  We study the dynamics of a pair of extremal (half-BPS) black holes in
$\mathcal{N}=8$ supergravity, as a potentially solvable model of gravitational
dynamics. As a diagnosis of hidden symmetries, we ask whether the perihelion of
the orbits precesses over time. We consider black hole charge vectors with
arbitrary misalignment. First, we use scattering amplitude methods to compute
the leading post-Newtonian correction for general mass ratios. This computation
is greatly simplified by introducing a suitable on-shell superspace. Second, we
study the probe limit to all orders in velocity and Newton's constant through a
ten-dimensional brane setup. In all cases we find no precession. We relate this
to the absence of scalar triangle integrals.
