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USEFUL CONSTANTS
USEFUL CONSTANTS 
  This table undergoes permanent improvements and adds. Any suggestion are welcome, please send it to christian.bizouard[at]obspm.fr. Thanks to Pr. "Sonny" Mathews (Madras) for his help.
Updated February 13 2014

N.B. : the present relative uncertainty on the earth's orientation parameters is about 10-4 = 100 10-6.

 
Earth's rotation | Geodesy | Gravity | Cosmology | Physics | Conversion of units

Constant Symbol Value
(Uncertainty on the last digits are indicated in parentheses)
   Units    Relative
uncertainty
in 10-6 (ppm)
Sources - Remarks
Earth's rotation constants
Mean angular velocity of the Earth Ω   7.292 115 0(1) 10-5 rad/s 0.014 IERS Numerical Standards
(IAG 1999).
Nominal angular velocity of the Earth ΩN 7.292 115 146 706 4 10-5 rad/s exact Reference angular velocity corresponding to the epoch 1820
Conventional duration of the mean solar day D 86 400 s exact Corresponds to the duration of the mean solar day in the first mid of the nineteen century; presently the mean solar day (the seasonal variation is removed) exceeds 86400 s by about 0.2 ms.
Ratio mean solar day/sidereal day k 1.002 737 909 350 795 - exact Aoki et al, 1982, "The New definition of Universal Time", Astron. Astrophys., 105, 359-361 (1982)
Conventional duration of the sidereal day DS=D/k  86164.090 530 832 88 s exact from k given in Aoki et al, 1982, "The New definition of Universal Time", Astron. Astrophys., 105, 359-361 (1982)
Ratio mean solar day/stellar day k' 
1.002 737 811 911 354 48
- exact IERS Conventions (2003). Value consistent with the nominal Earth angular velocity ΩN
Stellar day D/k'=2 π/ΩN 86164.098 903 691 s exact From k'. The stellar day referred to the stars is not affected by the precession and therefore is slightly larger than the sidereal day
General precession in longitude p 5028.792(2) " per century 0.4 from MHB 2000 nutation model
Obliquity of the ecliptic for the epoch J2000.0 ε0 23°26'21".4119
(sin ε0=0.397776995)
- exact Definition constant (IAU 1976)
Chandler frequency (in the terrestrial frame) FC 0.8433(30) cycle per tropical year 4000 Vicente, R.O., Wilson 1997, C.R., JGR, Vol. 102, B9, pp 20439-20446
Chandler period (in the terrestrial frame) TC 433.1(1.7) mean solar day D 4000 id
Quality factor of Chandler peak QC 170 - - Wilson and Vicente, 1980, Geophys. J. R. Astr. Soc., 62, 605-616.
Free Core Nutation (FCN) period (in the celestial frame) TF 430.2(3) mean solar day D 700 Nutation model MHB 2000
Quality factor of the FCN QF 20000 - - Nutation model MHB 2000
Sidereal year - 365.256 363 004
(365d 6h 9m 9.76s)
mean solar day
[D=86400s]
  From the mean longitude referred to the mean ecliptic and the equinox J2000 given in Simon et al., 1994, Astron. Astrophys., 282, 663
Tropical year - 365.242 190 402
(365d 5h 48m 45.25s)
mean solar day [D=86400s]   From the mean longitude referred to the mean ecliptic and the equinoxof the date given in Simon et al., 1994, Astron. Astrophys., 282, 663
Mean motion of the Moon - 2π / 27.32166155(1) rad/mean solar day [=86400s]   IERS Conventions 2003
Geodetic constants
Earth's equatorial radius a 6 378 136.6(1) m 0.015 IERS Numerical Standards
(IAG 1999)
First equatorial moment of inertia A 8.010 1(2) 1037 kg m2 25

IAG 1999

    8.010 082 9(84) 1037 kg m2 0.1 Chen & Shen (2010) Tab 2a
Second equatorial moment of inertia B     8.010 3(2) 1037 kg m2 25 IAG 1999
    8.010 259 4(84) 1037 kg m2 0.1 Chen & Shen (2010) Tab 2a
Mean equatorial moment of inertia A=(A+B)/2 8.010 171 1(84)     from Chen & Shen (2010) Tab 2a
Axial moment of inertia C

8.0365(2)

1037 kg m2 25 IAG 1999
   

8.0364807(84)

1037 kg m2 0.1 Chen & Shen (2010) Tab 2a
Longitude of the principal inertia axis A λA -14.9291(10) ° 100 IAG 1999
    −14.928509(75) ° 5 Chen & Shen (2010) Tab 2b
Colatitude of the principal inertia axis A θA 0.00003788(48) ° 20000 Chen & Shen (2010) Tab 2b
First equatorial moment of inertia of the core Af 9.115 237 9
1036 kg m2   Chen & Shen (2010) Tab 3
Second equatorial moment of inertia of the core Bf 9.115 399 7 1036 kg m2   Chen & Shen (2010) Tab 3
Axial moment of inertia of the core Cf 9.139 353 0 1036 kg m2   Chen & Shen (2010) Tab 3
First equatorial moment of inertia of the mantle Am = A-Af 7.016 5 1037 kg m2 ? Barnes et al, 1983, Proc. R. Soc. Lond., A 387, 31-73
    7.098 56 1037 kg m2   from Chen & Shen (2010)
Second equatorial moment of inertia of the core Bm=B-Bf 7.098 72     from Chen & Shen (2010)
Axial moment of inertia of the core Cm=C-Cf 7.040 0 1037 kg m2 ? Barnes et al, 1983, Proc. R. Soc. Lond., A 387, 31-73
    7.122 55 1037 kg m2   from Chen & Shen (2010)
Earth flattening f 1/298.25642(1) - 0.03 IERS Numerical Standards
(IAG 1999)
"Astronomical" dynamical ellipticity H 3.2737949(1) 10-3 - 0.03 H=(C-A)/C
Nutation model MHB 2000
Dynamical ellipticity e=(C - A)/A

