| 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 March 13 2021 |
||
|
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 | |
| 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) | 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 | Chen & Shen (2010) | |||
| Second equatorial moment of inertia of the core | Bm=B-Bf | 7.098 72 | Chen & Shen (2010) | ||
| Axial moment of inertia of the mantle | 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 | 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 | |
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° |
||||
| 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 | ||||
Chen Shen (2010), New estimates of the inertia tensor and rotation of the triaxial nonrigid Earth, JGR 115, B12419, doi:10.1029/2009JB007094, 2010
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