  We recently introduced in [1910.03008] a "boundary-to-bound" dictionary
between gravitational scattering data and observables for bound states of
non-spinning bodies. In this paper, we elaborate further on this (holographic)
map. We start by deriving the following -- remarkably simple -- formula
relating the periastron advance to the scattering angle: $\Delta \Phi(J,{\cal
E}) =\chi(J,{\cal E}) + \chi (-J,{\cal E})$, via analytic continuation in
angular momentum and binding energy. Using explicit expressions from
[1910.03008], we confirm its validity to all orders in the Post-Minkowskian
(PM) expansion. Furthermore, we reconstruct the radial action for the bound
state directly from the knowledge of the scattering angle. The radial action
enables us to write compact expressions for dynamical invariants in terms of
the deflection angle to all PM orders, which can also be written as a function
of the PM-expanded amplitude. As an example, we reproduce our result in
[1910.03008] for the periastron advance, and compute the radial and azimuthal
frequencies and redshift variable to two-loops. Agreement is found in the
overlap between PM and Post-Newtonian (PN) schemes. Last but not least, we
initiate the study of our dictionary including spin. We demonstrate that the
same relation between deflection angle and periastron advance applies for
aligned-spin contributions, with $J$ the (canonical) total angular momentum.
Explicit checks are performed to display perfect agreement using
state-of-the-art PN results in the literature. Using the map between test- and
two-body dynamics, we also compute the periastron advance up to quadratic order
in the spin, to one-loop and to all orders in velocity. We conclude with a
discussion on the generalized "impetus formula" for spinning bodies and black
holes as "elementary particles".
