  The design and launch of large-scale satellite networks create an imminent
demand for efficient and delay-minimising routing methods. With the rising
number of satellites in such constellations, pre-computing all shortest routes
between all satellites and for all times becomes more and more infeasible due
to space and time limitations. Even though distributed on-demand routing
methods were developed for specific LEO satellite network configurations, they
are not suited for increasingly popular mega-constellations based on Walker
Delta formations.
  The contributions of this paper are twofold. First, we introduce a formal
model that mathematically captures the time-evolving locations of satellites in
a Walker Delta constellation and use it to establish a formula to compute the
minimum number of ISL hops between two given satellites. In the second part, we
present an on-demand hop-count-based routing algorithm that approximates the
optimal path while achieving superior performance compared to classical
shortest-path algorithms like Dijkstra.
