Author: CislunarSpace

Website: https://cislunarspace.cn

Source: https://cislunarspace.cn

L1 Near-Rectilinear Halo Orbit

Position and Geometry

The Earth-Moon L1 libration point lies on the Earth-Moon line at approximately 84% of the Earth-Moon distance from Earth (about 326,400 km). At this point, the gravitational pull of Earth and the Moon balance each other, allowing a spacecraft to maintain relative rest or oscillate slightly in the vicinity.

The L1 NRHO exhibits a near-rectilinear geometry in the rotating frame: the spacecraft traverses a path that is nearly straight but slightly curved, moving back and forth near the L1 point. Unlike standard circular or elliptical orbits, the NRHO trajectory's projection in the xx-zz plane resembles an elongated "figure-8" or crescent shape.

Dynamical Characteristics

The core dynamical constraint of L1 NRHO arises from the conservation of the Jacobi constant in the Circular Restricted Three-Body Problem (CR3BP):

CJ=2−v2+2(1−μ)r1+2μr2C_J = 2 - v^2 + \frac{2(1-\mu)}{r_1} + \frac{2\mu}{r_2}

where μ=0.0121505853\mu = 0.0121505853 is the Earth-Moon mass ratio parameter.

The quasi-periodicity of NRHO stems from the intersection of stable and unstable manifolds near the L1 point. In the linearized system, perturbations along the stable manifold direction decay exponentially; however, in a real ephemeris model, perturbations (such as solar gravity and the Moon's non-spherical terms) cause the orbit to gradually drift, requiring periodic orbit maintenance maneuvers.

Another dynamical characteristic of L1 NRHO is the frozen inclination: in the CR3BP model, there exists a special inclination value (corresponding to the frozen-dipole condition) that reduces the orbit's sensitivity to certain perturbations.

Design Constraints

NRHO orbit design must satisfy the following key constraints:

  1. Amplitude constraint: The NRHO amplitude ratio Az/AxA_z/A_x must exceed a certain threshold (typically Az/Ax>0.5A_z/A_x > 0.5) to maintain the near-rectilinear characteristic
  2. Jacobi constant: The CJC_J value must lie within the range where stable manifolds exist; too high or too low a value will lead to orbital escape
  3. Lunar collision avoidance: The orbit design must ensure the spacecraft does not penetrate below the lunar surface

A typical L1 NRHO has a period of approximately 6.5-8 Earth days, with a lateral amplitude AxA_x reaching 3,000-4,000 km.

Representative Missions

  1. Early missions: Although ISE-3 (1978) was not strictly an NRHO, its orbital design already embodied the halo orbit concept near L1; the ACE mission (1997) also operated in an L1 orbit of this type
  2. Gateway missions: NASA's selected Gateway NRHO is located near the L1 point with Ax≈3100A_x \approx 3100 km and a period of approximately 6.5 days, supporting the Artemis lunar surface missions

Simulation Experiment

You can set L1 NRHO initial conditions in the Satellite Orbit Simulation Laboratory to observe its orbital morphology in the rotating frame.