2*pi/86400 + phase + freq*(t-tr) + 1/2*accel*(t-tr)**2 } # # E2 = [ PM_amp_cos + PM_vel_cos*(t-t0) ] * # sin { (ut1-tdt)*2*pi/86400 + phase + freq*(t-tr) + 1/2*accel*(t-tr)**2 } # - [ PM_amp_sin + PM_vel_sin*(t-t0) ] * # cos { (ut1-tdt)*2*pi/86400 + phase + freq*(t-tr) + 1/2*accel*(t-tr)**2 } # # E3 = [ E3_amp_cos + E3_vel_cos*(t-t0) ] * # cos { (ut1-tdt)*2*pi/86400 + phase + freq*(t-tr) + 1/2*accel*(t-tr)**2 } # + [ E3_amp_sin + E3_vel_sin*(t-t0) ] * # sin { (ut1-tdt)*2*pi/86400 + phase + freq*(t-tr) + 1/2*accel*(t-tr)**2 } # # Where # # E1 -- rotation around 1 axis (+Y angle of the polar motion) # E2 -- rotation around 2 axis (+X angle of the polar motion) # E3 -- rotation around 3 axis (-Ut1 angle of the Earth's rotation) # # t-tr -- The interval of time in scale TDT elapsed since # 01 January 2000, 12 hours TDT, in seconds # t-t0 -- The interval of time in scale TDT elapsed since the reference # epoch for the expansion defined in the E-record, in seconds. # # # Format of a A-record # --------------------- # # Field 1:1 A1 -- Record ID: letter A (decimal code 65). # field 2:3 a2 -- Delimiters: blanks. # Field 4:11 A8 -- 8-letter long harmonic name. The harmonic name # must be defined in a preceding H-record. # field 12:13 a2 -- Delimiters: blanks. # Field 14:25 F12.0 -- PM_amp_cos -- cosine amplitude of the small angle # of polar motion. Units: prad. # field 26:26 a1 -- delimiter: blank. # Field 27:38 F12.0 -- PM_amp_sin -- sine amplitude of the small angle # of polar motion. Units: prad. # field 39:39 a2 -- Delimiters: blanks. # Field 41:52 F12.0 -- E3_amp_cos -- cosine amplitude of the small angle # of the Earth rotation around 3 axis. Units: prad. # field 53:53 a1 -- Delimiter: blank. # Field 54:65 F12.0 -- E3_amp_sin -- sine amplitude of the small angle # of the Earth rotation around 3 axis. Units: prad. # # # 6) A velocity record specifies rates of changes of the amplitudes of # the harmonic of the variation of the Earth orientation: in phase polar # motion (PM_vel_cos), out_of_phase polar motion (PM_vel_sin), in_phase # rotation around E3 axis (E3_vel_cos), out_of_phase rotation around # E3 axis (E3_vel_sin). A file cannot contain more than one velocity # record for the same harmonic. The harmonic referred in an velocity record # must be defined in the preceding harmonic definition record. # # # Format of a V-record # --------------------- # # Field 1:1 A1 -- Record ID: letter A (decimal code 65). # field 2:3 a2 -- Delimiters: blanks. # Field 4:11 A8 -- 8-letter long harmonic name. The harmonic name # must be defined in a preceding H-record. # field 12:13 a2 -- Delimiters: blanks. # Field 14:25 F12.0 -- PM_vel_cos -- rate of change of the cosine amplitude # of the small angle of polar motion. # Units: 10^{-21} rad/sec. # field 26:26 a1 -- delimiter: blank. # Field 27:38 F12.0 -- PM_amp_sin -- rate of change of the sine amplitude # of the small angle of polar motion. # Units: 10^{-21} rad/sec. # field 39:39 a2 -- Delimiters: blanks. # Field 41:52 F12.0 -- E3_amp_cos -- rate of change of the cosine amplitude # of the small angle of the Earth rotation around 3 axis. # Units: 10^{-21} rad/sec. # field 53:53 a1 -- Delimiter: blank. # Field 54:65 F12.0 -- E3_amp_sin -- rate of change of the sine amplitude # of the small angle of the Earth rotation around # 3 axis. Units: 10^{-21} rad/sec. # # # 7) Trailer record is the same as the header record. # #============================ End of format description: ======================= # # Name of the model # N VLBI solution heo_05c produced at 2005.02.27-09:41:16 # # Epoch for the model (TAI) # E 1995.01.01-00:00:00.0 # # # Harmonic Phase Frequency Acceleration Comment # rad rad/sec rad/sec^2 # H Term_001 4.417253402 -2.107783540565D-04 0.0000D+00 H Term_002 0.489624095 -2.081391510038D-04 0.0000D+00 H Term_003 3.991352402 -1.484922171179D-04 0.0000D+00 H Term_004 1.808913402 -1.484815201555D-04 0.0000D+00 H Term_005 2.246161402 -1.458637110275D-04 0.0000D+00 H Term_006 0.063723095 -1.458530140651D-04 0.0000D+00 H Term_007 4.164468402 -1.458423171028D-04 0.0000D+00 H Term_008 4.572942402 -1.456432012082D-04 0.0000D+00 H Term_009 1.388224402 -1.454441043329D-04 0.0000D+00 H Term_010 1.345099095 -1.452450074576D-04 0.0000D+00 H Term_011 2.419278402 -1.432138110124D-04 0.0000D+00 H Term_012 0.236839095 -1.432031140500D-04 0.0000D+00 H Term_013 3.262424402 -1.431806099036D-04 0.0000D+00 H Term_014 0.004823095 -1.431581057571D-04 0.0000D+00 H Term_015 0.602187095 -1.428049012801D-04 0.0000D+00 H Term_016 5.545097402 -1.407179995796D-04 0.0000D+00 H Term_017 5.501972402 -1.405189027044D-04 0.0000D+00 H Term_018 0.177940095 -1.405082057420D-04 0.0000D+00 H Term_019 2.317254402 -1.403198058291D-04 0.0000D+00 H Term_020 2.957743402 -1.401656982274D-04 0.0000D+00 H Term_021 0.976979095 -1.382329041286D-04 0.0000D+00 H Term_022 1.574342402 -1.378796996516D-04 0.0000D+00 H Term_023 2.533495402 -1.378690026892D-04 0.0000D+00 H Term_024 1.458334402 -1.378571955051D-04 0.0000D+00 H Term_025 3.332534402 -1.355937010758D-04 0.0000D+00 H Term_026 3.929898402 -1.352404965989D-04 0.0000D+00 H Term_027 5.688090402 -1.329544980231D-04 0.0000D+00 H Term_028 2.047040968 -8.581967459751D-05 -1.0786D-24 H Term_029 6.147787075 -8.580897763545D-05 -8.3538D-24 H Term_030 3.805233245 -8.353367602136D-05 -4.4523D-23 H Term_031 1.622794045 -8.352297905930D-05 -5.1798D-23 H Term_032 0.301850759 -8.319116850644D-05 3.7235D-23 H Term_033 4.402596866 -8.318047154438D-05 2.9960D-23 H Term_034 2.220157666 -8.316977458231D-05 2.2685D-23 H Term_035 5.129734738 -8.312476628880D-05 -4.9672D-23 H Term_036 5.727098359 -8.277156181181D-05 2.4811D-23 H Term_037 2.060043036 -8.090516993029D-05 -6.2087D-24 H Term_038 6.160789143 -8.089447296823D-05 -1.3484D-23 H Term_039 3.978349943 -8.088377600616D-05 -2.0759D-23 H Term_040 0.604741708 -8.083876771265D-05 -9.3116D-23 H Term_041 2.657406657 -8.055196545331D-05 6.8274D-23 H Term_042 0.474967457 -8.054126849124D-05 6.0999D-23 H Term_043 4.575713564 -8.053057152918D-05 5.3724D-23 H Term_044 3.384544529 -8.049626019773D-05 -1.1358D-23 H Term_045 1.202105329 -8.048556323566D-05 -1.8633D-23 H Term_046 1.158980152 -8.028646636042D-05 -1.9172D-23 H Term_047 1.799468950 -8.013235875868D-05 5.5849D-23 H Term_048 5.736542220 -7.859777743001D-05 -6.4203D-23 H Term_049 0.093845711 -7.844366982827D-05 1.0818D-23 H Term_050 0.314852827 -7.827666383922D-05 3.2105D-23 H Term_051 4.415598934 -7.826596687716D-05 2.4830D-23 H Term_052 2.233159734 -7.825526991509D-05 1.7555D-23 H Term_053 0.050720534 -7.824457295303D-05 1.0280D-23 H Term_054 5.142736806 -7.821026162158D-05 -5.4802D-23 H Term_055 2.960297606 -7.819956465951D-05 -6.2078D-23 H Term_056 0.777858406 -7.818886769745D-05 -6.9353D-23 H Term_057 3.600786404 -7.804545705777D-05 1.2944D-23 H Term_058 2.917172429 -7.800046778428D-05 -6.2616D-23 H Term_059 5.740100427 -7.785705714459D-05 1.9681D-23 H Term_060 3.557661227 -7.784636018253D-05 1.2405D-23 H Term_061 1.375222027 -7.783566322047D-05 5.1301D-24 H Term_062 5.696975250 -7.765796026935D-05 1.9142D-23 H Term_063 3.514536050 -7.764726330729D-05 1.1867D-23 H Term_064 4.155024848 -7.749315570555D-05 8.6888D-23 H Term_065 4.882162720 -7.743745044997D-05 7.2557D-24 H Term_066 6.173791211 -7.597996830101D-05 -1.8614D-23 H Term_067 3.991352011 -7.596927133894D-05 -2.5889D-23 H Term_068 1.808912811 -7.595857437688D-05 -3.3164D-23 H Term_069 1.258232574 -7.577015544368D-05 -2.3225D-23 H Term_070 5.358978681 -7.575945848162D-05 -3.0500D-23 H Term_071 2.670408725 -7.563746078609D-05 6.3144D-23 H Term_072 0.487969525 -7.562676382402D-05 5.5869D-23 H Term_073 4.588715632 -7.561606686196D-05 4.8594D-23 H Term_074 2.406276432 -7.560536989990D-05 4.1318D-23 H Term_075 3.397546597 -7.558175553051D-05 -1.6488D-23 H Term_076 1.215107397 -7.557105856844D-05 -2.3764D-23 H Term_077 5.315853504 -7.556036160638D-05 -3.1039D-23 H Term_078 3.133414304 -7.554966464432D-05 -3.8314D-23 H Term_079 5.956342302 -7.540625400463D-05 4.3983D-23 H Term_080 4.655381861 -7.539445632995D-05 1.3478D-23 H Term_081 2.472942661 -7.538375936789D-05 6.2026D-24 H Term_082 1.171982219 -7.537196169321D-05 -2.4302D-23 H Term_083 5.272728327 -7.536126473114D-05 -3.1577D-23 H Term_084 3.994910218 -7.522855105352D-05 5.7994D-23 H Term_085 1.812471018 -7.521785409146D-05 5.0719D-23 H Term_086 5.913217125 -7.520715712940D-05 4.3444D-23 H Term_087 3.730777925 -7.519646016733D-05 3.6169D-23 H Term_088 2.539608890 -7.516214883588D-05 -2.8913D-23 H Term_089 0.357169690 -7.515145187382D-05 -3.6188D-23 H Term_090 4.457915797 -7.514075491175D-05 -4.3464D-23 H Term_091 1.769345841 -7.501875721622D-05 5.0181D-23 H Term_092 5.870091948 -7.500806025416D-05 4.2905D-23 H Term_093 5.979883354 -7.498554659739D-05 8.3283D-24 H Term_094 0.954533311 -7.479824739683D-05 3.8294D-23 H Term_095 4.250719063 -7.371756507422D-05 -1.0484D-24 H Term_096 2.289286979 -7.353986212311D-05 1.2963D-23 H Term_097 0.106847779 -7.352916516105D-05 5.6882D-24 H Term_098 4.207593886 -7.351846819899D-05 -1.5870D-24 H Term_099 0.833985651 -7.347345990547D-05 -7.3944D-23 H Term_100 4.428601001 -7.335146220994D-05 1.9700D-23 H Term_101 2.246161801 -7.334076524787D-05 1.2425D-23 H Term_102 0.063722601 -7.333006828581D-05 5.1496D-24 H Term_103 4.164468709 -7.331937132375D-05 -2.1256D-24 H Term_104 1.982029509 -7.330867436169D-05 -9.4009D-24 H Term_105 5.155738873 -7.329575695436D-05 -5.9932D-23 H Term_106 2.973299673 -7.328505999229D-05 -6.7208D-23 H Term_107 0.790860473 -7.327436303023D-05 -7.4483D-23 H Term_108 4.891606581 -7.326366606817D-05 -8.1758D-23 H Term_109 4.826056636 -7.317024021321D-05 0.0000D+00 H Term_110 5.796227672 -7.314164935261D-05 1.5089D-23 H Term_111 3.613788472 -7.313095239055D-05 7.8138D-24 H Term_112 1.431349272 -7.312025542848D-05 5.3862D-25 H Term_113 6.210573888 -7.310955138024D-05 0.0000D+00 H Term_114 1.531755876 -7.309938490561D-05 0.0000D+00 H Term_115 3.136123170 -7.308921843099D-05 0.0000D+00 H Term_116 4.740490464 -7.307905195636D-05 0.0000D+00 H Term_117 0.061672452 -7.306888548173D-05 0.0000D+00 H Term_118 1.666039746 -7.305871900710D-05 0.0000D+00 H Term_119 3.270407040 -7.304855253247D-05 0.0000D+00 H Term_120 4.874774335 -7.303838605785D-05 0.0000D+00 H Term_121 0.195956322 -7.302821958322D-05 0.0000D+00 H Term_122 1.800323616 -7.301805310859D-05 0.0000D+00 H Term_123 3.404690911 -7.300788663397D-05 0.0000D+00 H Term_124 5.009058205 -7.299772015934D-05 0.0000D+00 H Term_125 2.843525423 -7.298756077089D-05 8.6908D-23 H Term_126 0.661086223 -7.297686380883D-05 7.9632D-23 H Term_127 1.652356387 -7.295324943944D-05 2.1826D-23 H Term_128 5.753102495 -7.294255247737D-05 1.4550D-23 H Term_129 3.570663295 -7.293185551531D-05 7.2752D-24 H Term_130 1.388224095 -7.292115855325D-05 0.0000D+00 H Term_131 1.388224095 -7.292115855325D-05 0.0000D+00 H Term_132 5.488970202 -7.291046159118D-05 -7.2752D-24 H Term_133 3.306531002 -7.289976462912D-05 -1.4550D-23 H Term_134 2.587317089 -7.288757331455D-05 0.0000D+00 H Term_135 4.297801167 -7.287615025973D-05 -7.2357D-23 H Term_136 2.115361967 -7.286545329767D-05 -7.9632D-23 H Term_137 6.216108074 -7.285475633560D-05 -8.6908D-23 H Term_138 4.126582386 -7.284405228736D-05 0.0000D+00 H Term_139 5.723339134 -7.283393403886D-05 0.0000D+00 H Term_140 1.036910575 -7.282381579037D-05 0.0000D+00 H Term_141 2.633667323 -7.281369754187D-05 0.0000D+00 H Term_142 4.230424071 -7.280357929337D-05 0.0000D+00 H Term_143 5.827180819 -7.279346104487D-05 0.0000D+00 H Term_144 1.140752260 -7.278334279638D-05 0.0000D+00 H Term_145 2.737509008 -7.277322454788D-05 0.0000D+00 H Term_146 4.334265756 -7.276310629938D-05 0.0000D+00 H Term_147 5.931022504 -7.275298805088D-05 0.0000D+00 H Term_148 1.244593945 -7.274286980239D-05 0.0000D+00 H Term_149 3.527538117 -7.273275864007D-05 6.7366D-24 H Term_150 1.345098917 -7.272206167801D-05 -5.3862D-25 H Term_151 2.755850765 -7.271134569592D-05 -4.6109D-24 H Term_152 0.573411565 -7.270064873386D-05 -1.1886D-23 H Term_153 5.555636431 -7.268885105917D-05 -4.2391D-23 H Term_154 4.233576861 -7.267207689328D-05 0.0000D+00 H Term_155 4.168026916 -7.257865103833D-05 8.1758D-23 H Term_156 1.985587716 -7.256795407626D-05 7.4483D-23 H Term_157 6.086333823 -7.255725711420D-05 6.7208D-23 H Term_158 0.794418681 -7.253364274481D-05 9.4009D-24 H Term_159 4.895164788 -7.252294578275D-05 2.1256D-24 H Term_160 2.712725588 -7.251224882068D-05 -5.1496D-24 H Term_161 0.530286388 -7.250155185862D-05 -1.2425D-23 H Term_162 5.987047175 -7.247296278279D-05 0.0000D+00 H Term_163 0.034655798 -7.239840495350D-05 0.0000D+00 H Term_164 1.942462539 -7.236885720103D-05 7.3944D-23 H Term_165 6.049088540 -7.234063201794D-05 0.0000D+00 H Term_166 4.852039611 -7.232384890751D-05 1.5870D-24 H Term_167 2.669600411 -7.231315194544D-05 -5.6882D-24 H Term_168 0.487161211 -7.230245498338D-05 -1.2963D-23 H Term_169 1.457332181 -7.227386412351D-05 0.0000D+00 H Term_170 0.919827049 -7.215831825240D-05 0.0000D+00 H Term_171 4.808914433 -7.212475203227D-05 1.0484D-24 H Term_172 4.765789256 -7.192565515703D-05 5.0980D-25 H Term_173 5.371980749 -7.084495381440D-05 -3.5630D-23 H Term_174 3.189541549 -7.083425685234D-05 -4.2905D-23 H Term_175 4.601717699 -7.070156219474D-05 4.3464D-23 H Term_176 2.419278499 -7.069086523268D-05 3.6188D-23 H Term_177 1.228109464 -7.065655390122D-05 -2.8894D-23 H Term_178 5.328855571 -7.064585693916D-05 -3.6169D-23 H Term_179 3.146416371 -7.063515997710D-05 -4.3444D-23 H Term_180 0.963977171 -7.062446301503D-05 -5.0719D-23 H Term_181 5.969344370 -7.049174933741D-05 3.8853D-23 H Term_182 3.786905170 -7.048105237535D-05 3.1577D-23 H Term_183 2.485944728 -7.046925470067D-05 1.0726D-24 H Term_184 0.303505528 -7.045855773861D-05 -6.2026D-24 H Term_185 3.103291194 -7.043606310186D-05 -4.3983D-23 H Term_186 1.825473085 -7.030334942424D-05 4.5589D-23 H Term_187 5.926219193 -7.029265246218D-05 3.8314D-23 H Term_188 3.743779993 -7.028195550011D-05 3.1039D-23 H Term_189 1.561340793 -7.027125853805D-05 2.3764D-23 H Term_190 0.260380351 -7.025946086337D-05 -6.7413D-24 H Term_191 0.370171757 -7.023694720660D-05 -4.1318D-23 H Term_192 4.470917865 -7.022625024453D-05 -4.8594D-23 H Term_193 2.288478665 -7.021555328247D-05 -5.5869D-23 H Term_194 5.883094015 -7.009355558694D-05 3.7775D-23 H Term_195 3.700654815 -7.008285862488D-05 3.0500D-23 H Term_196 3.810446222 -7.006034496810D-05 -4.0770D-24 H Term_197 0.327046580 -7.003785033136D-05 -4.1857D-23 H Term_198 0.967535379 -6.988374272961D-05 3.3164D-23 H Term_199 5.068281486 -6.987304576755D-05 2.5889D-23 H Term_200 2.885842286 -6.986234880549D-05 1.8614D-23 H Term_201 0.924410201 -6.968464585437D-05 3.2626D-23 H Term_202 5.025156309 -6.967394889231D-05 2.5351D-23 H Term_203 4.904608648 -6.834916140095D-05 -8.6888D-23 H Term_204 1.444351339 -6.820575076127D-05 -4.5915D-24 H Term_205 5.545097447 -6.819505379920D-05 -1.1867D-23 H Term_206 3.583665362 -6.801735084809D-05 2.1451D-24 H Term_207 1.401226162 -6.800665388603D-05 -5.1301D-24 H Term_208 5.501972269 -6.799595692396D-05 -1.2405D-23 H Term_209 3.319533069 -6.798525996190D-05 -1.9681D-23 H Term_210 2.128364034 -6.795094863045D-05 -8.4762D-23 H Term_211 6.229110141 -6.794025166838D-05 -9.2038D-23 H Term_212 6.142461068 -6.784184932222D-05 6.2616D-23 H Term_213 2.659061426 -6.781935468547D-05 2.4836D-23 H Term_214 1.358100985 -6.780755701079D-05 -5.6687D-24 H Term_215 2.768852833 -6.779684102870D-05 -9.7410D-24 H Term_216 0.586413633 -6.778614406664D-05 -1.7016D-23 H Term_217 1.998589783 -6.765344940904D-05 6.9353D-23 H Term_218 6.099335891 -6.764275244698D-05 6.2078D-23 H Term_219 3.916896691 -6.763205548492D-05 5.4802D-23 H Term_220 2.725727655 -6.759774415346D-05 -1.0280D-23 H Term_221 0.543288455 -6.758704719140D-05 -1.7555D-23 H Term_222 4.644034563 -6.757635022934D-05 -2.4830D-23 H Term_223 6.166002120 -6.742114191497D-05 2.6962D-23 H Term_224 2.682602478 -6.739864727823D-05 -1.0818D-23 H Term_225 0.500163278 -6.738795031616D-05 -1.8093D-23 H Term_226 3.323091277 -6.724453967648D-05 6.4203D-23 H Term_227 1.140652077 -6.723384271442D-05 5.6928D-23 H Term_228 1.867789949 -6.717813745884D-05 -2.2704D-23 H Term_229 5.968536056 -6.716744049677D-05 -2.9980D-23 H Term_230 3.279966099 -6.704544280124D-05 6.3665D-23 H Term_231 3.159418439 -6.572065530988D-05 -4.8574D-23 H Term_232 0.976979239 -6.570995834782D-05 -5.5849D-23 H Term_233 1.617468037 -6.555585074607D-05 1.9172D-23 H Term_234 4.527045109 -6.551084245255D-05 -5.3185D-23 H Term_235 2.344605909 -6.550014549049D-05 -6.0460D-23 H Term_236 3.756782060 -6.536745083289D-05 2.5909D-23 H Term_237 1.574342860 -6.535675387083D-05 1.8633D-23 H Term_238 4.483919932 -6.531174557731D-05 -5.3724D-23 H Term_239 2.301480732 -6.530104861525D-05 -6.0999D-23 H Term_240 0.119041532 -6.529035165319D-05 -6.8274D-23 H Term_241 5.124408731 -6.515763797557D-05 2.1298D-23 H Term_242 2.941969531 -6.514694101350D-05 1.4023D-23 H Term_243 1.641009089 -6.513514333882D-05 -1.6482D-23 H Term_244 5.741755196 -6.512444637676D-05 -2.3758D-23 H Term_245 4.440794755 -6.511264870208D-05 -5.4262D-23 H Term_246 2.171706481 -6.500354939385D-05 9.3116D-23 H Term_247 5.081283553 -6.495854110033D-05 2.0759D-23 H Term_248 2.898844353 -6.494784413827D-05 1.3484D-23 H Term_249 0.716405153 -6.493714717620D-05 6.2087D-24 H Term_250 3.625982225 -6.489213888269D-05 -6.6148D-23 H Term_251 1.443543025 -6.488144192062D-05 -7.3424D-23 H Term_252 5.038158376 -6.475944422509D-05 2.0220D-23 H Term_253 2.855719176 -6.474874726303D-05 1.2945D-23 H Term_254 5.678647175 -6.460533662335D-05 9.5242D-23 H Term_255 3.496207975 -6.459463966128D-05 8.7967D-23 H Term_256 4.223345847 -6.453893440570D-05 8.3343D-24 H Term_257 5.514974337 -6.308145225675D-05 -1.7535D-23 H Term_258 3.332535137 -6.307075529468D-05 -2.4811D-23 H Term_259 6.242112209 -6.302574700116D-05 -9.7168D-23 H Term_260 4.059673009 -6.301505003910D-05 -1.0444D-22 H Term_261 0.599415700 -6.287163939942D-05 -2.2146D-23 H Term_262 4.700161807 -6.286094243736D-05 -2.9422D-23 H Term_263 3.929898758 -6.271755081770D-05 4.9672D-23 H Term_264 0.556290523 -6.267254252418D-05 -2.2685D-23 H Term_265 4.657036630 -6.266184556212D-05 -2.9960D-23 H Term_266 2.474597430 -6.265114860005D-05 -3.7235D-23 H Term_267 1.196779321 -6.251843492243D-05 5.2336D-23 H Term_268 3.996564987 -6.249594028569D-05 1.4556D-23 H Term_269 0.513165346 -6.247344564894D-05 -2.3224D-23 H Term_270 1.153654144 -6.231933804720D-05 5.1798D-23 H Term_271 5.254400251 -6.230864108513D-05 4.4523D-23 H Term_272 3.071961051 -6.229794412307D-05 3.7247D-23 H Term_273 5.981538123 -6.225293582955D-05 -3.5110D-23 H Term_274 1.110528967 -6.212024117196D-05 5.1259D-23 H Term_275 2.357607977 -6.058564082327D-05 -6.5590D-23 H Term_276 2.314482800 -6.038654394803D-05 -6.6129D-23 H Term_277 0.132043600 -6.037584698597D-05 -7.3404D-23 H Term_278 2.954971598 -6.023243634629D-05 8.8924D-24 H Term_279 2.911846421 -6.003333947105D-05 8.3538D-24 H Term_280 0.729407221 -6.002264250898D-05 1.0786D-24 H Term_281 3.509210042 -5.968013499406D-05 8.2837D-23 H Term_282 1.326770842 -5.966943803200D-05 7.5561D-23 H Term_283 4.670038698 -5.774734089490D-05 -3.5090D-23 H Term_284 5.267402319 -5.739413641791D-05 3.9393D-23 H Term_285 3.084963119 -5.738343945585D-05 3.2117D-23 H Term_286 5.864765940 -5.704093194093D-05 1.1388D-22 H Term_287 0.742409289 -5.510813784177D-05 -4.0515D-24 H Term_288 0.047276787 6.003333947172D-05 0.0000D+00 H Term_289 1.805469095 6.231933804749D-05 0.0000D+00 H Term_290 2.402832095 6.267254252446D-05 0.0000D+00 H Term_291 0.060278787 6.494784413786D-05 0.0000D+00 H Term_292 4.161024095 6.495854110023D-05 0.0000D+00 H Term_293 4.758388095 6.531174557720D-05 0.0000D+00 H Term_294 2.415834095 6.758704719061D-05 0.0000D+00 H Term_295 3.557457651 