Gaussian constant of gravity

The Gaussian gravitational constant  k (after Carl Friedrich Gauß , who introduced it) is the root of the gravitational constant : ${\displaystyle G}$

${\displaystyle k={\sqrt {G}}}$

namely not expressed in the usual, customary in the laboratory or in everyday life units (now SI base units ), but in units of the solar system :

• Length in astronomical units  A
• Time in sunny days  D (mean duration of one revolution of the earth )
• Mass in solar masses  S .

This has the advantage of being able to calculate the movement of the planets in the solar system without having to know the value of the astronomical unit in meters or the mass of the sun and planets in kilograms . The law of gravitation with the Gaussian gravitational constant reads :

${\displaystyle {\tilde {F}}=k^{2}{\frac {{\tilde {m}}{\tilde {M}}}{{\tilde {r}}^{2}}}}$

all sizes must be indicated with a tilde in the units listed above.

value

Gauss calculated the value of the (Gaussian) gravitational constant from Kepler's 3rd law , applied to the motion of the earth :

${\displaystyle {\begin{alignedat}{2}k\,&={\frac {2\,\pi }{\text{Länge eines Jahres in Tagen}}}&&\cdot {\frac {1}{D}}\cdot {\sqrt {\frac {A^{3}}{S}}}\\&\approx {\frac {2\,\pi }{365{,}256}}&&\cdot {\frac {1}{D}}\cdot {\sqrt {\frac {A^{3}}{S}}}\\&\approx 0{,}0172&&\cdot {\frac {1}{D}}\cdot {\sqrt {\frac {A^{3}}{S}}}\end{alignedat}}}$

The International Astronomical Union (IAU) set the following value as the defining constant of astronomy in 1939 and led u. a. the astronomical unit from it:

${\displaystyle k=0{,}01720209895\cdot {\frac {1}{D}}\cdot {\sqrt {\frac {A^{3}}{S}}}=0{,}01720209895\,\mathrm {\frac {m^{3/2}}{kg^{1/2}\cdot s}} }$

Not least because of this fractional exponent expressed in SI units, the IAU decided in 2012 to remove the Gaussian gravitational constant from the system of astronomical constants and to redefine the astronomical unit.

See also

• Vis-Viva equation

Individual evidence

1. ^ Resolution B2 of the 28th General Assembly of the IAU (PDF; 122 kB), Beijing, 2012.