= Standard gravitational parameter
{title2=$\mu$}
{wiki}
= Gravitational parameter
{synonym}
The product $\mu=GM$ of the <gravitational constant> and a central <mass> sets the strength of the exterior <Newtonian gravitational field>. Its dimensions are length cubed divided by time squared. In the exact relative <two-body problem>, the parameter is $G(M_1+M_2)$; using $GM$ for one source assumes the <test particle> approximation.
The combination is useful because orbital and falling-body observations constrain $\mu$ directly. A gravitational <circular orbit> of radius $a$ has <oscillation period> $T=2\pi\sqrt{a^3/\mu}$, so measuring $a$ and $T$ gives $\mu=4\pi^2a^3/T^2$. That measurement alone does not separately determine $G$ and $M$. Similarly, <radial free fall from rest> has a natural time scale $\sqrt{r_0^3/\mu}$.
Other interactions require a different model. Inverse-square <radiation pressure> can reduce the effective attraction for a dust <Kepler orbit>; calling that effective coefficient a gravitational parameter must not hide the added <force>.
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