= Gravitational field of an infinite uniform cylinder
{title2=$g_r=-2G\lambda/r\quad(r>b)$}
A circular infinite cylinder of radius $b$ and uniform <mass density> $\rho$ has <linear mass density> $\lambda=\pi b^2\rho$. A coaxial <Gaussian surface> of length $L$ has inward radial <gravitational field> and no end-cap <flux>. <Gauss's law for gravity> gives $2\pi rL g_r=-4\pi G\lambda L$ outside, hence the displayed result. Inside, enclosed <linear mass density> is $\pi r^2\rho$, so $g_r=-2\pi G\rho r$. An exterior <circular orbit> has <speed> $\sqrt{2G\lambda}$ independent of radius. The exterior formula presupposes circular axial symmetry; area alone would not specify the near field of a noncircular rod.
Back to article page
