= Gravitational constant
{title2=$G$}
{wiki}
The <gravitational constant> $G$ sets the strength of <Newton's law of universal gravitation>. Two <point masses> $M$ and $m$ a center-to-center distance $r$ apart attract with <force> magnitude
$$
F=\frac{GMm}{r^2}.
$$
For fixed <masses> and separation, doubling $G$ would double the <force>. For bodies with <spherical symmetry>, the same exterior formula follows from the <spherical shell theorem>; for arbitrary extended bodies, add the attractions of their <mass density> elements instead. The <gravitational constant> connects a laboratory attraction to the <Newtonian gravitational field> controlling a <Kepler orbit>.
The <gravitational constant> $G$ and local <gravitational acceleration> $g$ are different quantities. Applying <Newton's second law> to a <test particle> gives $g=F/m=GM/r^2$ for one spherical source. The source's <mass> and the observer's <position> change $g$; $G$ remains the same parameter of the law. A local falling-body experiment therefore measures a field, not $G$ alone. On rotating <Earth>, an instrument fixed to the surface also responds to <centrifugal acceleration>, while surrounding <mass density> and altitude change the gravitational contribution.
<Dimensional analysis> explains the units. Denote the base <physical dimensions> of <length>, <mass> and <time> by $\mathsf L,\mathsf M,\mathsf T$. Since <force> has dimension $\mathsf M\mathsf L\mathsf T^{-2}$,
$$
[G]=\frac{[F][r]^2}{[M][m]}=\mathsf L^3\mathsf M^{-1}\mathsf T^{-2},\qquad G\text{ has SI unit }\mathrm{m^3\,kg^{-1}\,s^{-2}}.
$$
By contrast, $[g]=\mathsf L\mathsf T^{-2}$ and the <standard gravitational parameter> $\mu=GM$ has dimension $\mathsf L^3\mathsf T^{-2}$. A small numerical value of a dimensional constant depends on the units chosen: it is the resulting <force> for specified physical <masses> and separation that conveys the laboratory scale.
NIST's current complete listing gives
$$
G=6.67430(15)\times10^{-11}\,\mathrm{m^3\,kg^{-1}\,s^{-2}}
$$
for the \i[2022 CODATA adjustment], the latest adjustment listed when checked on 14 October 2026. Parentheses indicate a <standard uncertainty> $u(G)=0.00015\times10^{-11}\,\mathrm{m^3\,kg^{-1}\,s^{-2}}$, approximately $22$ parts per million relative to $G$. The adjustment year is 2022; NIST's May 2024 data update is a different date.<Fundamental Physical Constants — Complete Listing by National Institute of Standards and Technology and others>[2022 CODATA adjustment, Newtonian constant of gravitation row: value, uncertainty and units]{ref} <Fundamental Physical Constants — Complete Listing by National Institute of Standards and Technology and others>[Current adjustment heading, next-adjustment notice and data-content update]{ref}
For an original scale calculation, stipulate two $1\,\mathrm{kg}$ <point masses> separated by $1\,\mathrm m$ and insert this recommended $G$: $F=6.67430\times10^{-11}\,\mathrm N$. The corresponding <acceleration> of either <mass> is $6.67430\times10^{-11}\,\mathrm{m\,s^{-2}}$ at that instant. Reducing the separation to $0.10\,\mathrm m$ multiplies both by $100$. These are ideal model predictions, not observations; their tiny scale explains why stray <forces> matter.
Being a constant of a physical law does not make the numerical value exact. The <SI> fixes the numerical values of seven defining constants, including the <speed of light> and <Planck constant>; $G$ is determined experimentally. Exact unit definitions still require physical realizations with <measurement uncertainty>: calibrating a <length> or a <mass> does not become error-free.<The International System of Units (SI), ninth edition, SI Brochure>[English §§1.3 and 2.2–2.2.1, printed pp. 122–124: realization, seven defining constants and exact numerical values]{ref}
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