In this paper, we propose a framework of connectivity analysis for aviation ad hoc networks on flight paths. First, a general analytical connectivity model for the common one-dimensional ad hoc network is newly developed. Then it is applied for modeling the connectivity of ad hoc networks among aircraft along flight paths where aircraft arrival process follows a Poisson distribution. Connectivity is expressed in terms of connectedness probability of two nodes in the network, connected distance, and network coverage extension factor. An exact closed form derivation of connectedness probability is proposed. The radical effect of mobility on the network connectedness of aircraft over a single flight path is analyzed. The network connectedness probability depends on node density and node distribution, which are derived from node arrival rate and node velocity. Based on these results, the proposed model is extended to the practical case of paths with multi-velocity air traffic classes. Using this model, the critical values of system parameters for the network of aircraft with certain connectivity requirements can be derived. It helps to evaluate network extension capability under the constraints of various system parameters.