6.759774411974D-05 1.0280D-23 H Term_296 0.598742787 6.799595692287D-05 0.0000D+00 H Term_297 5.133180095 6.988374272874D-05 0.0000D+00 H Term_298 5.730543095 7.023694720571D-05 0.0000D+00 H Term_299 5.614535095 7.025945135218D-05 0.0000D+00 H Term_300 2.356935095 7.028195549864D-05 0.0000D+00 H Term_301 0.174495787 7.029265246100D-05 0.0000D+00 H Term_302 2.954299095 7.063515997561D-05 0.0000D+00 H Term_303 4.390268095 7.232384890619D-05 0.0000D+00 H Term_304 4.347143095 7.252294578148D-05 0.0000D+00 H Term_305 4.755616095 7.272206167609D-05 0.0000D+00 H Term_306 3.753337095 7.291046158901D-05 0.0000D+00 H Term_307 4.894961211 7.292115851952D-05 0.0000D+00 H Term_308 2.530051095 7.293185551375D-05 0.0000D+00 H Term_309 4.669365095 7.312025542667D-05 0.0000D+00 H Term_310 1.936246095 7.331937132128D-05 0.0000D+00 H Term_311 0.187497787 7.520715712715D-05 0.0000D+00 H Term_312 0.784860787 7.556036160412D-05 0.0000D+00 H Term_313 4.885607095 7.557105856649D-05 0.0000D+00 H Term_314 2.543053095 7.784636017989D-05 0.0000D+00 H Term_315 6.049994095 7.824457294979D-05 0.0000D+00 H Term_316 3.867555095 7.825526991216D-05 0.0000D+00 H Term_317 2.122364095 8.088377600253D-05 0.0000D+00 H Term_318 3.371543095 1.329544980231D-04 0.0000D+00 H Term_319 5.129735095 1.352404965989D-04 0.0000D+00 H Term_320 5.727099095 1.355937010758D-04 0.0000D+00 H Term_321 1.318113787 1.378571955051D-04 0.0000D+00 H Term_322 0.242952787 1.378690026892D-04 0.0000D+00 H Term_323 1.202105787 1.378796996516D-04 0.0000D+00 H Term_324 1.799469095 1.382329041286D-04 0.0000D+00 H Term_325 6.101890095 1.401656982274D-04 0.0000D+00 H Term_326 0.459193787 1.403198058291D-04 0.0000D+00 H Term_327 2.598508095 1.405082057420D-04 0.0000D+00 H Term_328 3.557661095 1.405189027044D-04 0.0000D+00 H Term_329 3.514536095 1.407179995796D-04 0.0000D+00 H Term_330 2.174261095 1.428049012801D-04 0.0000D+00 H Term_331 2.771625095 1.431581057571D-04 0.0000D+00 H Term_332 5.797209095 1.431806099036D-04 0.0000D+00 H Term_333 2.539609095 1.432031140500D-04 0.0000D+00 H Term_334 0.357169787 1.432138110124D-04 0.0000D+00 H Term_335 1.431349095 1.452450074576D-04 0.0000D+00 H Term_336 1.388223787 1.454441043329D-04 0.0000D+00 H Term_337 4.486691095 1.456432012082D-04 0.0000D+00 H Term_338 4.895165095 1.458423171028D-04 0.0000D+00 H Term_339 2.712725095 1.458530140651D-04 0.0000D+00 H Term_340 0.530286787 1.458637110275D-04 0.0000D+00 H Term_341 0.967534787 1.484815201555D-04 0.0000D+00 H Term_342 5.068281095 1.484922171179D-04 0.0000D+00 H Term_343 2.286824095 2.081391510038D-04 0.0000D+00 H Term_344 4.642380095 2.107783540565D-04 0.0000D+00 # # Amplitudes of harmonic variations in the Earth rotation # # Harmonic PM_cos PM_sin E3_cos E3_sin # prad prad prad prad # A Term_001 5. 10. -10. 1. A Term_002 -21. -2. 13. -18. A Term_003 1. 27. 8. 3. A Term_004 11. 7. 10. 7. A Term_005 3. 25. -25. 2. A Term_006 -6. 25. 40. -31. A Term_007 116. 62. 162. -43. A Term_008 -1. -17. 16. 4. A Term_009 413. 424. 538. -31. A Term_010 8. 9. 35. -23. A Term_011 -9. -3. 12. 1. A Term_012 11. 0. -7. 13. A Term_013 14. 7. -3. -1. A Term_014 5. 29. 19. 15. A Term_015 -9. 7. 12. 8. A Term_016 -6. 12. -2. -6. A Term_017 282. 1125. 1196. 476. A Term_018 -9. 49. 40. 11. A Term_019 -11. -1. -20. -17. A Term_020 0. 20. -9. 12. A Term_021 4. 62. 36. -1. A Term_022 51. 182. 265. 101. A Term_023 -11. 4. 1. 7. A Term_024 -18. -4. 1. 8. A Term_025 -2. 39. 59. 44. A Term_026 17. 46. 49. 11. A Term_027 4. 21. 3. 12. A Term_028 -7. 2. 0. 0. A Term_029 25. -13. 0. 0. A Term_030 -34. 18. 0. 0. A Term_031 -29. 2. 0. 0. A Term_032 -21. 5. 0. 0. A Term_033 -9. 1. 0. 0. A Term_034 -8. -27. 0. 0. A Term_035 -21. 0. 0. 0. A Term_036 -20. 11. 0. 0. A Term_037 11. -8. 0. 0. A Term_038 12. 1. 0. 0. A Term_039 27. -17. 0. -5. A Term_040 -9. -16. 0. 0. A Term_041 -4. -19. 0. 0. A Term_042 5. 8. 0. 0. A Term_043 14. 13. 0. 0. A Term_044 19. 8. 0. 0. A Term_045 -24. 6. 0. 