In this paper, we begin by describing the Starlink constellation’s configuration plan, treating each satellite as a network node, naming and numbering the various nodes, and then classifying the laser interstellar links (LISLs) according to their orbital alignment and whether they are permanently visible. Whereupon, the method for calculating the respective theoretical interstellar distances required for establishing LISLs under two distinct orbital scenarios, co-orbital and hetero-orbital are analyzed, and the optimal phasing factors are proposed by solving an optimization algorithm for the shortest distance. The OneWeb and Starlink constellations, as well as the constellation states of various phasing factors are simulated, respectively. The Starlink constellation with F = 11 obtains the best coverage between 60° north and south latitudes predicated upon the analysis of the constellation N Asset Coverage. Following that, the first phase of the Starlink constellation deployment was modeled in order to analyze and count the number of permanent LISLs in orbit, adjacent to, and nearby. Subsequently, the characteristics of azimuthal, elevation, and range (AER) were subsequently analyzed to ascertain their variation law and to compile the number of permanent and temporary LISLs that could be established at various inter-distance ranges. Finally, predicated on the simulation results, the optimal LISLs connection strategy for the Starlink constellation is evaluated and a static topology for the constellation is constructed.