Astronomical & physical constants

Tropical year (1900)31,556,925.9747 s 
Gaussian gravitational constant0.01720209895= 0°.9856076686
Astronomical unit149,597,870 km 
Speed of light in vacuo299,792.458 km s-1 
Dynamical form factor J2
for the Earth
0.00108263 
Product of gravitational constant
and mass of the Earth
398,600.5 km3 s-2 
Earth-Moon mass ratio81.3007 
Moon's sidereal mean motion
(1900)
2.661699489x106 radians s-1= 0".5490149294 h-1
General precession in longitude
per tropical century (1900)
5025".64 
Obliquity of the ecliptic (1900)23° 27' 08".26 
Constant of nutation in obliquity (1900)9".2109 
Solar parallax8".794148 
Light-time for unit distance499s.004782= 0d.005775518
Constant of aberration20".49552 
Mean distance Earth to Moon384,400 km 
Constant of sine Moon's parallax3422".451 
Lunar inequality6".43987 
Parallactic inequality124".986 
 

Length of the year

Tropical (equinox to equinox)365d.24219
Sidereal (fixed star to fixed star)365d.25636
Anomalistic (apse to apse)365d.25964
Eclipse (Moon's node to Moon's node)346d.62003
Gaussian (Kepler's law for a = 1)365d.25690
 

Length of the month

Tropical (equinox to equinox)27d.32158
Sidereal (fixed star to fixed star)27d.32166
Anomalistic (apse to apse)27d.55455
Draconic (node to node)27d.21222
Synodic (New Moon to New Moon)29d.53059
 

Length of the day

Mean solar day24h 03m 56s.5555= 1d.00273791 mean sidereal time
Mean sidereal day23h 56m 04s.091= 0d.99726957 mean solar time
Sidereal rotation period of the Earth23h 56m 04s.099= 0d.99726966 mean solar time
 

Figure of the Earth

ρ = Geocentric distance in equatorial radii
φ = Geographic or geodetic latitude
φ' = Geocentric latitude
h = Height in metres

Equatorial radius6,378.1366 km
Polar radius6,356.7519 km
Reciprocal flattening298.257
ρ sin φ' = S sin φ, where
S = 0.99497418 - 0.00167082 cos 2φ + 10-8(210 cos 4φ + 15.7 h)
ρ cos φ' = C cos φ, where
C = 1.00167997 - 0.00168208 cos 2φ + 10-8(212 cos 4φ + 15.7 h)
ρ = 0.99832707 + 0.00167644 cos 2φ - 10-8(352 cos 4φ - 15.7 h) + 10-8 cos 6φ
tan φ' = [0.9933054 + (0.11 x 10-8 h)] tan φ
φ - φ' = 692".74 sin 2φ - 1".16 sin 4φ
1° of latitude = [111.1333 - 0.5598 cos 2φ + 0.0012 cos 4φ] km
1° of longitude = [111.4133 cos φ - 0.0935 cos 3φ + 0.0001 cos 5φ] km
Acceleration due to gravity g = 9.780310 [1 + 0.00530239 sin2 φ - 0.00000587 sin2 φ - (31.55 x 10-8) h] m s-2
Length of seconds pendulum l =[0.9935769 - 0.0026272 cos 2φ + 0.0000029 cos 4φ - (31.55 x 10-8) h] m
Constant of gravitation G =6.672 x 10-11 kg-1 m3s-2
Mass of the Earth5.9742 x 1024 kg
Mass of the Moon7.3483 x 1022 kg
Mass of the Sun1.989 x 1030 kg
 

Earth's orbit

T = Time measured in Julian centuries from 1900.0

Annual general precessionp = 50".2564 + 0".0222 T
Node of moving on fixed eclipticΠ = 173° 57'.06 + 54'.77 T
Speed of rotation of eclipticπ = 0".4711 - 0".0007 T
Invariable plane of the solar systemΩ = 106° 35' 01" + 3452" T
i=1° 34' 59" - 18" T
 

Solar radiation

Solar constant1.39 x 103 J m-2
Radiation emitted3.90 x 1026 J s-1
Radiation emittance at surface6.41 x 107 J m-2 s-1
Total internal radiant energy2.8 x 1040 J
Radiation emitted per unit mass1.96 x 10-4 J s-1 kg-1
Visual absolute magnitude (Mv)+4.79
Colour indices (B-V, U-B)+0.62, +0.10
Spectral typeG2V
Effective temperature5,800 K
 

The galactic system

Pole of galactic plane (1950)α 12h 49m.0, δ +27° 24'
Point of zero longitude (1950)α 17h 42m.4, δ - 28° 55'
Galactic Longitude of North Celestial Pole123°.00
Mass1.1 x 1011 solar masses= 2.2 x 1041 kg
Average density0.1 solar mass pc-3 = 7 x 10-21 kg m-3
Diameter25,000 pc
Thickness4,000 pc
Distance of Sun from centre8,200 pc
Distance of Sun above galactic plane8 pc
Solar apex (1950) from bright starsα 18h 06m, δ +30°
Solar motion from bright stars20.0 km s-1
Period of revolution of Sun about centre2.2x 108 yr
 

Conversion factors

Light-year9.4607 x 1012 km = 63,240 a.u. = 0.30660 pc
Parsec30.857 x 1012 km = 206,265 a.u. = 3.2616 L.y.
 

Miscellaneous data

NameValuelog10
π3.14159 265360.497 1499
e2.71828 182850.434 2945
M = log10 e0.43429 448191.637 7843
1/M = loge 102.30258 509300.362 2157
1 radian57°.29577 951311.758 1226
3437'.74677 0783.536 2739
206264" 806255.314 4251
0.01745 32925 radian2.241 8774
1'0.00029 088824.463 7261
1"0.00000 48481376.685 5749
1 revolution = 360°= 1,296,000" = 24h = 86,400s 
1 sphere = 12.5664 steradians= 41,253 square degrees 
1 Julian year = 365.25 days= 31,557,600 seconds 
Annual precession in R.A.= 3s.0730+1s.3362 sin α tan δ 
Annual precession in Dec.= 20".043 cos α 
 

Telescope formulae

D = diameter of aperture in mm

Resolving power (Rayleigh limit)= 138 / D arc seconds
Resolving power (Dawes limit)= 116 / D arc seconds
Theoretical visual limiting magnitude
(optical system 100% efficient)
= 2 + 5 log10 D
Practical visual limiting magnitude
(optical system 65% efficient)
= 1 + 5 log10 D
 

Greek alphabet

Α α alphaΒ β betaΓ γ gammaΔ δ deltaΕ ε epsilonΖ ζ zeta
Η η etaΘ θ thetaΙ ι iotaΚ κ kappaΛ λ lambdaΜ μ mu
Ν ν nuΞ ξ xiΟ ο omicronΠ π piΡ ρ rhoΣ σ sigma
Τ τ tauΥ υ upsilonΦ φ phiΧ χ chiΨ ψ psiΩ ω omega

Section Director
Steve Harvey

Section Director, Steve Harvey

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