IAU Working Group Numerical Standards for Fundamental Astronomy (original) (raw)

Constant of gravitation

G = 6.674 28 x 10−11 m3kg−1s−2

G

Uncertainty:

6.7 x 10−15 m3kg−1s−2

Status:

Notes:

  1. The value for the constant of gravitation, G, has been changed from the CODATA 1998 value to the value adopted by CODATA 2006.

References:

  1. CODATA 2006, physics.nist.gov/cuu/Constants
  2. Mohr, P. J. and Taylor, B. N., 2000, "CODATA recommended values of the fundamental physical constants: 1998,"Rev. Mod. Phys., 72, pp. 351-495.
  3. Mohr, P. J., Taylor, B. N., and Newell, D. B., 2008, "The CODATA recommended values of the fundamental physical constants: 2006,"Rev. Mod. Phys., 80, pp. 633-730.

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Average value of
1−d(TCG)/d(TCB)

_L_C = 1.480 826 867 41 x 10−8

_L_C

Uncertainty:

2 x 10−17

Status:

Notes:

  1. The value for _L_C is taken from Irwin and Fukushima (1999) and is the most recent published determination. It is based on the DE405.
  2. _L_C is used in some analtical formulas for the transformation between TCG and TCB.
  3. Before 2006, _L_C was used to compute_L_B but since the adoption of IAU 2006 Resolution B3, that is no longer true.
  4. Before IAU 2006, _L_B was computed as_L_B = _L_C +_L_G −_L_C × _L_G. This relation does not hold [exactly] between the defining values of_L_B and_L_G and a value of_L_C computed from an ephemeris.

References:

  1. Irwin, A. and Fukushima, T., 1999, "A numerical time ephemeris of the Earth,"Astron. Astrophys., 348, pp. 642-652.

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Solar mass parameter

_GM_S = 1.327 124 420 99 x 1020 m3s−2 [TCB-compatible]
_GM_S = 1.327 124 400 41 x 1020 m3s−2 [TDB-compatible]

_GM_S

Uncertainty:

1.0 x 1010 m3s−2 [TCB-compatible]
1.0 x 1010 m3s−2 [TDB-compatible]

Status:

Notes:

  1. The IAU GA 2012 Resolution B2 defined the astronomical unit (au) as a conventional value, thus breaking the historical relationship between _GM_S, k, and the au. Thus noting (3) and recommends (4) of the resolution states that _GM_S, the solar mass parameter, previously know as the heliocentric gravitational constant be determined observationally in SI units.
  2. This value for _GM_S given is taken from the Folkner et al. (2008) fit to the DE421 ephemerides. It was not derived using the value of au, but the TDB-compatible value of _GM_S given is consistent with the value of au given (Pitjeva and Standish, 2009) to within the errors of the estimate.
  3. The previous definitions for _GM_S, k and the au are given in the archive.

References:

  1. Folkner, W.M., Williams, J.G., and Boggs, D.H., 2008, "The Planetary and Lunar Ephemeris DE 421," Memorandum IOM 343R-08-003, 31 pp.
  2. Pitjeva, E.V. and Standish, E.M., 2009, "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the astronomical unit,"Celest. Mech. Dyn. Astr., 103, pp. 365-372, doi: 10.1007/s10569-009-9203-8.
  3. The IAU GA 2012 Resolution B2

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Equatorial radius of the Earth

_a_E = 6.378 1366 x 106 m [TT-compatible]

_a_E

Uncertainty:

1 x 10−1 m [TT-compatible]

Status:

Notes:

  1. _a_E is taken from Burša, et al. (1998) and was included in the International Association of Geodesy (IAG) Special Commission 3 (SC3) Report in Groten (2000).
  2. The value of _a_E is the "zero tide" value. See the IERS Conventions for more explanation of the terminology "zero tide".
  3. Although the value is listed as TT-compatible, the TCG-compatible value is equivalent to the number of decimal places listed.

References:

  1. Groten, E., 2000, Geodesists Handbook 2000, Part 4, www.gfy.ku.dk/~iag/HB2000/part4/groten.htm. See also "Parameters of Common Relevance of Astronomy, Geodesy, and Geodynamics,"J. Geod., 74, pp. 134-140.
  2. Burša, M., Kouba, J., Radej, K., True, S.A., Vatrt, V., Vojtišková, M., 1998, "Mean Earth's Equipotential Surface from Topex/Poseidon Altimetry,"Studia Geoph. et Geod., 42, pp. 459-466, doi: 10.1023/A:1023356803773.
  3. IERS Conventions, 2003, McCarthy, D.D. and Petit, G.,IERS Technical Note 32., Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main, 127 pp.

