Fatal attraction

Consider a universe where gravity is proportional to the distance between two masses. That is to say, any mass \(m_{i}\) attracts any other mass \(m_{j}\) with a force given by
\[\vec{ F}_{ij}=G m_{i}m_{j} (\vec{r}_{i}-\vec{r}_{j}) \] with \(G=1\times 10^{-34}~\mbox{N}/(\mbox{m}\cdot \mbox{kg}^{2})\). Here \(\vec{r}_{i}\) and \(\vec{r}_{j}\) are the positions of the masses \(m_{i}\) and \(m_{j}\). In this odd universe, an isolated star with mass \(M= 1\times 10^{30 }~\textrm{kg} \) explodes into many fragments. It turns out that after some time \(\tau \) all the fragments coalesce, that is, they meet at a single point even if the explosion is anisotropic. Find the time \(\tau\) in seconds. Assume that Newton's law holds true in this universe and that the star was initially at rest.

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