Selected Astronomical Constants, 2009 ------------------------------------- This is the ASCII version of pages K6-K7 of The Astronomical Almanac 2009. The following nomenclature is used in this file: (a) greek letters, as in TeX, are spelt out, e.g., alpha, (b) the symbols ^ and _ are used (as in TeX) to indicate superscripts and subscripts, respectively, (c) the symbols *, / and +/- denote multiplication, division, and plus-minus uncertainty bounds, respectively, and (d) numerical exponents are given with the Fortran D format. The units meter (m), kilogram (kg), and SI second (s) are the units of length, mass and time in the International System of Units (SI). The astronomical unit of time is a time interval of one day (D) of 86400 seconds. An interval of 36525 days is one Julian century. The astronomical unit of mass is the mass of the Sun (S). The astronomical unit of length is that length (A) for which the Gaussian gravitational constant (k) takes the value 0.01720209895 when the units of measurement are the astronomical units of length, mass and time. The dimensions of k^2 are those of the constant of gravitation (G), i.e., A^3/S/D^2. Some constants from the JPL DE405 ephemeris are consistent with TDB seconds (see The Astronomical Almanac page L2). For these quantities both TDB and SI compatible values are given, which are indicated in brackets. |++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++| | | Description of Quantity | Symbol = Value | Unit | Uncertainty | Ref. | |++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++| | | Defining constants | |--------------------------------------------------------------------------------------------------------------------------------------| | 1 | Gaussian gravitational constant | k = 0.01720209895 | | | I* | |--------------------------------------------------------------------------------------------------------------------------------------| | 2 | Speed of light | c = 299792458 | m/s | | C E J A | |--------------------------------------------------------------------------------------------------------------------------------------| | 3 | L_G | L_G = 6.969290134D-10 | | | I E | |--------------------------------------------------------------------------------------------------------------------------------------| | 4 | L_B | L_B = 1.55051976772D-08 | | [2D-17] | I06 E | |++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++| | | Other constants and quantities: | |--------------------------------------------------------------------------------------------------------------------------------------| | 5 | L_C | L_C = 1.48082686741D-08 | | [2D-17] | I E | |--------------------------------------------------------------------------------------------------------------------------------------| | 6 | Light-time for unit distance | tau_A = 499.0047838061 | s (TDB) | [2D-08s] | J E A | | | | tau_A = 499.0047863852 | s (SI) | | | | | | 1/tau_A = 173.1446326847 | AU/d (TDB) | | | |--------------------------------------------------------------------------------------------------------------------------------------| | 7 | Unit distance, astronomical unit (c*tau_A) | A = 1.49597870691D11 | m (TDB) | [6] | J E | | | | A = 1.49597871464D11 | m (SI) | | | |--------------------------------------------------------------------------------------------------------------------------------------| | 8 | Equatorial radius for Earth | a_e = 6378136.6 | m | [0.10] | G E A | |--------------------------------------------------------------------------------------------------------------------------------------| | 9 | Flattening factor for Earth | f = 0.0033528197 | | | G E A | | | f = 1/298.25642 | | [1/0.00001] | | |--------------------------------------------------------------------------------------------------------------------------------------| | 10 | Dynamical form-factor for the Earth | J_2 = 0.0010826359 | | [1D-10] | G E | |--------------------------------------------------------------------------------------------------------------------------------------| | 11 | Nominal mean angular velocity of Earth rotation | omega = 7.292115D-05 | rad/s | [variable] | I E G | |--------------------------------------------------------------------------------------------------------------------------------------| | 12 | Potential of the geoid | W_0 = 6.26368560D07 | m^2/s^2 | [0.5] | G E | |--------------------------------------------------------------------------------------------------------------------------------------| | 13 | Geocentric gravitational constant | GE = 3.986004329D14 | m^3/s^2 (TDB)| [8D05] | J A | | | | GE = 3.986004391D14 | m^3/s^2 (SI) | | | | | | GE = 3.986004418D14 | m^3/s^2 | | G E | |--------------------------------------------------------------------------------------------------------------------------------------| | 14 | Heliocentric gravitational constant (A^3*k^2/D^2) | GS = 1.32712440017987D20 | m^3/s^2 (TDB)| [5D10] | J A | | | | GS = 1.32712442076D20 | m^3/s^2 (SI) | | E | |--------------------------------------------------------------------------------------------------------------------------------------| | 15 | Constant of gravitation | G = 6.67428D-11 | m^3/kg/s^2 | [0.067D-13] | C | | | | G = 6.673D-11 | m^3/kg/s^2 | [1.0D-13] | E | |--------------------------------------------------------------------------------------------------------------------------------------| | 16 | General precession in longitude at J2000 | p_A = 5028.796195 | " /Julian cy | | I06 A P | | | | p_A = 5028.79695 | " /Julian cy | | P I E | |--------------------------------------------------------------------------------------------------------------------------------------| | 17 | Mean obliquity of the ecliptic at J2000 | epsilon_0 = 84381.406 | " | [0.0001] | I06 A | | | | epsilon_0 = 84381.4059 | " | | E | | | | epsilon_0 = 84381.448 | " | [0.0003] | I* I | |--------------------------------------------------------------------------------------------------------------------------------------| | 18 | Ratio: mass of Moon to that of the Earth | mu = 1/81.30056 | | [5D-10] | E J | | | | mu = 0.0123000383 | | | | |--------------------------------------------------------------------------------------------------------------------------------------| | 19 | Ratio: mass of Sun to that of the Earth (S/E) | GS/GE = 332946.050895 | | | J | |--------------------------------------------------------------------------------------------------------------------------------------| | 20 | Ratio: mass of Sun to that of the Earth + Moon | (S/E)/(1+mu) = 328900.561400 | | | J | |--------------------------------------------------------------------------------------------------------------------------------------| | 21 | Mass of the Sun (GS/G) | S = 1.9884D30 | kg | | | |--------------------------------------------------------------------------------------------------------------------------------------| | 22 | Constant of nutation at epoch J2000.0 | N = 9.2052331 | " | | I | |--------------------------------------------------------------------------------------------------------------------------------------| | 23 | Solar parallax (sin^{-1}(a_e/A)) | pi_odot = 8.794143 | " | | | |--------------------------------------------------------------------------------------------------------------------------------------| | 24 | Constant of aberration at epoch J2000.0 | kappa = 20.49551 | " | | | |++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++| | 25 | Ratios of mass of Sun to masses of the planets: JPL DE405 Ephemeris (J) | | | |-------------------------------------------------------------------------------------------------------| | | | Mercury | 6023600 | | | | Venus | 408523.71 | | | | Earth + Moon | 328900.561400 | | | | Mars | 3098708 | | | | Jupiter | 1047.3486 | | | | Saturn | 3497.898 | | | | Uranus | 22902.98 | | | | Neptune | 19412.24 | | | | Pluto | 135200000 | | |++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++| | | 26 | Minor planet masses: mass in solar mass | | | |-------------------------------------------------------------------------------------------------------| | | | | Hilton (H) | Uncertainty | JPL DE405 (J) | | | |-------------------------------------------------------------------------------------------------------| | | | 1 | Ceres | 4.39D-10 | [+/-0.04] | 4.7D-10 | | | | 2 | Pallas | 1.59D-10 | [+/-0.05] | 1.0D-10 | | | | 4 | Vesta | 1.69D-10 | [+/-0.11] | 1.3D-10 | | |++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++| | | 27 | Masses of the larger natural satellites: mass satellite/mass of the planet (see pages F3, F5) | | | |-------------------------------------------------------------------------------------------------------| | | | Planet | Satellite | Mass Ratio | | | |--------------|-----------|----------------------------------------------------------------------------| | | | Jupiter | | | | | | | Io | 4.70D-05 | | | | | Europa | 2.53D-05 | | | | | Ganymede | 7.80D-05 | | | | | Callisto | 5.67D-05 | | | | Saturn | | | | | | | Titan | 2.37D-04 | | | | Uranus | | | | | | | Titania | 4.06D-05 | | | | | Oberon | 3.47D-05 | | | | Neptune | | | | | | | Triton | 2.09D-04 | | |++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++| | | 28 | Equatorial radii in km: Cartographic Coordinates 2007 (CC) and JPL DE405 Ephemeris (J) | | | |-------------------------------------------------------------------------------------------------------| | | | Body | CC A | Uncertainty | JPL (J) | Unit/Comment | | | |--------------|-----------|--------------|------------|------------------------------------------------| | | | Mercury | 2439.7 | [ +/- 1.0 ] | 2439.76 | km | | | | Venus | 6051.8 | [ +/- 1.0 ] | 6052.3 | km | | | | Earth | 6378.14 | [ +/- 0.01 ] | 6378.137 | km | | | | Mars | 3396.19 | [ +/- 0.1 ] | 3397.515 | km | | | | Jupiter | 71492 | [ +/- 4 ] | | km | | | | Saturn | 60268 | [ +/- 4 ] | | km | | | | Uranus | 25559 | [ +/- 4 ] | | km | | | | Neptune | 24764 | [ +/-15 ] | | km | | | | Pluto | 1195 | [ +/- 5 ] | | km | | | | Moon | 1737.4 | [ +/- 1 ] | | km, mean radius | | | | Sun |696000 | | | km, IAU 1976 value | | |++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++| |Ref.| The references indicate where the constant has been used, quoted or derived from: | |--------------------------------------------------------------------------------------------------------------------------------------| | A | Constants used in The Astronomical Almanac 2009. | | C | CODATA 2006, http://physics.nist.gov/constants page 1. | | CC | Report 10 of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements: 2007, Seidelmann, P.K. et al., | | | Cel. Mech., & Dyn Astro., 98, 155-180, 2007, http://astrogeology.usgs.gov./Projects/WGCCRE. | | E | IERS Conventions 2003, Technical Note 32, McCarthy, D.D. & Petit, G., Chapter 1. | | G | IAG XXII GA, 1999, Special Commission SC3, Fundamental Constants, Groten, E., Geodesists Handbook 2000, | | | `Parameters of Common Relevance of Astronomy, Geodesy, and Geodynamics', J. Geod., 74, 134-140. | | H | Hilton, J. Astrophysical Journal, 117, 1077-1086, 1999. | | I06| IAU XXVI General Assembly (2006) resolutions, including the Report of the IAU Division I Working Group on | | | Precession and the Ecliptic, Cel. Mech. & Dyn. Astr., 94, 351-367, 2006. | | I | IAU XXIV General Assembly (2000) resolutions B1.5, B1.6, B1.9, & IAU2000A precession-nutation. | | I*| IAU 1976 System of Astronomical Constants. | | J | JPL IOM 312.F-98-048, Standish, E.M., 1998 (DE405/LE405 Ephemeris). | | P | Capitaine, N., Wallace, P.T., & Chapront, J., Astronomy & Astrophysics, 412, 567-586, 2003. | |++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++| |++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++| | Updated 2007 October 18 | |++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++|