  We prove the presence of topological chaos at high internal energies for a
new class of mechanical refraction billiards coming from Celestial Mechanics.
Given a smooth closed domain $D\in\mathbb{R}^2$, a central mass generates a
Keplerian potential in it, while, in $\mathbb{R}^2\setminus \overline{D}$, a
harmonic oscillator-type potential acts. At the interface, Snell's law of
refraction holds. The chaoticity result is obtained by imposing progressive
assumptions on the domain, arriving to geometric conditions which hold
generically in $C^1$. The workflow starts with the existence of a symbolic
dynamics and ends with the proof of topological chaos, passing through the
analytic non-integrability and the presence of multiple heteroclinic
connections between different equilibrium saddle points. This work can be
considered as the final step of the investigation carried on in
arXiv:2108.11159 [math.DS] and arXiv:2105.02108 [math.DS].
