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## Main Question or Discussion Point

**Shortest path on dynamic "graph"**

Suppose you have n objects orbiting Earth with velocities v1, ..., vn. Starting from t=0, the objects are at positions x1,..., xn; how do you calculate at what point they will be at a state such that the shortest path (arcs of great cirlces) connecting all of them will exist? Is it possible that no such configuration exists (there will always be a shorter one)?