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# Astrophysical constants and parameters

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(Barred spiral galaxy, Eridanus constellation)

The following table contains the values of the constants and parameters commonly used in astrophysics and also more particularly in cosmology. Concerning the cosmological parameters, the ΛCDM model which is the basis of the standard model of the cosmology is used and the numerical values correspond to the best fit within a confidence interval of 68% (except explicit mention).

These values are gathered in the annual review of the Particle Data Group.

Quantity Symbol, equation Value
Speed of light in a vacuum c 299 792 458 m·s-1
Newtonian constant of gravitation GN 6,673 84(80)×10-11 m3·kg-1·s-2
Astronomical unit (constant) ua 149 597 870 700 m
Tropical year (from equinox to equinox) year 149 597 870 700 m
Sidereal year (from fixed star to fixed star) 31 558 149,8 s
Average sidereal day 23 h 56 min 04,090 53 s
Jansky Jy 1×10-26 W·m-2·Hz-1
Planck mass √(ℏc/GN) 12,209 0(9)×1018 GeV/c2 = 21,764 5(16)×10-9 kg
Planck length √(ℏGN/c3) 1,616 24(12)×10-35 m
Planck time √(ℏGN/c5) 5,39121×10-44 s
Planck temperature TP = √(ℏc5/GNk2) 1,41679×1032 K
Current Hubble constant H0 100 h·km·s-1·Mpc-1 = h × (9,77813 Ga)−1
Standardized Hubble constant h 0,73+0,04−0,03
Hubble length c/H0 ≈ 120×1021 km
Parsec (1 UA / 1 arc sec) pc 30,856775814672×1012 km = 3,26… al
Light-year yl 0,306 6…pc = 9,461…×1012 km
Schwarzschild radius of the Sun 2GNMS/c2 2,95325008 km
Sun mass MS 1,988 44(30)×1030 kg
Equatorial radius of the Sun RS 696 100 km
Brightness of the Sun LS 384,6±0,8×1024 W
Schwarzschild radius of Earth 2GNME/c2 8,87005622 mm
Earth mass ME 5,972 3(9)×1024 kg
Earth’s average equatorial radius RE 6,378140×106 m
Speed of the Sun around the center of the Milky Way Θo 220(20) km·s-1
Distance from the Sun to the galactic center Ro 8,0(5) kpc
Local density of the galactic disc ρdisc 3-12×10-24 g·cm-3 ~ 2-7 GeV/c2·cm-3
Local density of the galactic halo ρhalo 2-13×10-25 g·cm-3 ~ 0,1-0,7 GeV/c2·cm-3
Current CMB Temperature T0 2,725±0,001 K
Current CMB dipole range 3,346±0,017 mK
Speed of the Sun in relation to the CMB 369±2 km·s-1 in the direction of (l,b) = (263,86°±0,04°, 48,24°±0,010°)
Speed of the local group compared to the CMB vLG 627±22 km·s-1 in the direction of (l,b) = (276°±3°, 30°±3°)
Boltzmann constant (or entropy density) s/k 2 889,2 (T/2,725)3·cm-3
CMB photon density nγ 410,5±0,5 cm-3
Scaling factor for the cosmological constant c2/3H02 2,853×1051 h-2·m2
Critical mass density of the Universe ρc = 3H02/8πGN 2,77536627×1011 h2·MS·Mpc-3 = 1,878 37(28)×10-29 h2·g·cm-3 = 1,053 69(16)×10-5 h2·(GeV/c2)·cm-3
Density of matter without pressure in the universe Ωm = ρmc 0,127+0,007−0,009h-2 ⇒ 0,24+0,03−0,04
Density of baryons in the universe Ωb = ρbc 0,0223+0,0007−0,0009h-2 ⇒ 0,042+0,003−0,005
Density of dark matter in the universe Ωdm = Ωm − Ωb 0,105+0,007−0,010h-2 ⇒ 0,20+0,02−0,04
Density of radiation in the universe Ωγ = ργc (2,471±0,004)h×10-5 h-2 ⇒ (4,6±0,5)×10-5
Density of neutrinos in the universe Ων < 0,007 h-2 ⇒ < 0,014 (at a confidence level of 95%)
Dark energy density in the universe ΩΛ 0,76+0,04−0,06
Total energy density in the universe Ωtot = Ωm + Ωγ + Ων + ΩΛ 1,003+0,013−0,017
Baryons/photons ratio η = nb/nγ 4,7×10-10 < η < 6,5×10-10 (95 %)
Density of number of baryons nb 1,9×10-7 cm-3 < nb < 2,7×10-7 cm-3
Parameter of equation of state for dark energy w -0,97+0,07−0,09
Amplitude fluctuation at scale 8: h−1·Mpc σ8 0,74+0,05−0,06
Scalar spectral index of the adjustment of the power law to the observations ns 0,951+0,015−0,019
Variation of the spectral index for k0 = 0,05 Mpc-1 dns/d ln ⁡ k -0,055+0,029−0,035
Relationship of tensor/scalar perturbations in the CMB for k0 = 0,05 Mpc-1 r = T/S < 0,55 (95 %)
Optical reionization depth τ 0,09±0,03
Age of the universe t0 13,7+0,1−0,2 Gy