= Zero-velocity surface
In a rotating restricted three-body model, the <Jacobi constant> can be written $C=2\Omega-|\dot x|^2$, where $\Omega$ is the <effective potential>. The <zero-velocity surface> $2\Omega=C$ bounds the accessible region: motion requires $2\Omega\geq C$.
The surface is an <energy> constraint, not a physical wall or a trajectory. As $C$ changes, narrow connections can open near <Lagrange points>, permitting passage between previously separated regions. In a planar section these boundaries appear as zero-velocity curves. Actual passage still depends on the dynamics within the allowed region.
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