3.284 547 9(1) 10-3

- 0.0 Nutation model MHB 2000
    3.284 517 8 10-3     Chen & Shen (2010) Tab. 4
Dynamical ellipticity of the core ef=(Cf - Af)/Af 2.646(2) 10-3 - 750 Nutation model MHB 2000
    2.645 575 8 10-3     Chen & Shen (2010) Tab. 4
Second degree term in Earth's gravity potential J2 1.082 635 9(1) 10-3 - 0.09 IERS Numerical Standards
(IAG 1999)
J2=-(A+B-2C)/(2MR2)
Secular rate of J2 d( J2 )/dt -2.6(3) 10-11 year-1 115000 IAG 1999
Love number k2 0.3 - - IAG 1999
Secular Love number ks 0.9383 - - IAG 1999
Gravitational constants
Mean equatorial gravity g 9.780 327 8 (10) m s-2 0.1 recommended by CODATA (july 2000)
Gravitational constant G 6.673 84(80) 10-11 m3kg-1s-2 100 recommanded by CODATA 2010
  G 6.675 59(27) 10-11 m3kg-1s-2 40 Quinn et al., Phys. Rev. Lett. 87 (2001)
Geocentric constant of gravitation GM 3.986 004 418(8) 1014 m3s-2 0.002 IERS numerical standard
(IAG1999)
Heliocentric constant of gravitation GS 1.327 124 420 76(50) 1020 m3s-2 0.0004 IERS numerical standard
(from Standish, 1998)
Mass Moon/ Mass Earth µ 0.012 300 038 3(5) - 0.04 IERS numerical standard
(from Standish, 1998)
Cosmological constant
Hubble constant H 73 (3) km s-1Mpc-1 41095 recommanded by CODATA 2006
Hubble length R = c/H 1.27(5) 1026 m 41095 recommanded by CODATA 2006
Age of the Universe t0 13.73(15) Giga year 10924 recommanded by CODATA 2006
Physical constants from http://physics.nist.gov/cuu/Constants/index.html recommended by CODATA 2010
Speed of light in ether or so-called vacuo c 299 792 458 ms-1 (by definition) CODATA
permeability of the free space μ0 4 π 10-7 NA-2 (exact) CODATA
    = 12.566 370 614... 10-7 NA-2 (calculated) CODATA
permittivity of the free space ε0 1/(μ0 c2) =8.854 187 817 10-12 Fm-1 (calculated) CODATA
Gravitational constant G 6.673 84(80) 10-11 m3kg-1s-2 100 CODATA
Planck constant h 6.626 069 57(29) 10-34 Js 0.05 CODATA
h/2π h 1.054 571 726(47) 10-34 Js 0.05 CODATA
Electron charge e 1.602 176 565(35) 10-19 C 0.025 CODATA
Electron mass me 9.109 382 91(40) 10-31 kg 0.05 CODATA
Proton mass mp 1.672 621 777(74) 10-27 kg 0.05 CODATA
Ratio masses proton-electron mp/me 1836.152 672 45(75)   0.0004 CODATA
Fine-structure constant a 7.297 352 5698(24) 10-3 0.0003 CODATA
Inverse of the fine- struture constant a-1 137.035 999 074(44)   0.0003 CODATA
Avogadro number NA, L 6.022 141 29(27) 1023 mol-1 0.04 CODATA
Boltzmann constant, R/ NA k 1.380 6488(13) 10-23 JK-1 0.9 CODATA
Stefan-Boltzmann constant σ 5.670 373(21) 10-8 Wm-2K-4 4 CODATA
Units and conversion of units
1 astronomical unit UA 149 597 870.691(6) km 0.00004 numerical IERS Standards
From milliarcseconds (mas) to radians 1 mas =4.8481(1) 10-9 rad
What represents an arc of 1mas from the center of the Earth at distance equal to the polar radius (6 356 755 m)? 3.1(1) cm
Conversion of arc units in hour, minute, second to arc units in degre, arcminute, arcsecond

24 h = 360°       1 h = 15°
1 min = 15'      1 s = 15"
1 ms = 15 mas

From modified julian (MJD) day to "julian" year (JY) JY=2000-(51544.5-MJD)/365.25
From modified julian (MJD) day to besselian year (BJ) BY=2000-(51544.33 3981-MJD)/365.242 198 781 (SOFA)
From julian year (JY) to modified julian date (MJD) MJD=(JY - 2000) * 365.25 + 51544.5