Astron. Astrophys. 346, 652-662 (1999)

## 4. Possible regions of escape

From relative distances of the participating bodies for small value of t, it may be possible to point out the body which is likely to escape with the formation of a binary. We may have and When we combine each of with each of for small values of we get the following cases.

Case (I) : when and .

It means is the smallest and therefore may escape and form a binary.

Case (II) : when and .

Thus we have may escape and form a binary.

Case (III) : when and .

We cannot take a decision as it is not possible to point out the smallest distance.

Case (IV) : when and .

Thus we have may escape and form a binary.

Case (V) : when and .

Now there are three possibilities according as

1. (a) When , we have may escape and form a binary.

2. (b) When , it means is smallest and therefore may escape and form a binary.

3. (c) When . We can not take a decision due to equality sign.

Case (VI) : when and .

Thus we get may escape and form a binary.

Case (VII) : when and .

Here, we can not take a decision due to equality sign.

Case (VIII) : when and .

It means may escape and form a binary.

Case (IX) : when and .

Here, we cannot take a decision due to equality sign.

The above results may change for higher values of t corresponding to certain directions of the perturbing velocities given to the participating bodies but escaper must be opposite to the smallest relative distance of the participating bodies.

From the above analysis, we conclude that out of the 9 cases, we may be able to take a decision only in 6 cases.

In the literature, many escape conditions exist. By Sundman (1912), it is sufficient for escape that

According to the above escape condition, form a binary and escapes. It has to be modified according to the escaper.

In our case, the above condition is satisfied and escape does occur for sufficiently small values of (i = 1, 2, 3). This follows from the fact that as The asymmetric triple close approaches after reaching generates sufficiently large values of I and for escape with the formation of a binary. After attaining of one of the three bodies that is opposite to the shortest distance escapes and the remaining two form a binary.

© European Southern Observatory (ESO) 1999

Online publication: May 21, 1999