Heteroclinic Orbit Transfer
Editor Source: 郭建宇 (2020) "基于双基不变流形法的平动点轨道设计及保持策略研究"
Website: https://cislunarspace.cn
Definition
A heteroclinic orbit is an orbit connecting two different equilibrium points of a dynamical system. In the Circular Restricted Three-Body Problem (CR3BP), heteroclinic orbits connect two different libration points (such as L1 and L2), or connect libration points with periodic orbits. Transfer along heteroclinic orbits is an extremely low-energy transfer method, regarded as an important component of the "Interplanetary Superhighway."
Theoretical Foundation
Mathematical Definition of Heteroclinic Orbits
In dynamical systems theory, a heteroclinic orbit satisfies:
Where and are two different equilibrium points (libration points). When , it is called a homoclinic orbit.
Existence in CR3BP
The existence of heteroclinic orbits between collinear libration points in the Earth-Moon system has been proven. These heteroclinic orbits travel along channels formed by unstable manifolds connecting two libration points.
Transfer Mechanism
Using Heteroclinic Orbits for Transfer
In 郭建宇 (2020)'s research, a heteroclinic orbit was used to find a path from Earth orbit to a Halo periodic orbit near the Earth-Moon L2 libration point:
- Depart from Earth orbit, apply initial impulse to enter heteroclinic orbit
- Evolve naturally along heteroclinic orbit, no additional propellant needed
- Orbit naturally connects to Halo periodic orbit near L2 point
- Captured by target periodic orbit
Relationship with Invariant Manifolds
Heteroclinic orbits are essentially a special form of invariant manifolds:
| Orbit Type | Start Point | End Point |
|---|---|---|
| Homoclinic orbit | Libration point | Libration point (self) |
| Heteroclinic orbit | Libration point | Libration point (different) |
| Periodic orbit | Libration point | Libration point (homoclinic special case) |
Interplanetary Superhighway
Heteroclinic orbits are core components of the "Interplanetary Superhighway" theory. Martin Lo proposed that using invariant manifolds at libration points and heteroclinic orbits, a low-energy transfer network connecting various planetary orbits in the solar system can be constructed.
Interplanetary Superhighway Characteristics
- Low energy: Using natural dynamical channels significantly reduces transfer energy requirements
- Networked: Manifolds at various libration points interconnect, forming a transfer network
- Time scale: Transfer time may be very long (months to years)
Application Value
Heteroclinic orbit transfers provide extremely low-energy transfer solutions for deep space exploration:
| Application | Description |
|---|---|
| Cislunar missions | Low-energy transfer from Earth orbit to L2 Halo orbit |
| Mars exploration | Low-energy transfer design using Sun-Mars L1/L2 heteroclinic orbits |
| Asteroid exploration | Multi-target exploration missions using heteroclinic orbits |
| Deep space navigation | As "main roads" for interplanetary routes |
Core Elements
Mathematical Definition
A heteroclinic orbit connects two different equilibrium points of a dynamical system; in CR3BP, it connects two different libration points or a libration point with a periodic orbit.
Key Properties
Transfer along heteroclinic orbits requires no or minimal energy consumption, making it an important approach for low-energy deep space transfers.
Numerical Methods
Computing heteroclinic orbits requires precise numerical integration of invariant manifolds, along with detection and verification of homoclinic/heteroclinic orbits.
Related Concepts
- Primary Impulse Orbit Transfer
- Invariant Manifold
- Libration Point
- Interplanetary Superhighway
- Low Energy Transfer Orbit
- Halo Orbit
References
- 郭建宇. 基于双基不变流形法的平动点轨道设计及保持策略研究[D]. 北京工业大学, 2020.
- Martin Lo W. The Interplanetary Superhighway and the Genesis Mission[R]. JPL, 2002.
- Koon W S, Lo M W, Marsden J E, et al. Dynamical systems, the three-body problem and space mission design[J]. 2006.