Studying the movement of a particle on bound orbits around a black hole I found a fact that seemed a little strange for me -- that on these orbits particle's total energy on infinity must be less than unit (E<1). As far as I understrand, it is not so horrible, since here we deal with an unobservable quantity, because a particle never reaches infinity (namely because its orbit is bound). But in this case I have a question: what if a particle moves from infinity (where naturally its total energy cannot be less than 1) towards a black hole. Does the fact that its E≥1 on infinity implies that it can never move on bound orbits? How then is it possible to get on a bound orbit at all?