- Gaussian gravitational constant
Carl Friedrich Gauss expressed thegravitational constant in units of thesolar system rather thanSI units. The benefit is that the motion of the planets can be accurately described, without exact knowledge of the scale of the solar system or the masses of theSun andplanet s expressed in mundane units like those of the SI system.Gauss used the following units:

*length A: astronomical unit (the mean radius of the orbit of the Earth around the Sun).

*time D: mean solar day (the mean rotation period of the Earth around its axis, with respect to the Sun).

*mass S: the mass of the Sun.From Kepler's 3rd law applied to the motion of the Earth, he derived his gravitational constant:

: "k" = 0.01720209895 "A"

^{3/2}"S"^{−1/2}"D"^{−1}.In 1939 the

International Astronomical Union adopted the above value as a defining constant in astronomy. The value of theastronomical unit is derived from it, and is no longer defined by the actual orbit of the Earth. In modern ephemerides, the mean orbital axis of the Earth is slightly longer than 1 A.U., and thesidereal year is slightly shorter than 1Gaussian year .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. The day defined by this constant was later understood as the basis of the rate of

Ephemeris Time , and in modern usage this day is understood to be measured in units ofBarycentric Dynamical Time (TDB). 1/86400 of the day defined by this constant was known as the ephemeris second, and the length of the ephemeris second as measured by clocks on the surface of the earth was adopted as the SI second.**References**[

*http://scienceworld.wolfram.com/physics/GaussianGravitationalConstant.html Gaussian Gravitational Constant, Wolfram ScienceWorld*]

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