A spacecraft of mass $m$ moves under the gravitational influence of the Sun of mass $M$ and with universal gravitation constant $G$. After a disastrous manoeuvre, the unfortunate spacecraft finds itself exactly in a parabolic orbit about the Sun: the orbit with zero total energy. Using the conservation of energy and angular momentum, or otherwise, show that in the subsequent motion the distance of the spacecraft from the Sun $r(t)$ satisfies

$$\left(r-r_{0}\right)\left(r+2 r_{0}\right)^{2}=\frac{9}{2} G M\left(t-t_{0}\right)^{2},$$

with constants $r_{0}$ and $t_{0}$.