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Carl Friedrich Gauss
Carl Friedrich Gauss

Johann Carl Friedrich Gauss. was a Germans mathematician and scientist who contributed significantly to many fields, including number theory, statistics, mathematical analysis, Differential geometry and topology, geodesy, electrostatics, astronomy and optics....
 expressed the gravitational constant
Gravitational constant

The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitation between objects with mass....
 in units of the solar system
Solar System

The Solar System consists of the Sun and those Astronomical object bound to it by gravity: the eight planets and five dwarf planets, their 173 known Natural satellite, and billions of Small Solar System body....
 rather than SI
Si

Si, si, or SI may refer to :...
 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 the Sun
Sun

The Sun , a G V star, is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 98.6% of the Solar System's mass....
 and planet
Planet

A planet , as 2006 definition of planet by the International Astronomical Union , is a celestial body orbiting a star or Stellar evolution#Stellar remnants that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared the neighbourhood of planetesimals....
s expressed in mundane units like those of the SI system.

Gauss used the following units:

From Kepler's 3rd law
Kepler's laws of planetary motion

In astronomy, Kepler's three laws of planetary motion are*"The orbit of every planet is an ellipse with the sun at a Focus ."*"A line joining a planet and the sun sweeps out equal areas during equal intervals of time."...
 applied to the motion of the Earth, he derived his gravitational constant:

k = 0.01720209895 A3/2 S−1/2 D−1.


In 1939 the International Astronomical Union
International Astronomical Union

The International Astronomical Union is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy....
 adopted the above value as a defining constant in astronomy.






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Carl Friedrich Gauss
Carl Friedrich Gauss

Johann Carl Friedrich Gauss. was a Germans mathematician and scientist who contributed significantly to many fields, including number theory, statistics, mathematical analysis, Differential geometry and topology, geodesy, electrostatics, astronomy and optics....
 expressed the gravitational constant
Gravitational constant

The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitation between objects with mass....
 in units of the solar system
Solar System

The Solar System consists of the Sun and those Astronomical object bound to it by gravity: the eight planets and five dwarf planets, their 173 known Natural satellite, and billions of Small Solar System body....
 rather than SI
Si

Si, si, or SI may refer to :...
 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 the Sun
Sun

The Sun , a G V star, is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 98.6% of the Solar System's mass....
 and planet
Planet

A planet , as 2006 definition of planet by the International Astronomical Union , is a celestial body orbiting a star or Stellar evolution#Stellar remnants that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared the neighbourhood of planetesimals....
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
    Solar mass

    The solar mass is a standard way to express mass in astronomy, used to describe the masses of other stars and galaxy. It is equal to the mass of the Sun, about two Names of large numbers kilograms or about 332,950 times the mass of the Earth, or 1,048 times the mass of Jupiter....
    .


From Kepler's 3rd law
Kepler's laws of planetary motion

In astronomy, Kepler's three laws of planetary motion are*"The orbit of every planet is an ellipse with the sun at a Focus ."*"A line joining a planet and the sun sweeps out equal areas during equal intervals of time."...
 applied to the motion of the Earth, he derived his gravitational constant:

k = 0.01720209895 A3/2 S−1/2 D−1.


In 1939 the International Astronomical Union
International Astronomical Union

The International Astronomical Union is a collection of professional astronomers, at the Ph.D. level and beyond, active in professional research and education in astronomy....
 adopted the above value as a defining constant in astronomy. The value of the astronomical unit
Astronomical unit

An astronomical unit is a unit of length based on the mean distance from the Earth to the Sun. The precise value of the AU is currently accepted as 149,597,870,691 Plus-minus sign 6 metres ....
 is derived from it, and is no longer defined by the actual orbit of the Earth. In modern ephemerides
Ephemeris

An ephemeris is a table of values that gives the positions of astronomical objects in the sky at a given time or times. Different kinds are used for astronomy and astrology....
, the mean orbital axis of the Earth is slightly longer than 1 A.U., and the sidereal year
Sidereal year

The sidereal year is a misnomer for solar orbit. It is the time taken for the Sun to return to the same position with respect to the stars of the celestial sphere....
 is slightly shorter than 1 Gaussian year
Gaussian year

A Gaussian year is defined as 365.2568983 days. It was adopted by Carl Friedrich Gauss as the length of the sidereal year in his studies of the dynamics of the solar system....
.

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
Ephemeris time

The term ephemeris time is in itself apt to refer to time in connection with any Astronomical Ephemeris. It has been used more specifically to refer:-...
, and in modern usage this day is understood to be measured in units of Barycentric Dynamical Time
Barycentric Dynamical Time

Barycentric Dynamical Time was a time standard used to take account of time dilation when calculating orbits of planets, asteroids, comets and interplanetary spacecraft in the Solar system....
 (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.