Earth–Moon normalized units. Orbit is generated via symmetry-based differential correction:
choose x₀ = xL1 − d, solve for ẏ₀ and T/2 such that
y(T/2) = 0 and ẋ(T/2) = 0.
Tip: if a large d fails, increase Integrator steps per period or reduce d slightly.
Z burns stored but have no effect on 2D dynamics. Trajectory is solid before the burn, dashed after.
Re-enter Lyapunov orbit at next y=0 crossing
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Computes the ΔV correction burn needed to return to the reference Lyapunov orbit after the chosen coast,
using the State Transition Matrix to map accumulated position error to a velocity correction at the burn point.
Note: A mathematically exact periodic orbit has zero position error after any integer number of periods,
so ΔV ≈ 0 with no nav error. The position noise σ simulates realistic navigation uncertainty —
the gap between where the spacecraft actually is and where the nav system thinks it is.
A value of 1–5 km is realistic for DSN ground-tracking at L1 distances.
Each click resamples the random error, so results will vary.
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Two-burn transfer between two Lyapunov orbit sizes. The first burn departs the initial orbit;
the second burn inserts into the target orbit. Initial orbit = selected SC's d. Set target d below.
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Ready.
L1-centered (90° CCW)
SC-1 RTN (−Y → Earth)
SC-1 RTN (−Y → Moon)
SC-1 RTN (−Y → L2)
View: rotating barycentric frame. Earth at (−μ,0), Moon at (1−μ,0). L1 is between them.