Earth–Moon CR3BP L1 Planar Lyapunov Orbit (Interactive)

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.

Spacecraft color

Lyapunov size (d = xL1 − x0) [nondim]

Solved ydot₀

Tip: if a large d fails, increase Integrator steps per period or reduce d slightly.

Start phase (0.0→closest-to-Earth, 0.5→opposite)

Burn (impulse)

Burn phase (0..1)

Δv (m/s) Direction

Notes: This is planar CR3BP, so Z burns are stored but won’t change the 2D plots unless you add an out-of-plane model/plot.

Burn to enter new Lyapunov orbit

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Animation speed

Integrator steps per period (higher = smoother)

Show Lagrange points (L1–L5)

Show GEO orbit about Earth

Show Sun–Earth L1/L2 (rotating)

Show L1 stable/unstable eigenvectors

Show Jacobi energy contours

Jacobi value C

Axis units

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.