Suppose there are $n$ unit-mass particles whose initial positions
are uniformly distributed in a unit-radius disk.
Each particle is assigned a randomly oriented initial velocity vector of length $1$
(green below).
Then the particles act upon one another via inverse-square gravity.
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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [![NBodyRand8][1]][1]
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&nbsp; &nbsp; &nbsp;
<sup>
Dots show initial positions inside unit disk.
Green vectors: initial velocity; red vectors: final velocity.
</sup>
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> ***Q***. What is the probability that $k \ge 1$ of the $n$ particles remain within
a disk of some radius $R \ge 1$ forever?

In the illustration above, $n=8$ and $R=3$.

I am wondering if the answer is: **zero**, independent of $k$ and $R$ and the 
gravitational constant?
Perhaps the answer differs for points in $\mathbb{R}^2$ vs. points in $\mathbb{R}^3$ (or $\mathbb{R}^d$, $d > 3$)?

  [1]: https://i.sstatic.net/h6JSZ.jpg