The smallness parameter of the approximation method is defined in terms of the non-dimensional initial distance between target and chaser satellite. In the case of a circular target orbit, compact analytical expressions are obtained for the interception travel time up to third order. For eccentric target orbits, an explicit result is worked out to first order, and the tools are prepared for numerical evaluation of higher order contributions. The possible transfer orbits are examined within Lambert’s theorem. For an eventual rendezvous it is assumed that the directions of the angular momenta of the two orbits enclose an acute angle. This assumption, together with the property that the travel time should vanish with vanishing initial distance, leads to a condition on the admissible initial positions of the chaser satellite. The condition is worked out explicitly in the general case of an eccentric target orbit and a non-coplanar transfer orbit. The condition is local. However, since during a rendezvous maneuver, the chaser eventually passes through the local space, the condition propagates to non-local initial distances. As to quantitative accuracy, the third order approximation reproduces the elements of Mars, in the historical problem treated by Gauss, to seven decimals accuracy, and in the case of the International Space Station, the method predicts an encounter error of about 12 m for an initial distance of 70 km.