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Dynamical form factor

_J_2 = 1.082 6359 x 10−3

_J_2

Uncertainty:

1 x 10−10

Status:

Notes:

  1. The dynamical form factor is taken from the International Association of Geodesy (IAG) Special Commission 3 (SC3) Report provided by Groten (2000).
  2. The value for _J_2 is the "zero tide" value (see IERS Conventions for an explanation of the terminology). Values according to other conventions can be found in Groten (2000).

References:

  1. Groten, E., 2000, Geodesists Handbook 2000, Part 4, www.gfy.ku.dk/~iag/HB2000/part4/groten.htm. See also "Parameters of Common Relevance of Astronomy, Geodesy, and Geodynamics,"J. Geod., 74, pp. 134-140.
  2. IERS Conventions, 2003, McCarthy, D.D. and Petit, G.,IERS Technical Note 32., Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main, 127 pp.

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Time rate of change in _J_2

d_J_2/dt = −3.0 x 10−9 cy−1

d_J_2/dt

Uncertainty:

6 x 10−10 cy−1

Status:

Notes:

  1. The time rate of change in _J_2 is a value adopted in IAU 2006 Resolution B1 that is consistent with the adopted IAU 2006 precession model.
  2. The value is taken from Capitaine et al. (2005).
  3. A discussion about the uncertainty can be found in Bourda and Capitaine (2004) and in Hilton et al. (2006) while a discussion about the components of the_J_2 variation can be found in Cheng and Tapley (2004) with a 2008 AGU update ( 2008AGUFM.G33A0673C).

References:

  1. International Astronomical Union (IAU), 2006, "Proceedings of the Twenty-Sixth General Assembly,"Transactions of the IAU, XXVIB.
  2. Capitaine, N., Wallace, P.T., and Chapront, J., 2005, "Improvement of the IAU 2000 precession model,"Astron. Astrophys., 432, pp. 355-367.
  3. Bourda, G. and Capitaine, N., 2004, "Precession, nutation and space geodetic determination of the Earth's variable gravity field,"Astron. Astrophys., 428, pp. 691-702.
  4. Cheng and Tapley, 2004, "Variations in the Earth's oblateness during the past 28 years,"Journ. Goephys. Res., 109, B09402, doi: 10.1029/2004JB003028.
  5. Hilton, J.L., Capitaine, N., Chapront, J., Ferrandiz, J.M., Fienga, A., Fukushima, T., Getino, J., Mathews, P., Simon, J.-L., Soffel, M., Vondrak, J., Wallace, P., and Williams, J., 2006, "Report of the International Astronomical Union Division I Working Group on Precession and the Ecliptic,"Celest. Mech. Dyn. Astr., 94, pp. 351-367, doi: 10.1007/s10569-006-0001-2.

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Geocentric gravitational constant

_GM_E = 3.986 004 418 x 1014 m3s−2 [TCB-compatible]
_GM_E = 3.986 004 415 x 1014 m3s−2 [TT-compatible]
_GM_E = 3.986 004 356 x 1014 m3s−2 [TDB-compatible]

_GM_E

Uncertainty:

8 x 105 m3s−2 [TCB-compatible]
8 x 105 m3s−2 [TT-compatible]
8 x 105 m3s−2 [TDB-compatible]

Status:

References:

  1. Ries, J. C., Eanes, R. J., Shum, C. K., and Watkins, M. M., 1992, "Progress in the Determination of the Gravitational Coefficient of the Earth,"Geophys. Res. Lett., 19(6), pp. 529-531.

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Potential of the geoid

_W_0 = 62 636 853.4 m2s−2

_W_0

Uncertainty:

The formal error is 0.02 m2s−2; however, as convention the adopted value is understood free of error.

Status:

References:

  1. Sánchez L., Cunderlík R., Dayoub N., Mikula K., Minarechová Z., Šíma Z., Vatrt V., Vojtíšková M., 2016, "A conventional value for the geoid reference potential W0", Journal of Geodesy, 10.1007/s00190-016-0913-x https://www.math.sk/mikula/W0_JoGE.pdf. See also Working Group on Vertical Datum Standardization http://ggos.org/en/focus-areas/unified-height-system/working-group/011-vds/

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Nominal mean angular velocity of the Earth

ω = 7.292 115 x 10−5 rad s−1 [TT-compatible]

ω

Uncertainty:

(see Notes)

Status:

Notes:

  1. ω is a nominal value and was chosen to have the number of significant digits limited to those for which the value can be considered constant.
  2. Although the value is listed as TT-compatible, the TCG-compatible value is equivalent to the number of decimal places listed.