0. A Term_046 8. 5. 0. 0. A Term_047 -8. -19. 0. 0. A Term_048 5. 13. 0. 0. A Term_049 10. -17. 0. 0. A Term_050 0. 9. 0. 0. A Term_051 12. -3. 0. 0. A Term_052 -14. -37. 40. 29. A Term_053 -41. -55. 40. 30. A Term_054 24. 10. 0. 0. A Term_055 6. -5. 0. 0. A Term_056 -9. -9. 0. 0. A Term_057 11. -4. 0. 0. A Term_058 -2. 25. 0. 0. A Term_059 -21. 27. 0. 0. A Term_060 -15. -17. 15. 4. A Term_061 1. -3. 0. 0. A Term_062 -22. -32. 0. 0. A Term_063 6. 7. 0. 0. A Term_064 -8. -9. 0. 0. A Term_065 -9. 24. 0. 0. A Term_066 -6. 3. 0. 0. A Term_067 -16. -9. 0. 0. A Term_068 7. -24. 0. 0. A Term_069 19. -4. 0. 0. A Term_070 7. -5. 0. 0. A Term_071 -3. 5. 0. 0. A Term_072 0. -21. 0. 0. A Term_073 7. -4. 0. 0. A Term_074 22. 8. 0. 0. A Term_075 -35. -6. 0. 0. A Term_076 -14. 3. -1. 25. A Term_077 -26. -69. 47. 84. A Term_078 4. -5. 0. 0. A Term_079 -5. 2. 0. 0. A Term_080 -8. 19. 0. 0. A Term_081 17. -3. 0. 0. A Term_082 2. -14. 0. 0. A Term_083 -13. -9. 0. 0. A Term_084 -24. -8. 0. 0. A Term_085 2. 6. 0. 0. A Term_086 -9. 9. -6. -9. A Term_087 -6. 13. 0. 0. A Term_088 -2. 11. 0. 0. A Term_089 -11. -4. 0. 0. A Term_090 5. 13. 0. 0. A Term_091 -30. 4. 0. 0. A Term_092 -22. -15. 0. 0. A Term_093 20. 3. 0. 0. A Term_094 -2. 1. 0. 0. A Term_095 -20. -25. 0. 0. A Term_096 -14. -13. 0. 0. A Term_097 4. 0. 0. 0. A Term_098 -4. 3. 0. 0. A Term_099 2. 0. 0. 0. A Term_100 57. 29. 0. 0. A Term_101 35. -1. 0. 0. A Term_102 15. 7. 0. 0. A Term_103 -72. -35. -3. 9. A Term_104 15. -10. 0. 0. A Term_105 -35. -10. 0. 0. A Term_106 0. -44. 0. 0. A Term_107 -6. -17. 0. 0. A Term_108 3. -5. 0. 0. A Term_109 -56. -8. 0. 0. A Term_110 -2. -77. 0. 0. A Term_111 -124. -54. 0. 0. A Term_112 -87. 111. 0. 1. A Term_113 -91. -153. 0. 0. A Term_114 163. 438. 0. 0. A Term_115 380. -266. 0. 0. A Term_116 97. -15. 0. 0. A Term_117 3. 227. 0. 0. A Term_118 -6. -196. 0. 0. A Term_119 -14. 74. 0. 0. A Term_120 -15. -57. 0. 0. A Term_121 13. 33. 0. 0. A Term_122 23. -50. 0. 0. A Term_123 -65. 19. 0. 0. A Term_124 105. 46. 0. 0. A Term_125 80. 17. 0. 0. A Term_126 74. 27. 0. 0. A Term_127 -29. 3. 0. 0. A Term_128 47. -23. 0. 0. A Term_129 -182. -233. 67. 150. A Term_130 0. 0. 0. 0. A Term_131 -622. -57. 666. 1272. A Term_132 -523. 112. -24. -49. A Term_133 45. 142. 0. 0. A Term_134 -98. -6. 0. 0. A Term_135 -28. 38. 0. 0. A Term_136 45. 20. 0. 0. A Term_137 -17. -9. 0. 0. A Term_138 5. 29. 0. 0. A Term_139 7. 21. 0. 0. A Term_140 56. 30. 0. 0. A Term_141 -4. -43. 0. 0. A Term_142 0. 6. 0. 0. A Term_143 29. 3. 0. 0. A Term_144 7. -59. 0. 0. A Term_145 -60. -13. 0. 0. A Term_146 27. -30. 0. 0. A Term_147 -58. 2. 0. 0. A Term_148 42. 23. 0. 0. A Term_149 1. -52. 0. 0. A Term_150 -11. 32. 24. 82. A Term_151 -51. 66. 0. 0. A Term_152 -13. -16. 0. 0. A Term_153 -21. -5. 0. 0. A Term_154 4. -14. 0. 0. A Term_155 -11. -3. 0. 0. A Term_156 3. 1. 0. 0. A Term_157 25. -18. 0. 0. A Term_158 -8. -13. 0. 0. A Term_159 54. 83. -260. -404. A Term_160 0. -24. 0. 0. A Term_161 -8. 12. 0. 0. A Term_162 -7. 1. 0. 0. A Term_163 4. -9. 0. 0. A Term_164 1. -15. 0. 0. A Term_165 -19. 27. 0. 0. A Term_166 43. 17. -3. -7. A Term_167 12. -23. 0. 0. A Term_168 4. -19. 0. 0. A Term_169 32. -12. 0. 0. A Term_170 2. 15. 0. 0. A Term_171 12. 2. 0. 0. A Term_172 12. 19. 0. 0. A Term_173 5. 9. 0. 0. A Term_174 -7. 14. 0. 0. A Term_175 27. 18. 0. 0. A Term_176 28. -19. 0. 0. A Term_177 11. -5. 0. 0. A Term_178 -17. -2. 0. 0. A Term_179 0. -1. 12. 9. A Term_180 -4. -8. 0. 0. A Term_181 -31. 25. 0. 0. A Term_182 -8. -23. 0. 0. A Term_183 -7. -22. 0. 0. A Term_184 22. -28. 0. 0. A Term_185 -26. -3. 0. 0. A Term_186 9. 9. 0. 0. A Term_187 -4. -5. 10. 9. A Term_188 45. 11. 51. 78. A Term_189 6. 11. 0. 0. A Term_190 -23. -25. -41. -5. A Term_191 46. 2. 18. 52. A Term_192 -17. 21. 0. 0. A Term_193 6. 23. 0. 0. A Term_194 28. 14. 0. 0. A Term_195 9. -6. 0. 0. A Term_196 2. -25. 0. 0. A Term_197 -8. 21. 0. 0. A Term_198 -12. -10. 13. -19. A Term_199 12. 2. 0. 