KPL/PCK P_constants (PcK) SPICE kernel file =========================================================================== By: Nat Bachman (NAIF) 1997 November 19 Organization -------------------------------------------------------- The contents of this file are as follows. Introductory Information: -- Version description -- Disclaimer -- Sources -- Explanation -- Body numbers and names Pck Data: -- Orientation constants for the Sun and planets -- Orientation constants for satellites -- Orientation constants for asteroids Gaspra and Ida -- Radii of Sun and planets -- Radii of satellites, where available -- Radii of asteroids Gaspra and Ida Version description -------------------------------------------------------- This file was created on November 19, 1997. This is a "bug fix" release which corrects errors found in the previous version of this file: PCK00005.TPC, released June 25, 1995. A corrections have been made to the W0 term for Metis; the value published in the 1994 IAU report was incorrect. Also, corrections have been made to the assignments of values for Phobos: the RA, Dec, and W assignments for Phobos had extraneous trailing zeros in their coefficient sets, and the nutation precession coefficient sets lacked a final set of trailing zeros. This error caused incorrect evaluation of Phobos's orientation on some computer systems. The data in the file are based primarily on the `Report of the IAU/IAG/COSPAR Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: 1994'. See `Sources' below for details. This file contains updates of constants contained in the previous version of the file, plus data for the asteroids Gaspra and Ida. The use of the `PCK_version' kernel variable has been discontinued. The previous file version was pck00004.tpc. 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 file are: 1. `Report of the IAU/IAG/COSPAR Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: 1994', to be published. 2. `The Astronomical Almanac', 1993. 3. `Planetary Geodetic Control Using Satellite Imaging', Journal of Geophysical Research, Vol. 84, No. B3, March 10, 1979, by Thomas C. Duxbury. This paper is cataloged as NAIF document 190.0. 4. Letter from Thomas C. Duxbury to Dr. Ephraim Lazeryevich Akim, Keldish Institute of Applied Mathematics, USSR Academy of Sciences, Moscow, USSR. This letter is catalogued as NAIF document number 195.0. 5. `Geophysical Coordinate Transformations', by Christopher T. Russell. Cosmic Electrodynamics 2 (1971) 184-186. NAIF document 181.0. 6. `Placeholder' values were supplied by NAIF for some radii of the bodies listed below: Body NAIF ID code ---- ------------ Thebe 514 Metis 516 Helene 612 Larissa 807 See the discussion below for further information. 7. The correct value of the Metis W0 term is given in JPL IOM 312.F-97-059 "Revised rotation angle for Jupiter satellite 516 Metis," September 16, 1997, by J. H. Lieske. Most values are from the `IAU/IAG/COSPAR Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: 1994'. All exceptions are commented where they occur in this file. The exceptions are: -- Radii for the Sun are from [2]. -- The values for the latitude and longitude of the Northern hemisphere projection of the Earth's magnetic dipole are from [5]. -- The second nutation precession angle (M2) for Mars is represented by a quadratic polynomial in the 1994 IAU report. The SPICELIB subroutine BODEUL can not handle this term (which is extremely small), so we truncate the polynomial to a linear one. -- The expressions for the pole and prime meridian of Neptune given in