Fatal attraction

Consider a universe where gravity is proportional to the distance between two masses. That is to say, any mass mim_{i} attracts any other mass mjm_{j} with a force given by
Fij=Gmimj(rirj)\vec{ F}_{ij}=G m_{i}m_{j} (\vec{r}_{i}-\vec{r}_{j}) with G=1×1034 N/(mkg2)G=1\times 10^{-34}~\mbox{N}/(\mbox{m}\cdot \mbox{kg}^{2}). Here ri\vec{r}_{i} and rj\vec{r}_{j} are the positions of the masses mim_{i} and mjm_{j}. In this odd universe, an isolated star with mass M=1×1030 kgM= 1\times 10^{30 }~\textrm{kg} explodes into many fragments. It turns out that after some time τ\tau all the fragments coalesce, that is, they meet at a single point even if the explosion is anisotropic. Find the time τ\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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