The SI unit of the gravitational constant GGG is expressed as:
Newton meter2 per kilogram2=N m2 kg−2\text{Newton meter}^2\text{ per kilogram}^2=\text{N m}^2\text{ kg}^{-2}Newton meter2 per kilogram2=N m2 kg−2
This can also be written in base SI units as:
m3 kg−1 s−2\text{m}^3\text{ kg}^{-1}\text{ s}^{-2}m3 kg−1 s−2
This unit arises from Newton's law of universal gravitation:
F=Gm1m2r2F=G\frac{m_1m_2}{r^2}F=Gr2m1m2
where FFF is force in newtons (N), m1m_1m1 and m2m_2m2 are masses in kilograms (kg), and rrr is distance in meters (m). Rearranging for GGG and substituting units gives:
G=Fr2m1m2 ⟹ units of G=N⋅m2kg2=N m2 kg−2G=\frac{Fr^2}{m_1m_2}\implies \text{units of }G=\frac{\text{N}\cdot \text{m}^2}{\text{kg}^2}=\text{N m}^2\text{ kg}^{-2}G=m1m2Fr2⟹units of G=kg2N⋅m2=N m2 kg−2
Since 1 Newton (N) = 1 kg·m/s², this can be expanded to:
units of G=kg⋅m/s2⋅m2kg2=m3 kg−1 s−2\text{units of }G=\frac{\text{kg}\cdot \text{m/s}^2\cdot \text{m}^2}{\text{kg}^2}=\text{m}^3\text{ kg}^{-1}\text{ s}^{-2}units of G=kg2kg⋅m/s2⋅m2=m3 kg−1 s−2
The accepted value of GGG in SI units is approximately 6.6743×10−11 m3kg−1s−26.6743\times 10^{-11},\text{m}^3\text{kg}^{-1}\text{s}^{-2}6.6743×10−11m3kg−1s−2