the IAU report include trigonometric terms which BODEUL doesn't yet handle. We omit these terms. See the comments accompanying the data for Neptune for further information. -- For several satellites, the 1994 IAU report either gives a single radius value or a polar radius and a single equatorial radius. NAIF Toolkit software that uses body radii expects to find three radii whenever these data are read from the kernel pool. In the cases listed below, NAIF has supplied an additional radius value in order to allow the software to function. Wherever this was done, the fact has been noted, and comments indicate which radius values were given by the IAU report. The `invented' values were created by NAIF and should not be used in any application requiring values sanctioned by an authoritative source. The affected satellites are: Body NAIF ID code ---- ------------ Thebe 514 Metis 516 Helene 612 Larissa 807 -- The W0 term for Metis is from [7]. `Old values' listed are from the SPICE P_constants file dated June 25, 1990. Most of these values came from the 1988 IAU report. Explanation -------------------------------------------------------- The NAIF Toolkit software that uses this file is documented in the NAIF `Required Reading' file PCK.REQ. See that document for a detailed explanation of the NAIF text kernel file format. PCK.REQ is available in both printed and electronic form. This file, which is logically part of the SPICE P-kernel, contains constants used to model the orientation and shape of the Sun, planets, and satellites. The orientation models express the direction of the pole and location of the prime meridian of a body as a function of time. The shape models 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. Orientation models All of the orientation models use three Euler angles to describe body orientation. To be precise, the Euler angles 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 J2000 (also called `EME2000'), but other frames can be specified in the file. See the PCK Required Reading for details. The first two angles, in order, are the 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 the Sun and planets, the expressions for the north pole's right ascension and declination, as well as prime meridian location, are always (as far as the models that appear in this file are concerned) quadratic polynomials, where the independent variable is time. Some coefficients may be zero. In this file, the time arguments in expressions always refer to Barycentric Dynamical Time (TDB), measured in centuries or days past the a reference epoch. By default, the reference epoch is the J2000 epoch, which is Julian ephemeris date 2451545.0, but other epochs can be specified in the file. See the PCK Required Reading for details. Example: 1991 IAU Model for orientation of the Earth. Note that these values are used as an example only; see the data area below for current values. alpha = 0.00 - 0.641 T ( RA ) 0 delta = 90.0 - 0.557 T ( DEC ) 0 W = 190.16 + 360.9856235 d ( Prime meridian ) T represents centuries past J2000 ( TDB ), d represents days past J2000 ( TDB ). In this file, the polynomials' coefficients above are assigned to the symbols BODY399_POLE_RA BODY399_POLE_DEC BODY399_POLE_PM as follows: BODY399_POLE_RA = ( 0. -0.641 0. ) BODY399_POLE_DEC = ( +90. -0.557 0. ) BODY399_PM = ( 190.16 +360.9856235 0. ) Note the number `399'; this is the NAIF ID code for the Earth. You'll see an additional symbol grouped with the ones listed here; it is BODY399_LONG_AXIS This term is zero for all bodies except