Cislunar Formation Flight Design Tool

Explore quasi-periodic relative motion near selected cislunar periodic orbits. The viewer shows a linearized quasi-periodic relative torus (QPRT) family computed from precomputed state transition data.

A quasi-periodic relative torus (QPRT) is a relative-motion torus around a reference periodic orbit, displayed here in two co-moving frames. The black curve is the central trajectory, corresponding to ε = 0. The blue surface is the torus for the selected ε, and the orange curve is the realized trajectory on that torus for the selected phase.

LVLH is aligned with the local radial direction. VNB is aligned with the velocity direction in the Earth-Moon rotating frame.

dt: along-track offset in seconds
ε: torus radius; ε = 0 gives the black centerline
θ: phase around the torus cross-section
Propagation: propagation time in reference-orbit revolutions

References

Elliott IL. Relative Trajectory Design and Control near Periodic Orbits in Multi-Body Systems using Local Toroidal Coordinates . University of Colorado at Boulder; 2022.
Takubo Y, Manuel W, Foss E, D’Amico S. Safe and optimal N-spacecraft swarm reconfiguration in non-keplerian cislunar orbits . Journal of Guidance, Control, and Dynamics. 2026 Feb;49(2):305-24.

Chief Orbit - Rotating frame

Relative Motion - LVLH frame

Relative Motion - VNB frame