Primary Impulse Orbit Transfer

Source: Guo Jianyu (2020) "Research on libration point orbit design and station-keeping strategies based on the two-dominant invariant manifold method"

Website: https://cislunarspace.cn

Definition

Primary Impulse Orbit Transfer is an orbital transfer method that utilizes invariant manifolds near libration points. This method requires only a single impulse at the transfer starting point, after which the spacecraft naturally glides along the invariant manifold into the target orbit. Compared to the traditional Hohmann two-impulse transfer, primary impulse transfer exploits natural dynamical corridors and can significantly reduce energy consumption.

Core Principles

Invariant Manifold Properties

Stable and unstable manifolds exist near libration points, possessing the following properties:

  • Stable manifold WsW_s: A spacecraft moving along this manifold naturally approaches the libration point periodic orbit without energy expenditure
  • Unstable manifold WuW_u: A spacecraft moving along this manifold naturally departs from the periodic orbit without energy expenditure

Transfer Mechanism

Primary impulse orbit transfer exploits this property:

  1. A single impulse is applied on a near-celestial-body orbit (e.g., Earth orbit)
  2. The spacecraft enters the invariant manifold connecting the near-celestial-body orbit with the libration point periodic orbit
  3. The spacecraft glides along the invariant manifold without additional propellant consumption
  4. The spacecraft ultimately arrives at the target libration point periodic orbit

Comparison with Hohmann Two-Impulse Transfer

FeaturePrimary Impulse TransferHohmann Two-Impulse Transfer
Number of impulses12
Energy consumptionLower (uses invariant manifold)Higher
Transfer timeLongerShorter
Orbit accuracyDepends on manifold computation accuracyHigher

Earth-Moon System Applications

In the Earth-Moon restricted three-body model, primary impulse orbit transfer can accomplish the following missions:

Typical Transfer Scenarios

OriginTargetCharacteristics
Lunar orbitL1 libration pointRelatively short transfer time
Lunar orbitL2 libration pointUses L2 unstable manifold
Earth orbitL1 libration pointLong-distance transfer
Earth orbitL2 libration pointRequires larger impulse

Orbital Parameters

Simulation analysis shows that typical primary impulse transfer orbital parameters include:

  • Transfer time: Several days to several months (depending on origin and target)
  • Energy consumption: Significantly lower than traditional Hohmann transfer
  • Impulse magnitude: Typically on the order of hundreds of m/s

Core Elements

Mathematical Definition

Primary impulse orbit transfer exploits the tubular structure of invariant manifolds near libration points, applying a single impulse on a near-celestial-body orbit to place the spacecraft into the invariant manifold corridor connecting the near-celestial-body orbit with the target libration point periodic orbit.

Key Properties

Transfer is achieved through the natural dynamical corridor of invariant manifolds, significantly reducing energy consumption, though transfer time is typically longer.

Numerical Methods

Computation of invariant manifolds typically requires numerical integration and Lyapunov exponent analysis, with patch point selection being a critical step.

Application Value

Primary impulse orbit transfer provides a low-energy transfer scheme for deep space exploration missions, particularly suitable for:

  • Missions that are time-insensitive but fuel-consumption-sensitive
  • Scenarios requiring transfer from near-celestial-body orbits to libration point periodic orbits
  • As a component of constructing an "Interplanetary Superhighway"

References

  • Guo J Y. Research on libration point orbit design and station-keeping strategies based on the two-dominant invariant manifold method[D]. Beijing University of Technology, 2020. (in Chinese)
  • Lo M W, Ross S D. Low-energy interplanetary transfers using the invariant manifolds of L1, L2 halo orbits[C]. AAS/AIAA Astrodynamics Specialist Conference, 1998.
  • Martin Lo W. The Interplanetary Superhighway and the Genesis Mission[R]. 2002.