Astronomical & physical constants
| Tropical year (1900) | 31,556,925.9747 s | |
| Gaussian gravitational constant | 0.01720209895 | = 0°.9856076686 |
| Astronomical unit | 149,597,870 km | |
| Speed of light in vacuo | 299,792.458 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 ratio | 81.3007 | |
Moon's sidereal mean motion
(1900) | 2.661699489x10-6 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 parallax | 8".794148 | |
| Light-time for unit distance | 499s.004782 | = 0d.005775518 |
| Constant of aberration | 20".49552 | |
| Mean distance Earth to Moon | 384,400 km | |
| Constant of sine Moon's parallax | 3422".451 | |
| Lunar inequality | 6".43987 | |
| Parallactic inequality | 124".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 day | 24h 03m 56s.5555 | = 1d.00273791 mean sidereal time |
| Mean sidereal day | 23h 56m 04s.091 | = 0d.99726957 mean solar time |
| Sidereal rotation period of the Earth | 23h 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 radius | 6,378.1366 km |
| Polar radius | 6,356.7519 km |
| Reciprocal flattening | 298.257 |
| 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 Earth | 5.9742 x 1024 kg |
| Mass of the Moon | 7.3483 x 1022 kg |
| Mass of the Sun | 1.989 x 1030 kg |
Earth's orbit
T = Time measured in Julian centuries from 1900.0
| Annual general precession | p = 50".2564 + 0".0222 T |
| Node of moving on fixed ecliptic | Π = 173° 57'.06 + 54'.77 T |
| Speed of rotation of ecliptic | π = 0".4711 - 0".0007 T |
| Invariable plane of the solar system | Ω = 106° 35' 01" + 3452" T |
| i=1° 34' 59" - 18" T |
Solar radiation
| Solar constant | 1.39 x 103 J m-2 |
| Radiation emitted | 3.90 x 1026 J s-1 |
| Radiation emittance at surface | 6.41 x 107 J m-2 s-1 |
| Total internal radiant energy | 2.8 x 1040 J |
| Radiation emitted per unit mass | 1.96 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 type | G2V |
| Effective temperature | 5,800 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 Pole | 123°.00 |
| Mass | 1.1 x 1011 solar masses= 2.2 x 1041 kg |
| Average density | 0.1 solar mass pc-3 = 7 x 10-21 kg m-3 |
| Diameter | 25,000 pc |
| Thickness | 4,000 pc |
| Distance of Sun from centre | 8,200 pc |
| Distance of Sun above galactic plane | 8 pc |
| Solar apex (1950) from bright stars | α 18h 06m, δ +30° |
| Solar motion from bright stars | 20.0 km s-1 |
| Period of revolution of Sun about centre | 2.2x 108 yr |
Conversion factors
| Light-year | 9.4607 x 1012 km = 63,240 a.u. = 0.30660 pc |
| Parsec | 30.857 x 1012 km = 206,265 a.u. = 3.2616 L.y. |
Miscellaneous data
| Name | Value | log10 |
|---|
| π | 3.14159 26536 | 0.497 1499 |
| e | 2.71828 18285 | 0.434 2945 |
| M = log10 e | 0.43429 44819 | 1.637 7843 |
| 1/M = loge 10 | 2.30258 50930 | 0.362 2157 |
| 1 radian | 57°.29577 95131 | 1.758 1226 |
| 3437'.74677 078 | 3.536 2739 |
| 206264" 80625 | 5.314 4251 |
| 1° | 0.01745 32925 radian | 2.241 8774 |
| 1' | 0.00029 08882 | 4.463 7261 |
| 1" | 0.00000 4848137 | 6.685 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 alpha | Β β beta | Γ γ gamma | Δ δ delta | Ε ε epsilon | Ζ ζ zeta |
| Η η eta | Θ θ theta | Ι ι iota | Κ κ kappa | Λ λ lambda | Μ μ mu |
| Ν ν nu | Ξ ξ xi | Ο ο omicron | Π π pi | Ρ ρ rho | Σ σ sigma |
| Τ τ tau | Υ υ upsilon | Φ φ phi | Χ χ chi | Ψ ψ psi | Ω ω omega |
