Selected Astronomical Constants, 2011
-------------------------------------
This is the ASCII version of pages K6-K7 of The Astronomical Almanac 2011. 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 Defining Constants (1) and Current Best Estimates (2) were adopted by the IAU 2009 GA, while the planetary equatorial |
| radii (3), are taken from the report of the IAU WG on Cartographic Coordinates and Rotational Elements. For each quantity the |
| list tabulates its description, symbol, value with the units, and to the right, as appropriate, its uncertainty in units that |
| the quantity is given in. Further information is given at the end of this file. |
|---|---------------------------------------------------------------------------------------------------------------------------|
| | Description of Quantity | Symbol = Value | Unit | Uncertainty |
|+++|+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++|+++++++++++++|
|1 |Defining Constants |
| |---------------------------------------------------------------------------------------------------------------------------|
|1.1|Natural Defining Constant: | | | |
| | Speed of light | c = 299792458 | m/s | |
| |-------------------------------------------|----------------------------------------|------------------------|-------------|
|1.2|Auxiliary Defining Constants: | | | |
| | Gaussian gravitational constant | k = 0.01720209895 | | |
| | 1-d(TT)/d(TCG) | L_G = 6.969290134D-10 | | |
| | 1-d(TDB)/d(TCB) | L_B = 1.550519768D-08 | | |
| | TDB-TCB at T_0 = 2443144.5003725 | TDB_0 = -6.55D-05 | s | |
| | Earth rotation angle (ERA) at J2000.0 UT1 | theta_0 = 0.7790572732640 | revolutions | |
| | Rate of advance of ERA | d(theta)/dUT1 = 1.00273781191135448 | revs/UT1-day | |
|+++|+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++|+++++++++++++|
|2. |Current Best Estimates (IAU 2009) | |
| |-------------------------------------------------------------------------------------------------------------|-------------|
|2.1|Natural Measurable Constant: | | | |
| | Constant of gravitation | G = 6.67428D-11 | m^3/kg/s^2 | +/- 6.7D-15 |
| |-------------------------------------------|----------------------------------------|------------------------|-------------|
|2.2|Derived Constants: | | | |
| | Astronomical unit (unit distance)# | au =A = 149597870700 | m | +/- 3 |
| | Average value of 1-d(TCG)/d(TCB) | L_C = 1.48082686741D-08 | | +/- 2D-17 |
| |-------------------------------------------|----------------------------------------|------------------------|-------------|
|2.3|Body Constants: | | | |
| | Mass Ratio: Moon to Earth | M_M / M_ E = 1.23000371D-02 | | +/- 4D-10 |
| | Mass Ratio: Sun to Mercury | M_S / M_ Me = 6.0236D06 | | +/- 3D02 |
| | Mass Ratio: Sun to Venus | M_S / M_ Ve = 4.08523719D05 | | +/- 8D-03 |
| | Mass Ratio: Sun to Mars | M_S / M_ Ma = 3.09870359D06 | | +/- 2D-02 |
| | Mass Ratio: Sun to Jupiter | M_S / M_ J = 1.047348644D03 | | +/- 1.7D-05 |
| | Mass Ratio: Sun to Saturn | M_S / M_ Sa = 3.4979018D03 | | +/- 1D-04 |
| | Mass Ratio: Sun to Uranus | M_S / M_ U = 2.290298D04 | | +/- 3D-02 |
| | Mass Ratio: Sun to Neptune | M_S / M_ N = 1.941226D04 | | +/- 3D-02 |
| | Mass Ratio: Sun to Pluto | M_S / M_ P = 1.36566D08 | | +/- 2.8D04 |
| | Mass Ratio: Sun to Eris | M_S / M_ Eris = 1.191D08 | | +/- 1.4D06 |
| | | | | |
| | Mass Ratio: Ceres to Sun | M_Ceres /M_S = 4.72D-10 | | +/- 3D-12 |
| | Mass Ratio: Pallas to Sun | M_Pallas /M_S = 1.03D-10 | | +/- 3D-12 |
| | Mass Ratio: Vesta to Sun | M_Vesta /M_S = 1.35D-10 | | +/- 3D-12 |
| | | | | |
| | Equatorial radius for Earth | a_E = a_e = 6378136.6 | m | +/- 0.10 |
| | Dynamical form-factor for the Earth | J_2 = 0.0010826359 | | +/- 1D-10 |
| | Long-term variation in J_2 | \dot{J_2} = -3.001D-09 | per cy | +/- 6D-10 |
| | | | | |
| | Heliocentric gravitational constant | GMS = A^3k^2/D^2 = 1.32712442099D20 | m^3/s^2 (TCB) | +/- 1D10 |
| | | = 1.32712440041D20 | m^3/s^2 (TDB) | +/- 1D10 |
| | | | | |
| | Geocentric gravitational constant | GME = 3.986004418D14 | m^3/s^2 (TCB) | +/- 8D05 |
| | | = 3.986004415D14 | m^3/s^2 (TT) | +/- 8D05 |
| | | = 3.986004356D14 | m^3/s^2 (TDB) | +/- 8D05 |
| | | | | |
| | Potential of the geoid | W_0 = 6.26368560D07 | m^2/s^2 | +/- 0.5 |
| | | | | |
| | Nominal mean angular vel.of Earth rotation| omega = 7.292115D0-5 | rad/s | |
| |-------------------------------------------|----------------------------------------|------------------------|-------------|