References:

  1. Groten, E., 2000, Geodesists Handbook 2000, Part 4, www.gfy.ku.dk/~iag/HB2000/part4/groten.htm. See also "Parameters of Common Relevance of Astronomy, Geodesy, and Geodynamics,"J. Geod., 74, pp. 134-140.

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Ratio mass of the Moon to the Earth

_M_M/_M_E = 1.230 003 71 x 10−2

_M_M/_M_E

Uncertainty:

4 x 10−10

Status:

Notes:

  1. This value is equivalent to _M_E / _M_M = 81.300 5678 ± 2.7 × 10-6.

References:

  1. Pitjeva, E.V. and Standish, E.M., 2009, "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the astronomical unit,"Celest. Mech. Dyn. Astr., 103, pp. 365-372, doi: 10.1007/s10569-009-9203-8.

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Ratio of the mass of the Sun to Mercury

_M_S/_M_Me = 6.023657330 x 106

_M_S/_M_Me

Uncertainty:

2.35 x 10−1

Status:

References:

  1. Mazarico, E., Genova, A., Goossens, S., Lemoine, F.G., Neumann, G.A., Zuber, M.T., Smith, D.E., Solomon, S.C., 2014, "The gravity field, orientatation, and ephemeris of Mercury from MESSENGER observations after three years in orbit,"J. Geophys. Res.: Planets, 119, pp. 337-349, doi:10.1002/2014JE004675.

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Ratio of the mass of the Sun to Venus

_M_S/_M_Ve = 4.085 237 19 x 105

M_S/M_Ve

Uncertainty:

8 x 10−3

Status:

References:

  1. Konopliv, A.S., Banerdt, W.B., and Sjogren, W.L., 1999, "Venus Gravity: 180th Degree and Order Model,"Icarus, 139, pp. 3-18.

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Ratio of the mass of the Sun to Mars

_M_S/_M_Ma = 3.098 703 59 x 106

_M_S/_M_Ma

Uncertainty:

2 x 10−2

Status:

Notes:

  1. Includes the sum of the masses of the body and its satellites.

References:

  1. Konopliv, A.S., Yoder, C.F., Standish, E.M., Yuan, D.N., Sjogren, W.L., 2006, "A global solution for the Mars static and seasonal gravity, Mars orientation, Phobos and Deimos masses, and Mars ephemeris,"Icarus, 182(1), pp. 23-50.

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Ratio of the mass of the Sun to Jupiter

_M_S/_M_J = 1.047 348 644 x 103

_M_S/_M_J

Uncertainty:

1.7 x 10−5

Status:

Notes:

  1. Includes the sum of the masses of the body and its satellites.

References:

  1. Jacobson, R.A., Haw, R.J., McElrath, T.P., and Antreasian, P.G., 2000, "A Comprehensive Orbit Reconstruction for the Galileo Prime Mission in the J2000 System,"J. Astronaut. Sci., 48(4), pp. 495-516.

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Ratio of the mass of the Sun to Saturn

_M_S/_M_Sa = 3.497 9018 x 103

_M_S/_M_Sa

Uncertainty:

1 x 10−4

Status:

Notes:

  1. Includes the sum of the masses of the body and its satellites.

References:

  1. Jacobson, R.A., Antreasian, P.G., Bordi, J.J., Criddle, K.E., Ionasescu, R., Jones, J.B., Mackenzie, R.A., Pelletier, F.J., Owen Jr., W.M., Roth, D.C. and Stauch, J.R., 2006, "The gravity field of the Saturnian system from satellite observations and spacecraft tracking data,"Astron. J., 132(6), pp. 2520-2526.

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Ratio of the mass of the Sun to Uranus

_M_S/_M_U = 2.290 295 1 x 104

_M_S/_M_U

Uncertainty:

1.7 x 10−2

Status:

Notes:

  1. Includes the sum of the masses of the body and its satellites.

References:

  1. Jacobson, R.A., 2014, "The orbits of the Uranian satellites and rings, the gravity field of the Uranian system, and the orientation of the pole of Uranus,"Astron. J., 148:76, 13 pp, doi:10.1088/0004-6256/148/5/76.

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Ratio of the mass of the Sun to Neptune

_M_S/_M_N = 1.941 226 x 104

_M_S/_M_N

Uncertainty:

3 x 10−2

Status:

Notes:

  1. Includes the sum of the masses of the body and its satellites.

References:

  1. Jacobson, R.A., 2009, "The Orbits of the Neptunian Satellites and the Orientation of the Pole of Neptune,"Astron. J., 137, pp. 4322-4329, doi: 10.1088/004-6256/137/5/4322.

