Why patrolling Jupiter is harder than patrolling Earth

A claim to control a planetary system has to be backed by enough surveillance and patrol capacity to enforce it. Jupiter raises a problem of scale as well as distance from a power's center. Glynn Stewart sketches roughly forty relevant Lagrange points around its larger moons, compared with about four near Earth in his example. He immediately questions how the moons' interactions would affect those positions and their reliability. He explicitly places that multi-body calculation outside his mathematical expertise, leaving the numerical sketch uncertain.