|2.4|Initial Values at J2000.0: | | | |
| | Mean obliquity of the ecliptic, epsilon_0 | epsilon_J2000.0 = 23 26 21.406 | o ' " | |
| | | = 84381.406 | " | +/- 0.001 |
|+++|+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++|
|3 |Constants from IAU WG on Cartographic Coordinates and Rotational Elements (2007) |
| |---------------------------------------------------------------------------------------------------------------------------|
| | Equatorial radii: | | | |
| | Mercury | = 2439.7 | km | +/- 1.0 |
| | Venus | = 6051.8 | km | +/- 1.0 |
| | Earth | = 6378.14 | km | +/- 0.01 |
| | Mars | = 3396.19 | km | +/- 0.1 |
| | Jupiter | = 71492 | km | +/- 4 |
| | Saturn | = 60268 | km | +/- 4 |
| | Uranus | = 25559 | km | +/- 4 |
| | Neptune | = 24764 | km | +/- 15 |
| | Pluto | = 1195 | km | +/- 5 |
| | Moon (mean) | = 1737.4 | km | +/- 1 |
| | Sun (IAU 1976) | = 696000 | km | |
|+++|+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++|
|4 |Other Constants |
| |---------------------------------------------------------------------------------------------------------------------------|
| | Light-time for unit distance# | tau_A = A/c = 499.00478384 | s | +/- 1D-08 |
| | | 1/tau_A = 173.144632674 | au/d | +/- 3D-09 |
| | | | | |
| | Mass Ratio: Earth to Moon | M_E/M_M = 1/mu = 81.300568 | | +/- 3D-06 |
| | Mass Ratio: Sun to Earth | GMS/GME = 332946.0487 | | +/- 0.0007 |
| | Mass of the Sun | M_S = S = GMS/G = 1.9884D30 | kg | +/- 2D26 |
| | Mass of the Earth | M_E = E = GME/G = 5.9722D24 | kg | +/- 6D20 |
| | Mass Ratio: Sun to Earth + Moon | (S/E)/(1 + mu) = 328900.5596 | | +/- 7D-04 |
| | | | | |
| | Earth, reciprocal of flattening IERS 2003 | 1/f = 298.25642 | | +/- 1D-05 |
| | | | | |
| | Rates of precession at J2000.0 (IAU 2006) | | | |
| | General precession in longitude | p_A = 5028.796195 | "/Julian century (TDB) | |
| | Rate of change in obliquity | d(epsilon)/dT = -46.836769 | "/Julian century (TDB) | |
| | Precession of the equator in longitude | d(psi)/dT = 5038.481507 | "/Julian century (TDB) | |
| | Precession of the equator in obliquity | d(omega)/dT = -0.025754 | "/Julian century (TDB) | |
| | | | | |
| | Constant of nutation at epoch J2000.0 | N = 9.2052331 | " | |
| | Solar parallax, pi_odot | sin^-1(a_e/A) = 8.794143 | " | |
| | Constant of aberration at epoch J2000.0 | kappa = 20.49551 | " | |
| | | | | |
| | Masses of the larger natural satellites: | | | |
| | Mass satellite/mass of the planet | | | |
| | Jupiter: Io | = 4.704D-05 | | |
| | Europa | = 2.528D-05 | | |
| | Ganymede | = 7.805D-05 | | |
| | Callisto | = 5.667D-05 | | |
| | Saturn: Titan | = 2.366D-04 | | |
| | Uranus: Titania | = 4.06D-05 | | |
| | Oberon | = 3.47D-05 | | |
| | Neptune: Triton | = 2.089D-04 | | |
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
| |
| Users are advised to check the website of the IAU WG on Numerical Standards for Fundamental Astronomy (NFSA) at |
| http://maia.usno.navy.mil/NSFA.html for the latest list of 'Current Best Estimates'. The NFSA website also has detailed |
| information about the constants, and all the relevant references. |
| |
| This almanac, in certain circumstances, may not use constants from this list. The reasons and those constants used are given |
| at the end of Section L Notes and References. |
| |
| Units |
| ----- |
| 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. Some constants that involve time, either directly or indirectly need to be compatible with the underlying |
| time-scales. In order to specify this (TDB) or (TCB) or (TT), as appropriate, is included after the unit to indicate that |
| the value of the constant is compatible with the specified time-scale, for example, TDB-compatible. |
| |
| The astronomical unit of mass is the mass of the Sun (M_S). The dimensions of k^2 are those of the constant of gravitation |
| (G), which are A^3/M_S/D^2, i.e. m^3/kg/s^2. |
| |
| #The astronomical unit# of length (the au) in metres is that length A = cube root of (GMS*D^2/k^2), where k, the Gaussian |
| gravitational constant and GMS, the heliocentric gravitational constant (TDB-compatible value), are tabulated on the previous |
| page. Note: that at present (2009 September) the au is considered to be TDB-compatible and no TCB-compatible value has been |
| agreed. |
|+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++|
| 2010 February 2 |
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++