Gravitational field of an infinite plane sheet ($|g|=2\pi G\Sigma$)

An infinite plane sheet of surface mass density $\Sigma$ has constant gravitational-field magnitude $2\pi G\Sigma$ on either side, directed toward the sheet. A Gaussian pillbox has equal inward flux on its two caps and enclosed mass $\Sigma A$, so $-2gA=-4\pi G\Sigma A$. A uniform infinite slab has the same exterior formula with $\Sigma =\rho h$. Translating an infinite sheet does not change its exterior field, whereas adding a slab changes its surface mass density.

A mass above a sufficiently wide estuary experiences additional downward gravity when extra water is present. Approximating the tide as a plane slab of density $\rho$ and added thickness $h$ gives $\Delta g=2\pi G\rho h$. A linear spring with initial extension $x_0=mg/k$ changes by $\Delta x=(m/k)\Delta g=x_0\Delta g/g$. This isolates direct water attraction; it omits finite shoreline geometry, buoyancy, structural motion and terrestrial tides.