Mars. It represents the offset between the longest axis of the triaxial ellipsoid used to model a body and the prime meridian of the body. Expressions for satellites are a little more complicated; in addition to polynomial terms, there are trigonometric terms. The arguments of the trigonometric terms are linear polynomials. In this file, we call the arguments of these trigonometric terms `nutation precession angles'. In this file, the polynomial expressions for the nutation precession angles are listed along with the planet's RA, DEC, and prime meridian terms. Example: 1991 IAU nutation precession angles for Earth. Note that these values are used as an example only; see the data area below for current values. E1 = 125.045 - 0.052992 d E2 = 250.090 - 0.105984 d E3 = 260.008 + 13.012001 d E4 = 176.625 + 13.340716 d E5 = 357.529 + 0.985600 d d represents days past J2000 ( TDB ) Because the NAIF Toolkit software expects the time units for the angles to be CENTURIES (as in the IAU models for most bodies--the Earth is an exception), the linear coefficients are scaled by 36525.0 in the assignments: BODY3_NUT_PREC_ANGLES = ( 125.045 -1935.5328 250.090 -3871.0656 260.008 475263.336525 176.625 487269.6519 357.529 35999.04 ) As stated above, the satellite orientation models use polynomial and trigonometric terms, where the arguments of the trigonometric terms are the `nutation precession angles'. Example: 1988 IAU values for the Moon. Again, these values are used as an example only; see the data area below for current values. alpha = 270.000 + 0.003 T - 3.878 sin(E1) - 0.120 sin(E2) 0 + 0.070 sin(E3) - 0.017 sin(E4) (RA) delta = 66.541 + 0.013 T + 1.543 cos(E1) + 0.024 cos(E2) 0 - 0.028 cos(E3) + 0.007 cos(E4) (DEC) W = 38.317 + 13.1763582 d + 3.558 sin(E1) + 0.121 sin(E2) - 0.064 sin(E3) + 0.016 sin(E4) + 0.025 sin(E5) ( Prime meridian ) d represents days past J2000. E1--E5 are the nutation precession angles. The polynomial terms are assigned to symbols by the statements BODY301_POLE_RA = ( 270.000 0.003 0. ) BODY301_POLE_DEC = ( +66.541 0.013 0. ) BODY301_PM = ( 38.317 +13.1763582 0. ) The coefficients of the trigonometric terms are assigned to symbols by the statements BODY301_NUT_PREC_RA = ( -3.878 -0.120 +0.070 -0.017 0. ) BODY301_NUT_PREC_DEC = ( +1.543 +0.024 -0.028 +0.007 0. ) BODY301_NUT_PREC_PM = ( +3.558 +0.121 -0.064 +0.016 +0.025 ) Note that for the RA and PM (prime meridian) assignments, the ith term is the coefficient of sin(Ei) in the expression used in the IAU model, while for the DEC assignment, the ith term is the coefficient of cos(Ei) in the expression used in the IAU model. NAIF 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. Eventually, the software will handle more complex expressions, we expect. Shape models There is only one kind of shape model supported by the NAIF Toolkit software at present: the triaxial ellipsoid. The 1994 IAU report does not use any other models. For each body, three radii are listed: The first number is the largest equatorial radius (the length of the semi-axis containing the prime meridian), the second number is the smaller equatorial radius, and the third is the polar radius. Example: Radii of the Earth. BODY399_RADII = ( 6378.14 6378.14 6356.75 ) Body numbers and names -------------------------------------------------------- 1 Mercury barycenter 2 Venus barycenter 3 Earth barycenter 4 Mars barycenter 5 Jupiter barycenter 6 Saturn barycenter 7 Uranus barycenter 8 Neptune barycenter 9 Pluto barycenter 10 Sun While not relevant to the P_constants kernel, we note here for completeness that 0 is used to represent the solar system barycenter. 