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Ratio of the mass of the Sun to (134340) Pluto

_M_S/_M_P = 1.360 5 x 108

_M_S/_M_P

Uncertainty:

2.1 x 105

Status:

Notes:

  1. Includes the sum of the masses of the body and its satellites.

References:

  1. Brozović, M., Showalter, M.R., Jacobson, R.A., and Buie, M.W., 2015, "The orbits and masses of satellites of Pluto,"Icarus, 246, pp. 317-329.

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Ratio of the mass of the Sun to (136199) Eris

_M_S/_M_Eris = 1.191 x 108

_M_S/_M_Eris

Uncertainty:

1.4 x 106

Status:

Notes:

  1. Includes the sum of the masses of the body and its satellites.
  2. Equivalently _M_Eris/_M_S = 8.396 x 10−9 ± 0.100 x 10−9.

References:

  1. Brown, M.E. and Schaller, E.L., 2007, "The mass of Dwarf Planet Eris," Science, 316, p. 1585, doi: 10.1126/science.1139415.

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Ratio of the mass of (1) Ceres to the Sun

_M_Ceres/_M_S = 4.72 x 10−10

_M_Ceres/_M_S

Uncertainty:

3 x 10−12

Status:

References:

  1. Pitjeva, E.V. and Standish, E.M., 2009, "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the astronomical unit,"Celest. Mech. Dyn. Astr., 103, pp. 365-372, doi: 10.1007/s10569-009-9203-8.

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Ratio of the mass of (2) Pallas to the Sun

_M_Pallas/_M_S = 1.03 x 10−10

_M_Pallas/_M_S

Uncertainty:

3 x 10−12

Status:

References:

  1. Pitjeva, E.V. and Standish, E.M., 2009, "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the astronomical unit,"Celest. Mech. Dyn. Astr., 103, pp. 365-372, doi: 10.1007/s10569-009-9203-8.

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Ratio of the mass of (4) Vesta to the Sun

_M_Vesta/_M_S = 1.302 684 6 x 10−10

_M_Vesta/_M_S

Uncertainty:

9 x 10−17

Status:

References:

  1. Konopliv, A.S., Asmar, S.W., Park, R.S., Bills, B.G., Centinello, F., Chamberlin, A.B., Ermakov, A., Gaskell, R.W., Rambaux, N., Raymond, C.A., Russell. C.T., Smith, D.E., Tricarico, P., Zuber, M.T., 2014, "The Vesta gravity field, spin pole and rotatin period, landmark positions, and ephemeris from the Dawn tracking and optical data,"Icarus, 240, pp. 103-117,

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Obliquity of the ecliptic at J2000.0

_ε_J2000 = 8.438 1406 x 104 "

_ε_J2000

Uncertainty:

1 x 10−3 "

Status:

Notes:

  1. The obliquity of the ecliptic at J2000.0 is from the Hilton et al. (2006) report from the IAU Working Group on precession and the ecliptic. This value is taken from the P03 precession model of Capitaine et al. (2003) and was adopted in IAU 2006 Resolution B1.
  2. The value was determined by Chapront et al. (2002) using lunar laser ranging observations.
  3. _ε_J2000 is a component of the IAU 2006 precession model that includes expressions that are time dependent.

References:

  1. International Astronomical Union (IAU), 2006 "Proceedings of the Twenty-Sixth General Assembly",Transactions of the IAU, XXVIB.
  2. Hilton, J.L., Capitaine, N., Chapront, J., Ferrandiz, J.M., Fienga, A., Fukushima, T., Getino, J., Mathews, P., Simon, J.-L., Soffel, M., Vondrak, J., Wallace, P., and Williams, J., 2006, "Report of the International Astronomical Union Division I Working Group on Precession and the Ecliptic,"Celest. Mech. Dyn. Astr., 94, pp. 351-367, doi: 10.1007/s10569-006-0001-2.
  3. Capitaine, N., Wallace, P., and Chapront, J., 2003, "Expressions for IAU 2000 precession quantities",Astron. Astrophys., 412, pp. 567-586.
  4. Chapront, J, Chapront-Touze, M., and Francou, G., 2002, "A new determination of lunar orbital parameters, precession constant and tidal acceleration from LLR measurements,"Astron. Astrophys., 387, pp. 700-709, doi: 10.1051/0004-6361:20020420.

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