Past exam of the physics B course of the University of Cambridge / 2018 / Paper 1 / Section C / C11 / a

For a point mass, $\mathbf{g}(\mathbf{R})=-GM\mathbf{R}/R^3$. Along the outward radial direction, $g_R=-GM/R^2$ andThus a small radial displacement $\mathbf{a}=a\hat{\mathbf{R}}$ has differential accelerationThe farther point falls inward less strongly, so its acceleration relative to the reference point points outward. The formula is first order in $|a|/R$.