0. A Term_200 -4. 1. 0. 0. A Term_201 17. -1. 0. 0. A Term_202 -8. 5. 0. 0. A Term_203 -7. -4. 0. 0. A Term_204 -8. 10. 0. 0. A Term_205 -13. -14. 0. 0. A Term_206 -9. 3. 0. 0. A Term_207 -8. -38. 0. 0. A Term_208 -10. -7. 2. -2. A Term_209 1. 1. 0. 0. A Term_210 10. -2. 0. 0. A Term_211 -4. -3. 0. 0. A Term_212 -8. -4. 0. 0. A Term_213 -2. -32. 0. 0. A Term_214 2. -17. 0. 0. A Term_215 -33. -2. 0. 0. A Term_216 -16. 34. 0. 0. A Term_217 -3. -11. 0. 0. A Term_218 12. 0. 0. 0. A Term_219 19. 12. 0. 0. A Term_220 -62. 6. -941. -1295. A Term_221 -23. 7. -160. -231. A Term_222 8. -5. 0. 0. A Term_223 24. 14. 0. 0. A Term_224 -4. -1. 0. 0. A Term_225 18. -8. 0. 0. A Term_226 -22. -1. 0. 0. A Term_227 5. 6. 0. 0. A Term_228 -6. 5. 0. 0. A Term_229 -18. -6. 0. 0. A Term_230 22. 10. 0. 0. A Term_231 19. 10. 0. 0. A Term_232 -2. 26. 0. 0. A Term_233 2. -17. 0. 0. A Term_234 30. 13. 0. 0. A Term_235 -7. -4. 0. 0. A Term_236 -11. -2. 0. 0. A Term_237 -10. 5. 0. 0. A Term_238 -4. 28. -57. -61. A Term_239 -13. 21. 0. 0. A Term_240 -30. 27. 0. 0. A Term_241 17. -4. 0. 0. A Term_242 0. 2. 0. 0. A Term_243 9. -2. 0. 0. A Term_244 15. -12. 0. 0. A Term_245 13. 12. 0. 0. A Term_246 21. -12. 0. 0. A Term_247 57. -32. -164. -376. A Term_248 3. 16. -25. -72. A Term_249 5. -11. 0. 0. A Term_250 10. 6. 0. 0. A Term_251 -20. -1. 0. 0. A Term_252 -9. -15. 0. 0. A Term_253 12. 1. 0. 0. A Term_254 -10. -4. 0. 0. A Term_255 -8. -18. 0. 0. A Term_256 15. -20. 0. 0. A Term_257 -29. -14. 0. 0. A Term_258 3. -16. 0. 0. A Term_259 0. 8. 0. 0. A Term_260 25. 13. 0. 0. A Term_261 -39. 6. 0. 0. A Term_262 -11. -20. 0. 0. A Term_263 -68. 13. 0. 0. A Term_264 36. 21. -15. -68. A Term_265 -3. -4. 0. 0. A Term_266 3. 16. 0. 0. A Term_267 -52. 19. 0. 0. A Term_268 -55. 21. 0. 0. A Term_269 -14. -6. 0. 0. A Term_270 35. 4. 17. -82. A Term_271 20. 23. 0. 0. A Term_272 12. 12. 0. 0. A Term_273 -8. 10. 0. 0. A Term_274 -19. -3. 0. 0. A Term_275 21. 9. 0. 0. A Term_276 0. -14. 0. 0. A Term_277 20. -15. 0. 0. A Term_278 -6. 9. 0. 0. A Term_279 6. -29. -9. -22. A Term_280 -23. -20. 0. 0. A Term_281 38. -34. 0. 0. A Term_282 1. 27. 0. 0. A Term_283 -7. 39. 0. 0. A Term_284 45. 6. 0. 0. A Term_285 -23. -17. 0. 0. A Term_286 24. 8. 0. 0. A Term_287 22. 26. 0. 0. A Term_288 5. -16. 0. 0. A Term_289 7. -6. 0. 0. A Term_290 12. -42. 0. 0. A Term_291 -13. -25. 0. 0. A Term_292 18. -139. 0. 0. A Term_293 9. -27. 0. 0. A Term_294 32. -126. 0. 0. A Term_295 -229. 634. 0. 0. A Term_296 14. -5. 0. 0. A Term_297 -4. 10. 0. 0. A Term_298 -11. 7. 0. 0. A Term_299 -2. 5. 0. 0. A Term_300 29. -21. 0. 0. A Term_301 -8. 8. 0. 0. A Term_302 9. -17. 0. 0. A Term_303 29. 7. 0. 0. A Term_304 97. -238. 0. 0. A Term_305 -71. -43. 0. 0. A Term_306 -21. -14. 0. 0. A Term_307 1009. -724. 0. 0. A Term_308 5. -114. 0. 0. A Term_309 17. -12. 0. 0. A Term_310 -16. -20. 0. 0. A Term_311 22. -16. 0. 0. A Term_312 3. -16. 0. 0. A Term_313 -20. 4. 0. 0. A Term_314 16. -2. 0. 0. A Term_315 43. -21. 0. 0. A Term_316 7. -3. 0. 0. A Term_317 25. 16. 0. 0. A Term_318 5. -2. 0. 0. A Term_319 -25. -4. 0. 0. A Term_320 -21. -8. 0. 0. A Term_321 -3. -8. 0. 0. A Term_322 -6. -12. 0. 0. A Term_323 -61. -58. 0. 0. A Term_324 -15. 6. 0. 0. A Term_325 8. -2. 0. 0. A Term_326 -6. -29. 0. 0. A Term_327 -9. -25. 0. 0. A Term_328 -225. -347. 0. 0. A Term_329 11. 13. 0. 0. A Term_330 -1. 3. 0. 0. A Term_331 2. -19. 0. 0. A Term_332 -7. 1. 0. 0. A Term_333 0. -8. 0. 0. A Term_334 -5. -11. 0. 0. A Term_335 -35. -7. 0. 0. A Term_336 -27. -147. 0. 0. A Term_337 -13. 0. 0. 0. A Term_338 -39. -94. 0. 0. A Term_339 -10. -16. 0. 0. A Term_340 2. -5. 0. 0. A Term_341 15. 3. 0. 0. A Term_342 6. 1. 0. 0. A Term_343 7. -9. 0. 0. A Term_344 7. 5. 0. 0. # # Rate of change of the amplitudes of harmonic variations in the Earth rotation # # Harmonic PM_rate_cos PM_rate_sin E3_rate_cos E3_rate_sin # 10^{-21} rad/s 10^{-21} rad/s # V Term_130 -3275. -1314. 0. 0. # HEO Format version of 2004.03.12