Later Definitions
Gauss was not fully aware of the secular increase in the length of the mean solar day and unaware of the relativistic differences in the rate of clocks. His original constant was not empirically measured for a full year.
When Canadian-American astronomer Simon Newcomb was appointed director of the Naval Almanac Office of the United States Naval Observatory in 1877, he set about a program of redetermination of the astronomical constants with George William Hill. Their efforts led to the preparation of Newcomb's Tables of the Sun in 1895, and correspond to a value for the Gaussian gravitational constant of 0.017 202 098 14 A3/2 D−1, where A is the length of the semi-major axis of the Earth's orbit and D is the mean solar day at J1900.0.
In 1938, the International Astronomical Union (IAU) adopted Gauss's original value (0.017 202 098 95) for all future ephemerides.
Gauss originally defined the gravitational constant in terms of the mean solar day. Due to tidal braking the length of the mean solar day is not constant, a change in the length of the mean solar day would cause a change in the numerical value of the gravitational constant. The first uniform time system Ephemeris Time was adopted in 1952. The ephemeris second and ephemeris day were introduced, the duration of an ephemeris day is constant and independent of the rotation of the Earth.
Newcomb was aware of the secular variation in the length of the mean solar day caused by tidal acceleration, but he does not appear to have fully corrected for it. By extrapolating from modern measurements, the date on which the mean solar day would have been exactly 86400 seconds long was about 1820, neatly in the middle of the data (from 1750–1890) which Newcomb used to prepare his Tables.
The astronomical system of units was redefined in 1976 to fix the value of k at precisely 0.017 202 098 95 A3/2 S−1/2 D−1. The value of the astronomical unit is no longer defined as the semi-major axis of the Earth's orbit, but instead that length which give exactly Gauss' original value of the gravitational constant. In modern ephemerides, the semimajor axis of the Earth is slightly longer than 1 AU, and the sidereal year is slightly shorter than 1 Gaussian year. The day was also redefined to be exactly 86400 SI seconds when measured at mean sea level on the Earth: in practice, it is measured in Barycentric Dynamical Time (TDB).
Read more about this topic: Gaussian Gravitational Constant
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