199 Mercury 299 Venus 399 Earth 301 Moon 499 Mars 401 Phobos 402 Deimos 599 Jupiter 501 Io 502 Europa 503 Ganymede 504 Callisto 505 Amalthea 506 Himalia 507 Elara 508 Pasiphae 509 Sinope 510 Lysithea 511 Carme 512 Ananke 513 Leda 514 Thebe 515 Adrastea 516 Metis 699 Saturn 601 Mimas 602 Enceladus 603 Tethys 604 Dione 605 Rhea 606 Titan 607 Hyperion 608 Iapetus 609 Phoebe 610 Janus 611 Epimetheus 612 Helene 613 Telesto 614 Calypso 615 Atlas 616 Prometheus 617 Pandora 618 Pan 799 Uranus 701 Ariel 702 Umbriel 703 Titania 704 Oberon 705 Miranda 706 Cordelia 707 Ophelia 708 Bianca 709 Cressida 710 Desdemona 711 Juliet 712 Portia 713 Rosalind 714 Belinda 715 Puck 899 Neptune 801 Triton 802 Nereid 803 Naiad 804 Thalassa 805 Despina 806 Galatea 807 Larissa 808 Proteus 999 Pluto 901 Charon 9511010 Asteriod Gaspra 2431010 Asteroid Ida Orientation constants for the Sun and planets -------------------------------------------------------- Sun Old values: Values for the Sun in the 1994 report are the same as in the 1991 report. Current values: \begindata BODY10_POLE_RA = ( 286.13 0. 0. ) BODY10_POLE_DEC = ( 63.87 0. 0. ) BODY10_PM = ( 84.10 +14.18440 0. ) BODY10_LONG_AXIS = ( 0. ) \begintext Mercury Old values: body199_pole_ra = ( 281.01, -0.033, 0. ) body199_pole_dec = ( 61.45, -0.005, 0. ) body199_pm = ( 329.71 +6.1385025 0. ) body199_long_axis = ( 0. ) Current values: \begindata BODY199_POLE_RA = ( 281.01, -0.033, 0. ) BODY199_POLE_DEC = ( 61.45, -0.005, 0. ) BODY199_PM = ( 329.68 +6.1385025 0. ) BODY199_LONG_AXIS = ( 0. ) \begintext Venus Old values: Values for the Venus in the 1994 report are the same as in the 1991 report. Current values: \begindata BODY299_POLE_RA = ( 272.76 0. 0. ) BODY299_POLE_DEC = ( +67.16 0. 0. ) BODY299_PM = ( 160.20 -1.4813688 0. ) BODY299_LONG_AXIS = ( 0. ) \begintext Earth Old values: Values shown are from the 1988 IAU report. body399_pole_ra = ( 0. -0.641 0. ) body399_pole_dec = ( +90. -0.557 0. ) body399_pm = ( 190.16 +360.9856235 0. ) body399_long_axis = ( 0. ) The linear terms before and after scaling: -.052992 --> -1935.5328 -.105984 --> -3871.0656 -13.012 --> -475263.3 13.340716 --> +487269.6519 -.9856 --> -35999.04 body3_nut_prec_angles = ( 125.045 -1935.5328 249.390 -3871.0656 196.694 -475263.3 176.630 +487269.6519 358.219 -35999.04 ) Current values: \begindata BODY399_POLE_RA = ( 0. -0.641 0. ) BODY399_POLE_DEC = ( +90. -0.557 0. ) BODY399_PM = ( 190.16 +360.9856235 0. ) BODY399_LONG_AXIS = ( 0. ) \begintext Nutation precession angles for the Earth-Moon system: The linear coefficients have been scaled up from degrees/day to degrees/century, because the SPICELIB PCK reader expects these units. The original constants were: 125.045D0 -0.0529921D0 250.089D0 -0.1059842D0 260.008D0 13.0120009D0 176.625D0 13.3407154D0 357.529D0 0.9856003D0 311.589D0 26.4057084D0 134.963D0 13.0649930D0 276.617D0 0.3287146D0 34.226D0 1.7484877D0 15.134D0 -0.1589763D0 119.743D0 0.0036096D0 239.961D0 0.1643573D0 25.053D0 12.9590088D0 \begindata BODY3_NUT_PREC_ANGLES = ( 125.045 -1935.5364525000 250.089 -3871.0729050000 260.008 475263.3328725000 176.625 487269.6299850000 357.529 35999.0509575000 311.589 964468.4993100001 134.963 477198.8693250000 276.617 12006.3007650000 34.226 63863.5132425000 15.134 -5806.6093575000 119.743 131.8406400000 239.961 6003.1503825000 25.053 473327.7964200000 ) \begintext Northern hemisphere projection of the Earth's magnetic dipole: Coordinates are planetocentric. Values are from [5]. \begindata