The phase space is \(\mathbb {R}^3 \times \mathbb {R}^3\). A point is written \((q, p)\) where \(q \in \mathbb {R}^3\) is the position and \(p \in \mathbb {R}^3\) is the momentum. The mass \(m {\gt} 0\) and gravitational parameter \(\mu {\gt} 0\) are positive real constants.

The radial distance is \(r = \| q\| \). The non-collision phase space is the subset where \(r \neq 0\), i.e., where the planet is not at the origin.