# Astronomical Constants

The IAU system of constants defines a system of astronomical units for length, mass and time, and also includes astronomical constants such as the speed of light and the constant of gravitation which allow transformations between astronomical units and SI units.

Introduction to Astronomy Series

- Introduction to Astronomy
- The Celestial Sphere - Right Ascension and Declination
- What is Angular Size?
- What is the Milky Way Galaxy?
- The Astronomical Magnitude Scale
- Sidereal Time, Civil Time and Solar Time
- Equinoxes and Solstices
- Parallax, Distance and Parsecs
- A Newbie's Guide to Distances in Space
- Luminosity and Flux of Stars
- Kepler's Laws of Planetary Motion
- What Are Lagrange Points?
- Glossary of Astronomy & Photographic Terms
**Astronomical Constants**

Quantity | Symbol | Value | Relative uncertainty |
---|---|---|---|

Defining constants | |||

Gaussian gravitational constant | k | 0.017 202 098 95 A^{3/2} S^{−1/2} D^{−1} | defined |

Speed of light | c | 299 792 458 m s^{−1} | defined |

Mean ratio of the TT second to the TCG second | 1 − L_{G} | 1 − 6.969 290 134×10^{−10} | defined |

Mean ratio of the TCB second to the TDB second | 1 − L_{B} | 1 − 1.550 519 767 72×10^{−8} | defined |

Primary constants | |||

Mean ratio of the TCB second to the TCG second | 1 − L_{C} | 1 − 1.480 826 867 41×10^{−8} | 1.4×10^{−9} |

Light-time for unit distance | ι_{A} | 499.004 786 3852 s | 4.0×10^{−11} |

Equatorial radius for Earth | a_{e} | 6.378 1366×10^{6} m | 1.6×10^{−8} |

Potential of the geoid | W_{0} | 6.263 685 60×10^{7} m^{2} s^{−2} | 8.0×10^{−9} |

Dynamical form-factor for Earth | J_{2} | 0.001 082 6359 | 9.2×10^{−8} |

Flattening factor for Earth | 1/ƒ | 0.003 352 8197 = 1/298.256 42 | 3.4×10^{−8} |

Geocentric gravitational constant | GE | 3.986 004 391×10^{14} m^{3} s^{−2} | 2.0×10^{−9} |

Constant of gravitation | G | 6.673 84×10^{−11} m^{3} kg^{−1} s^{−2} | 1.2×10^{−4} |

Ratio of mass of Moon to mass of Earth | µ | 0.012 300 0383 = 1/81.300 56 | 4.0×10^{−8} |

General precession in longitude, per Julian century, at standard epoch 2000 | ρ | 5029.796 195″ | * |

Obliquity of the ecliptic, at standard epoch 2000 | ε | 23° 26′ 21.406″ | * |

Derived constants | |||

Constant of nutation, at standard epoch 2000 | N | 9.205 2331″ | * |

Unit distance = cι_{A} | A | 149 597 870 691 m | 4.0×10^{−11} |

Solar parallax = arcsin(a_{e}/A) | π_{☉} | 8.794 1433″ | 1.6×10^{−8} |

Constant of aberration, at standard epoch 2000 | κ | 20.495 52″ | |

Heliocentric gravitational constant = A^{3}k^{2}/D^{2} | GS | 1.327 2440×10^{20} m^{3} s^{−2} | 3.8×10^{−10} |

Ratio of mass of Sun to mass of Earth = (GS)/(GE) | S/E | 332 946.050 895 | |

Ratio of mass of Sun to mass of (Earth + Moon) | (S/E)(1 + µ) | 328 900.561 400 | |

Mass of Sun = (GS)/G | S | 1.9818×10^{30} kg | 1.0×10^{−4} |

: Ratios of mass of Sun to mass of planetSystem of planetary masses | |||

Mercury | 6 023 600 | ||

Venus | 408 523.71 | ||

Earth + Moon | 328 900.561 400 | ||

Mars | 3 098 708 | ||

Jupiter | 1047.3486 | ||

Saturn | 3497.898 | ||

Uranus | 22 902.98 | ||

Neptune | 19 412.24 | ||

Pluto | 135 200 000 | ||

(outside the formal IAU System)Other constants | |||

Parsec = A/tan(1") | pc | 3.085 677 581 28×10^{16} m | 4.0×10^{−11} |

Light-year = 365.25cD | ly | 9.460 730 472 5808×10^{15} m | defined |

Hubble constant | H_{0} | 70.1 km s^{−1} Mpc^{−1} | 0.019 |

Solar luminosity | L_{☉} | 3.939×10^{26} W= 2.107×10 ^{−15}S D^{−1} | variable, ±0.1% |

Last updated on: Tuesday 16th January 2018

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