Geometrized Unit

In general relativity, it’s quite useful to use geometrized unit, where everything has unit of kilometers. [Schutz]

The principle of geometrized unit is to convert everything to length using \(c=G=1\). A precalculated value is

\[1 = G/c^2 = 7.425\times 10^{-28}\mathrm{m} \mathrm{kg}^{-1}.\]

In the spirit of this conversion, we have the mass of the Sun \(M_\odot=2.0\times 10^{30}\mathrm{kg} = 1.5\times 10^{3} \mathrm{m}\) and mass of earth \(M_\oplus = 6.0\times 10^{24}\mathrm{kg} = 4.4 \times 10^{-3} \mathrm{m}\).

References and Notes

[Schutz]A First Course in General Relativity (Second Edition)