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

Physical constants from http://physics.nist.gov/cuu/Constants/index.html recommended by CODATA 2010
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	Ω_N	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	D_S=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 Ω_N
Stellar day	D/k'=2 π/Ω_N	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)	F_C	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)	T_C	433.1(1.7)	mean solar day D	4000	id
Quality factor of Chandler peak	Q_C	170	-	-	Wilson and Vicente, 1980, Geophys. J. R. Astr. Soc., 62, 605-616.
Free Core Nutation (FCN) period (in the celestial frame)	T_F	430.2(3)	mean solar day D	700	Nutation model MHB 2000
Quality factor of the FCN	Q_F	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)			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	λ_A	-14.9291(10)	°	100	IAG 1999
		−14.928509(75)	°	5	Chen & Shen (2010) Tab 2b
Colatitude of the principal inertia axis A	θ_A	0.00003788(48)	°	20000	Chen & Shen (2010) Tab 2b
First equatorial moment of inertia of the core	A_f	9.115 237 9	10³⁶ kg m²		Chen & Shen (2010) Tab 3
Second equatorial moment of inertia of the core	B_f	9.115 399 7	10³⁶ kg m²		Chen & Shen (2010) Tab 3
Axial moment of inertia of the core	C_f	9.139 353 0	10³⁶ kg m²		Chen & Shen (2010) Tab 3
First equatorial moment of inertia of the mantle	A_m = A-A_f	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	B_m=B-B_f	7.098 72			Chen & Shen (2010)
Axial moment of inertia of the mantle	C_m=C-C_f	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	e_f=(C_f - A_f)/A_f	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
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	m_e	9.109 382 91(40)	10^-31 kg	0.05	CODATA
Proton mass	m_p	1.672 621 777(74)	10^-27 kg	0.05	CODATA
Ratio masses proton-electron	m_p/m_e	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

Chen Shen (2010), New estimates of the inertia tensor and rotation of the triaxial nonrigid Earth, JGR 115, B12419, doi:10.1029/2009JB007094, 2010