Existence of the continuations in theN-body problem

The method of obtaining the estimates of the maximalt-interval (_–,₊) on which the solution of theN-body problem exists and which is such that some fixed mutual distance (e. g.₁₂) exceeds some fixed non-negative lower bound, for allt contained in (_–,₊), is considered. For given masses and initial data, the increasing sequences of the numbers_k, each of which provides the estimate₊ >_k, are constructed. It appears that if₊ = +, then.