# Fundamental Astronomical Constants

## Fundamental Astronomical Constants

astronomical parameters that characterize the dimensions, positions, and motions of celestial bodies and whose values either always remain constant or change slowly with time.

Fundamental astronomical constants are used for converting from the directly observed topocentric coordinates of celestial bodies to geocentric or heliocentric coordinates, for performing coordinate transformations that take into account the precession and nutation of the earth’s axis, and for calculating the ephemerides of the sun, the moon, and the planets. Such constants are determined mainly from astronomical and radar observations; many of them may also be calculated by theoretical methods. The possibility of theoretical computation imposes the following substantial demands on fundamental astronomical constants: the numerical values derived from a large number of observations must satisfy with maximum precision the theoretical relationships between the constants and the differences between the computed and observed values should be small for each constant.

A set of fundamental astronomical constants that is specially selected on the basis of certain criteria is called a system of astronomical constants. The first such system, which included 14 constants, was adopted in 1896 at an international conference in Paris and remained in use for about 70 years. However, in the mid-20th century, problems associated with the exploration of space and with calculations of trajectories of artificial earth satellites and trajectories of flights to the moon and the other planets required the refinement of the fundamental astronomical constants, primarily the astronomical unit as the basis of the scale of the universe.

Table 1. Defining constants | |
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Number of ephemeris seconds in a tropical year (1900) ............... | s = 31,556,925.9747 |

Gaussian gravitational constant (radians), which defines the astronomical unit ............... | k = 0.01720209895 |

The system of astronomical constants in use today was developed in 1963 at the International Symposium on Astronomical Constants, which was held in Paris, and was approved in 1964 by the 12th General Assembly of the International Astronomical Union, which met in Hamburg. In this system, the fundamental astronomical constants are divided into four groups. The first group encompasses two defining constants (Table 1), while the second contains ten base constants (Table 2). The year (1900) for which the values of the fundamental astronomical constants are fixed is indicated in Table 1 and Table 2.

Table 2. Base constants | |
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Length of the astronomical unit (m) ............... | A = 149,600 × 10^{6} |

Speed of light (m/sec) ............... | c = 299,792.5 × 10^{3} |

Equatorial radius of the earth (m) ............... | a = 6,378,160_{e} |

Dynamical formfactor of the earth ............... | J = 0.0010827_{2} |

Geocentric gravitational constant (m^{3} sec^{–2}) ............... | fE = 398,603 × 10^{9} |

Ratio of the mass of the moon and the mass of the earth ............... | μ = 1/81.30 |

Sidereal mean motion of the moon (1900; rad/sec) ............... | n = 2.661699489 × 10_{⁽}^{–6} |

Centennial precession in longitude (1900) ............... | p = 5,025.64” |

Obliquity of the ecliptic (1900) ............... | ε = 23° 27’8.26” |

Constant of nutation (1900) ............... | N = 9.210” |

A more exact value for the Gaussian gravitational constant could have been obtained in the 1960’s and 1970’s. However, the value approved by the International Astronomical Union in 1938 was retained in the system of astronomical constants, because that value underlies most tables used in theoretical astronomy.

Before the introduction of the new system of constants in 1964, the astronomical unit was determined on the basis of the parallax of the sun and was identified with the semimajor axis *a* of the earth’s orbit, which is not included in the system of constants. Today, however, the semimajor axis *a* of the earth’s orbit is determined theoretically in terms of the Gaussian gravitational constant, while the astronomical unit in the new system is obtained from radar observations of the moon, Mercury, Venus, and Mars. As a result, a slight difference has arisen between the astronomical unit and the semimajor axis *a* of the earth’s orbit, namely, *a* = 1.00000023 astronomical units; that is, the semimajor axis turns out to be 34.4 km larger than the astronomical unit.

Table 3. Derived constants | |
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Solar parallax ............... | π⊙ = 8.79405” |

Constant of aberration ............... | k = 20.4958” |

Oblateness of the earth ............... | α = 0.0033529 |

= 1/298.25 | |

Heliocentric gravitational constant (m^{3}sec^{–2}) ............... | fS = 132,718 × 10^{15} |

Ratio of the mass of the sun and the mass of the earth ............... | S/E = 332,958 |

Mean distance of the moon from the earth (m) ............... | a_{⁽} =384,400 × 10^{3} |

In the new system, the values that were approved in 1896 for the three base constants that define the relative positions and motions of the equator and the ecliptic remain unchanged. These base constants are the precession in longitude, the mean obliquity of the ecliptic (1900), and the constant of nutation. The old values of these constants were retained in order to avoid the recalculation of all the proper motions of the stars and the revision of star catalogs.

The third group of fundamental astronomical constants consists of 11 derived constants, some of which are shown in Table 3.

The fourth group includes the masses of the principal planets (*see*PLANET).

### REFERENCES

Kulikov, K. A.*Fundamental’nye postoiannye astronomii*. Moscow, 1956.

Kulikov, K. A.

*Novata sistema astronomicheskikh postoiannykh*. Moscow, 1969.

*Spravochnoe rukovodstvo po nebesnoi mekhanike i astrodinamike*, 2nd ed. Edited by G. N. Duboshin. Moscow, 1976.

K. A. KULIKOV