Lagrange Point Halo Orbit Jacobi Constant Calculator

Circular Restricted Three-Body Problem (CR3BP): Compute the Jacobi energy integral ($C_J$), Hill’s zero-velocity forbidden regions, collinear equilibrium points, and halo orbit periods.

Three-Body System & Orbit State

Astrodynamic System Preset:

Mass Parameter $\mu = \frac{m_2}{m_1 + m_2}$:

System Characteristic Distance $L_*$ (km):

Collinear Equilibrium Point Focus:

Out-of-Plane Amplitude $A_z$ (km):

Rotating Frame Velocity $v_{\text{rot}}$ (m/s):

Jacobi Energy & Equilibrium Properties

Jacobi Constant ($C_J$)

vs C_L1: --

Distance to Secondary ($d_L$)

-- km

Dimensionless γ: --

Halo Orbit Period

-- days

-- months

Zero-Velocity Curve State

Bounded / Closed

Transit gate status

Critical Energy Levels:

• L1 Equilibrium Energy $C_{L1}$: --

• L2 Equilibrium Energy $C_{L2}$: --

• L3 Equilibrium Energy $C_{L3}$: --

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Lagrange Point Halo Orbit Jacobi Constant Calculator

Three-Body System & Orbit State

Jacobi Energy & Equilibrium Properties

Frequently Asked Questions