BODY399_MAG_NORTH_POLE_LON = ( -69.761 ) BODY399_MAG_NORTH_POLE_LAT = ( 78.565 ) \begintext Mars Old values: Values shown are from the 1991 IAU report. body499_pole_ra = ( 317.681 -0.108 0. ) body499_pole_dec = ( +52.886 -0.061 0. ) body499_pm = ( 176.868 +350.8919830 0. ) body4_nut_prec_angles = ( 169.51 -15916.2801 192.93 +41215163.19675 53.47 -662.965275 36.53 +662.965275 ) Current values: \begindata BODY499_POLE_RA = ( 317.681 -0.108 0. ) BODY499_POLE_DEC = ( +52.886 -0.061 0. ) BODY499_PM = ( 176.901 +350.8919830 0. ) \begintext Source [3] specifies the following value for the lambda_a term (BODY4_LONG_AXIS ) for Mars. This term is the POSITIVE WEST LONGITUDE, measured from the prime meridian, of the longest axis of the ellipsoid representing the `mean planet surface', as the article states. body499_long_axis = ( 110. ) Source [4] specifies the lambda_a value body499_long_axis = ( 104.9194 ) We list these lambda_a values for completeness. The IAU gives equal values for both equatorial radii, so the lambda_a offset does not apply to the IAU model. The 1994 IAU report defines M2, the second nutation precession angle, by: 2 192.93 + 1128.4096700 d + 8.864 T We truncate the M2 series to a linear expression, because the PCK software cannot handle the quadratic term. Again, the linear terms are scaled by 36525.0: -0.4357640000000000 --> -15916.28010000000 1128.409670000000 --> 41215163.19675000 -1.8151000000000000E-02 --> -662.9652750000000 We also introduce a fourth nutation precession angle, which is the pi/2-complement of the third angle. This angle is used in computing the prime meridian location for Deimos. See the discussion of this angle below in the section containing orientation constants for Deimos. \begindata BODY4_NUT_PREC_ANGLES = ( 169.51 -15916.2801 192.93 +41215163.19675 53.47 -662.965275 36.53 +662.965275 ) \begintext Jupiter Old values: Values are from the 1991 IAU report. body599_pole_ra = ( 268.05 -0.009 0. ) body599_pole_dec = ( +64.49 +0.003 0. ) body599_pm = ( 284.95 +870.536 0. ) body599_long_axis = ( 0. ) body5_nut_prec_angles = ( 73.32 +91472.9 198.54 +44243.8 283.90 +4850.7 355.80 +1191.3 119.90 +262.1 229.80 +64.3 352.25 +2382.6 113.35 +6070.0 146.64 +182945.8 397.08 +88487.6 ) Current values: The number of nutation precession angles is ten. The ninth and tenth are twice the first and second, respectively. \begindata BODY599_POLE_RA = ( 268.05 -0.009 0. ) BODY599_POLE_DEC = ( +64.49 +0.003 0. ) BODY599_PM = ( 284.95 +870.536 0. ) BODY599_LONG_AXIS = ( 0. ) 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 ) \begintext Saturn Old values: Values are from the 1991 IAU report. body699_pole_ra = ( 40.58 -0.036 0. ) body699_pole_dec = ( +83.54 -0.004 0. ) body699_pm = ( 38.90 +810.7939024 0. ) body699_long_axis = ( 0. ) body6_nut_prec_angles = ( 353.32 75706.7 28.72 75706.7 177.40 -36505.5 300.00 -7225.9 316.45 506.2 345.20 -1016.3 29.80 -52.1 706.64 151413.4 57.44 151413.4 ) Current values: \begindata BODY699_POLE_RA = ( 40.589 -0.036 0. ) BODY699_POLE_DEC = ( +83.537 -0.004 0. ) BODY699_PM = ( 38.90 +810.7939024 0. ) BODY699_LONG_AXIS = ( 0. ) \begintext The first seven angles given here are the angles S1 through S7 from the 1994 report; the eighth and ninth angles are 2*S1 and 2*S2, respectively. \begindata BODY6_NUT_PREC_ANGLES = ( 353.32 75706.7 28.72 75706.7 177.40 -36505.5 300.00 -7225.9 316.45 506.2 345.20 -1016.3 29.80 -52.1 706.64 151413.4 57.44 151413.4 ) \begintext Uranus Old values: Values are from the 1991 report. body799_pole_ra = ( 257.43 0. 0. ) body799_pole_dec = ( -15.10 0. 