I have to solve the following problem:
Two particles of masses $m_a=m$ and $m_b=2m$ interact by gravitational forces
$$\vec{F}_{ab}=-G\frac{m_am_b\vec{r}}{r^3} \; ,\qquad \vec{F}_{ba}=-\vec{F}_{ab}$$
where $\vec{r}$ is the relative position of $a$ on $b$. ¿When will they collide?
That's the problem. Then, the author gives a clue: Use the third Kepler's law for an elliptic orbit in the limit $L \rightarrow 0$ (angular momentum)?
Well, I tried to write the third Kepler's law in terms of $L$ to calculate the limit, but I can't. Is there another way to do it?
The solution is
$$t_c=\sqrt{\frac{\pi^2 d^3}{24Gm}}.$$
