# 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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