0. ) body799_pm = ( 203.81 -501.1600928 0. ) body799_long_axis = ( 0. ) body7_nut_prec_angles = ( 115.75 +54991.87 141.69 +41887.66 135.03 +29927.35 61.77 +25733.59 249.32 +24471.46 43.86 +22278.41 77.66 +20289.42 157.36 +16652.76 101.81 +12872.63 138.64 +8061.81 102.23 -2024.22 316.41 2863.96 304.01 -51.94 308.71 -93.17 340.82 -75.32 259.14 -504.81 204.46 -4048.44 632.82 5727.92 ) Current values: \begindata BODY799_POLE_RA = ( 257.311 0. 0. ) BODY799_POLE_DEC = ( -15.175 0. 0. ) BODY799_PM = ( 203.81 -501.1600928 0. ) BODY799_LONG_AXIS = ( 0. ) \begintext The first 16 angles given here are the angles U1 through U16 from the 1994 report; the 17th and 18th angles are 2*U11 and 2*U12, respectively. \begindata BODY7_NUT_PREC_ANGLES = ( 115.75 +54991.87 141.69 +41887.66 135.03 +29927.35 61.77 +25733.59 249.32 +24471.46 43.86 +22278.41 77.66 +20289.42 157.36 +16652.76 101.81 +12872.63 138.64 +8061.81 102.23 -2024.22 316.41 2863.96 304.01 -51.94 308.71 -93.17 340.82 -75.32 259.14 -504.81 204.46 -4048.44 632.82 5727.92 ) \begintext Neptune Old values: Values are unchanged in the 1994 IAU report. Current values: The RA and DEC expressions for Neptune in the 1994 IAU report (as in the 1991 report) involve trigonometric terms: alpha = 299.36 + 0.70 sin(N) 0 delta = 43.46 - 0.51 cos(N) 0 W = 253.18 + 536.3128492 d - 0.48 sin(N) N = 357.85 + 52.316 T Because the SPICELIB routine BODEUL (still) cannot handle the trigonometric terms, we truncate the expressions to polynomials. The errors we make (in degrees) are: RA DEC PM ---- ----- ---- Error bound (max abs value) 0.70 0.51 0.48 \begindata BODY899_POLE_RA = ( 299.36 0. 0. ) BODY899_POLE_DEC = ( +43.46 0. 0. ) BODY899_PM = ( 253.18 +536.3128492 0. ) BODY899_LONG_AXIS = ( 0. ) \begintext The 1994 report defines the nutation precession angles N, N1, N2, ... , N7 and also uses the multiples of N1 and N7 2*N1 and 2*N7, 3*N7, ..., 9*N7 In this file, we treat the angles and their multiples as separate angles. In the kernel variable BODY8_NUT_PREC_ANGLES the order of the angles is N, N1, N2, ... , N7, 2*N1, 2*N7, 3*N7, ..., 9*N7 Each angle is defined by a linear polynomial, so two consecutive array elements are allocated for each angle. The first term of each pair is the constant term, the second is the linear term. \begindata BODY8_NUT_PREC_ANGLES = ( 357.850 52.316 323.920 62606.600 220.510 55064.200 354.270 46564.500 75.310 26109.400 35.360 14325.400 142.610 2824.600 177.850 52.316 647.840 125213.200 355.700 104.632 533.550 156.948 711.400 209.264 889.250 261.580 1067.100 313.896 1244.950 366.212 1422.800 418.528 1600.650 470.844 ) \begintext Pluto Old values: Values are unchanged in the 1994 IAU report. Current values: \begindata BODY999_POLE_RA = ( 313.02 0. 0. ) BODY999_POLE_DEC = ( +9.09 0. 0. ) BODY999_PM = ( 236.77 -56.3623195 0. ) BODY999_LONG_AXIS = ( 0. ) \begintext Orientation constants for the satellites -------------------------------------------------------- Moon Old values: Values are from the 1988 IAU report. body301_pole_ra = ( 270.000 0. 0. ) body301_pole_dec = ( +66.534 0. 0. ) body301_pm = ( 38.314 +13.1763581 0. ) body301_long_axis = ( 0. ) body301_nut_prec_ra = ( -3.878 -0.120 +0.070 -0.017 0. ) body301_nut_prec_dec = ( +1.543 +0.024 -0.028 +0.007 0. ) body301_nut_prec_pm = ( +3.558 +0.121 -0.064 +0.016 +0.025 ) New values: \begindata BODY301_POLE_RA = ( 269.9949 0.0031 0. ) BODY301_POLE_DEC = ( 66.5392 0.0130 0. ) BODY301_PM = ( 38.3213 13.17635815 -1.4D-12 ) BODY301_LONG_AXIS = ( 0. ) BODY301_NUT_PREC_RA = ( -3.8787 -0.1204 +0.0700 -0.0172