  For the spatial generalized $N$-centre problem $$ \ddot{x} = -\sum_{i=1}^{N}
\frac{m_i (x - c_i)}{\vert x - c_i \vert^{\alpha+2}},\qquad x \in \mathbb{R}^3
\setminus \{c_1,\dots,c_N \}, $$ where $m_i > 0$ and $\alpha \in [1,2)$, we
prove the existence of positive energy entire solutions with prescribed
scattering angle. The proof relies on variational arguments, within an
approximation procedure via (free-time) boundary value problems. A
self-contained appendix describing a general strategy to rule out the
occurrence of collisions is also included.
