P_constants (PcK) SPICE kernel file =========================================================================== By: Nat Bachman (NAIF) 1993 August 11 Organization -------------------------------------------------------- The sections 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 -- Radii for all bodies Version description -------------------------------------------------------- This file was created on August 11, 1993. The data in the file are based primarily on the 1991 IAU report, which at this time has not been published. See `Sources' below for details. This file contains updates of constants contained in the previous version of the file, as well as new constants that were not present in the previous version. One item has been subtracted: the lambda_a offset for Mars is no longer used as data, but the value used in the previous PCK version is still listed in the comments in the Mars section. Official NAIF Version information: \begindata PCK_version += ( 00004 ) \begintext 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: 1991,'' proof. 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. Most values are from the ``IAU/IAG/COSPAR Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: 1991.'' All exceptions are commented where they occur in this file. The exceptions are: -- The polar and smaller equatorial radii of Helene (Body 612) are from the 1993 Almanac, as no values are present in the 1991 report. -- The second nutation precession angle (M2) for Mars is represented by a quadratic polynomial in the 1991 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. -- The values for the second equatorial radii of bodies 514 and 516 are retained from the last P_constants file since the 1991 IAU report does not give values. The values used agree with the 1993 Almanac. -- GM values for planets and satellites are taken from a draft of a paper by Dr. Robert Jacobson, of JPL section 314 (Navigation). `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 the explanation of the 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 the 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, also a function of time. For the Sun and planets, the expressions for the north pole direction and prime meridian location are always (as far as the models that appear in this file are concerned) a quadratic polynomial, 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: 1988 IAU Model for orientation of the Earth alpha = 0.00 - 0.641 T ( RA ) 0 delta = 90.0 - 0.557 T ( Dec ) 0 W = 190.16 + 360.9852635 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: 1988 IAU nutation precession angles for Earth. E1 = 125.045 - 0.052992 d E2 = 249.390 - 0.105984 d E3 = 196.694 - 13.012000 d E4 = 176.630 + 13.340716 d E5 = 358.219 - 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 249.390 -3871.0656 196.694 -475263.3 176.630 +487269.6519 358.219 -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: The Moon. alpha = 270.000 - 3.878 sin(E1) - 0.120 sin(E2) 0 + 0.070 sin(E3) - 0.017 sin(E4) ( RA ) delta = 66.534 + 1.543 cos(E1) + 0.024 cos(E2) 0 - 0.028 cos(E3) +